# Support and Scandals in GameFi dApps:
A Network Analysis of _The Sandbox_ Transactions

Fernando Spadea  Rensselaer Polytechnic Institute
Troy, NY
<EMAIL_ADDRESS>
Oshani Seneviratne  Rensselaer Polytechnic Institute
Troy, NY
<EMAIL_ADDRESS>

###### Abstract

We explore the burgeoning field of GameFi through a detailed network analysis
of _The Sandbox_ , a prominent decentralized application (dApp) in this
domain. Utilizing the bow-tie model, we map out transaction data within _The
Sandbox_ , providing a novel perspective on its operational dynamics. Our
study delves into the varying impacts of external support, uncovering a
surprising absence of enduring effects on network activity. We also
investigate the network’s response to several notable incidents, including the
Ronin Hack and the United States Securities and Exchanges Commission’s hearing
on cryptocurrencies, revealing a generally resilient structure with limited
long-term disturbances. A critical aspect of our analysis focuses on the
‘whales,’ or major stakeholders in _The Sandbox_ , where we uncover their
pivotal role in influencing network trends, noting a significant shift in
their engagement over time. This research sheds light on the intricate
workings of GameFi ecosystems and contributes to the broader discourse on the
intersection of the Web, AI, and society, particularly in understanding the
resilience and dynamics of emerging digital economies. We particularly note
the parallels of the long-tail behavior we see in web-based ecosystems
appearing in this niche domain of GameFi. Our findings hold significant
implications for the future development of equitable and sustainable GameFi
dApps, offering insights into stakeholder behavior and network resilience in
the face of external challenges and opportunities.

###### Index Terms:

Blockchain, _The Sandbox_ , _Ethereum_ , _SAND_ , Whales, Bow-Tie Model,
Public Perception, Data Analysis, Network Analysis, Decentralized Application

##  I Introduction

Our research explores several factors contributing to the market uncertainty
found in GameFi dApps. We analyze _The Sandbox_ , a popular GameFi dApp, by
studying the effects of support from traditional brands on its activity and
the effects of various scandals. On top of that, we determine the types of
users contributing to _The Sandbox_ ’s short-term and long-term success. We
leverage the bow-tie model to map out transaction data within _The Sandbox_ ,
offering a novel perspective on its operational dynamics and underlying graph
structure. Our study delves into the varying impacts of external support,
uncovering a surprising absence of enduring effects on network activity. We
also investigate the network’s response to several notable incidents,
including the Ronin Hack and the United States Securities and Exchanges
Commission’s hearing on cryptocurrencies, revealing a generally resilient
structure with limited long-term disturbances. Although GameFi dApps are
similar to traditional web-based games in many ways, they differ in that they
have whales or major stakeholders. A critical aspect of our analysis focuses
on the whales, where we uncover their pivotal role in influencing network
trends. We note a significant shift in their engagement over time,
highlighting their importance in understanding the short-term success of
GameFi platforms. However, we also find that a dApp’s long-term success relies
heavily on building a dedicated user base.

##  II Background

With the rise of blockchain technology and decentralized applications (dApp),
we have seen the rise and fall of decentralized finance (DeFi) over the past
few years. During that time, we have seen the volatile nature of society’s
perception of said technology. Because these DeFi dApps were largely not based
on any tangible value, this perception played a large role in the success and
failure of DeFi. Many events, both positive and negative, helped shape said
perception and thus affected how much people interacted with DeFi dApps.
Therefore, analyzing these events would reveal the resilience of DeFi markets
and different strategies for increasing or maintaining activity.

However, alongside DeFi, GameFi faced the same dilemma. As the name implies,
GameFi is similar to DeFi but has a gaming element. Games are built as dApps
that use a blockchain to manage in-game asset ownership. Gamification in the
blockchain space has been highly legitimized recently, even being used by the
Andiami project to fix the problem of centralization in decentralized
blockchains [1]. One of the most successful GameFi dApps was Axie
Infinity111https://axieinfinity.com/ in which players battled with monsters
called Axies. A player’s in-game items and monsters were tracked on the Ronin
blockchain as NFTs. The in-game currency also took the form of a token. This
gives players complete control over their game assets, opening up the
possibility of selling those assets to other players or investors to make a
profit. Thus, these GameFi games enable players to earn value by playing them.
This is known as the play-to-earn model, and it proved to be lucrative for
many players worldwide for a while, and many even started playing these games
full-time [2]. However, the GameFi market crashed along with DeFi, leaving
many of these players out of a job [3]. On top of this, Axie Infinity later
suffered a massive hack named the Ronin hack, which further crashed the GameFi
market [4]. This reflected a shift in public opinion on blockchain in general.
However, a separate GameFi dApp existed by the name of _The Sandbox_
222https://www.sandbox.game/.

###  II-A _The Sandbox_

_The Sandbox_ is a unique GameFi dApp because it is not so much a game as a
marketplace and game engine for developers to create games and assets for
players to interact with [5]. It is more so a competitor to
Roblox333https://www.roblox.com/ than to any traditional game. _The Sandbox_
is hosted on the Ethereum blockchain. In _The Sandbox_ , developers can buy
LAND NFTs representing plots of land in the game’s map that the players can
explore. _The Sandbox_ ’s world is designed and populated by its LAND owners,
so they have to host games and events on said LAND to attract players [5]. By
doing this, these developers can profit by monetizing their visitors via
entrance fees or possibly selling them in-game items. Other developers can
also profit by creating ASSETs, assets that can be used in games hosted by
LAND owners [5]. ASSETs can also target players, such as clothing or
equipment. All of this is tied together with the SAND token, which is the
currency that is used by players and developers alike when purchasing goods
and services in _The Sandbox_ [5]. This creates a marketplace with many
different types of users that interact with each other. It is not just the
LAND owners that can make money in _The Sandbox_ , but also any developers
willing to put time into creating ASSETs targeted at players and LAND owners.
As a result, _The Sandbox_ has a unique marketplace with many different types
of users, making it a more notable topic of study than other types of GameFi
dApps.

##  III The Data

###  III-A Transaction Graph

We have gathered transaction data from Etherscan for our analysis of _The
Sandbox_. This transaction data consists of all transactions involving any of
the contracts created by _The Sandbox_
Deployer4440x18dd4e0eb8699eA4FeE238dE41ECfb95e32272f8 and _The Sandbox_
Deployer 25550xe19ae8F9B36Ca43D12741288D0e311396140DF6F addresses on the
Ethereum blockchain. This includes normal, token, NFT, multi-token, and
internal transactions as defined by Ethereum and Etherscan. This is to say
that we have collected every transaction related to _The Sandbox_. Therefore,
this includes any transactions involving SAND, LAND, or ASSETs. The data spans
from October 10, 2019, to October 26, 2023, so it covers most of _The Sandbox_
’s lifespan up to this point. In total, we have 4,948,956 transactions
involving 659,248 addresses. We use the from, to, contractAddress, timestamp,
and value parameters of the data collected. The from parameter holds the
address that sent the transaction, while the to parameter holds the address
the transaction was targeted at. Sometimes, the to parameter is empty, so, in
those cases, we use the contractAddress parameter instead, which holds the
address of the contract invoked in the transaction. The timestamp parameter
holds when the transaction was sent, and the value parameter holds the amount
of Ethereum sent in the transaction.

To find potential vulnerabilities within _The Sandbox_ ’s codebase, we also
gathered GitHub issue data on all of _The Sandbox_ ’s repositories. However,
there are only 14 with a collective two issues, which do not raise any
concerns with _The Sandbox_ ’s code. One asks a question, and the other
answers a question found in the comments of one of the repository’s files.
_The Sandbox_ also scored a high AA on their CertiK audit [6], so it is fairly
safe to say that _The Sandbox_ ’s code does not have many if any, security
risks by current standards. Thus, this data bears no fruit.

###  III-B Bow-tie Model

To start, we create a directed network from our transaction data where the
nodes represent addresses, and the edges are the transactions from and to each
other. Then, we split this network into the Bow-tie Model to further analyze
its underlying graph structure [7]. The Bow-tie model comprises several
groups: SCC, IN, OUT, TUBES, TENDRILS IN, TENDRILS OUT, and OTHER. The SCC,
the strongly connected component, is the collection of nodes in the graph that
interact with each other. The IN group is the collection of nodes that
interact with the SCC but do not have the SCC interact with them. The OUT
group consists of the nodes that are interacted with by the SCC but do not
interact with the SCC. The TUBES are a series of nodes that connect the IN
group to the OUT group. The TENDRILS IN are nodes that are interacted with by
the IN group but are disconnected from the SCC and OUT groups. The TENDRILS
OUT are nodes that interact with the OUT group but are disconnected from the
SCC and IN groups. The OTHER nodes are just those that do not fit into any of
these categories [7].

Separating the network into these partitions shows the differences between
their activity levels at any given time. This helps us identify how these
different groups reacted to different events and whether those reactions were
positive or negative. We will also be able to better analyze the graph’s
structure as we will have similarly behaving addresses grouped for closer
analysis.

###  III-C _The Sandbox_ Support

A point of interest for _The Sandbox_ is the outside support it receives from
traditional brands. The brands from which _The Sandbox_ has received support
vary greatly in their fields. Some of the support has come from traditional
video game companies such as Square Enix with Dungeon Siege [8], Ubisoft with
Rabbids [9], Skybound Entertainment with The Walking Dead (also a comic book
and TV show) [10], Atari [11], and ZEPETO [12]. They have also received
support from several music artists such as Snoop Dogg [13], deadmau5 [14],
Steve Aoki [15], and the Warner Music Group [16]. Adidas [17] and Gucci Vault
[18] also provided support as fashion brands, and the Smurfs [19] and Care
Bears [20] were present as well as Cartoon Brands. We chose these brands as
our points of interest as these are the brands that _The Sandbox_ consistently
points to when discussing companies that are invested in _The Sandbox_.

###  III-D _The Sandbox_ Scandals

On the other end of support are the scandals that _The Sandbox_ has faced. As
discussed in the data section, _The Sandbox_ has a relatively good record
compared to its competitors, so it lacks scandals related to _The Sandbox_
code itself. But there are a few related scandals we will analyze. The first
scandal we looked at was the Ronin hack mentioned above. While this hack did
not directly involve _The Sandbox_ , it did affect the value of SAND [21], so
it is worth investigating the activity level after it occurred. The next
scandal we looked at involved an employee’s work computer being hacked and
used to send phishing emails to Sandbox users whose emails the computer had
access to [22]. While this event did not involve a vulnerability in _The
Sandbox_ ’s code, it reflected poorly on the company’s security standards so
that it could have alerted some users to action. Another similar scandal
involved the CEO’s Twitter being hacked and used to post a crypto scam [23].
Again, this did not directly involve the security of _The Sandbox_ , but it
reflects poorly upon its parent company. The last scandal we looked at was the
recent United States Securities and Exchanges Commission (SEC) hearing where
SAND was labeled an unregistered security [24]. While _The Sandbox_ has
claimed that they disagree with this claim [25], this is still a significant
event that affected the outlook of GameFi as a whole, so looking at how this
affected the transaction data is worthwhile.

###  III-E Whales

With our transaction data, we also look at the SAND whales of _The Sandbox_.
Whales, in the context of cryptocurrency, are addresses that hold a
substantial amount of cryptocurrency. This paper defines a whale as an address
that has received a net amount of SAND worth at least 1e22 Wei or 10,000 Eth.
By identifying these whales, we get insight into the number of whales involved
in _The Sandbox_ and their reactions to these events. We also identify the
change in whales over time and which sections of the bow-tie model they fit
into.

##  IV Methodology

As discussed in sections III-C and III-D, _The Sandbox_ has received support
from several traditional brands and has faced several scandals over time, but
the impact of these events on _The Sandbox_ ’s success is unclear. Thus, we
aim to analyze this impact using our transaction data. By looking at the dates
these collaborations were released, we see if they resulted in increased or
decreased transactions. Specifically, we look at the 30 days before and after
the events to identify any spikes and changes in patterns surrounding the
events. We also looked at the total value of these transactions in the same
61-day period to see if these events affected the volume of value sent. We
also use our bow-tie model to analyze the effects of these events on the
different partitions we made to see how the different groups react to each
event. With these separate groups, we can see how these events affected
activity among different types of users in _The Sandbox_ and if there were any
significant shifts in the graph’s structure. We analyze the shifting structure
of the transaction graph by calculating the bow-tie partitions before and
after these events to see how they affected their sizes and, thus, the graph’s
structure. We also specifically look at where these moving addresses are
coming from, whether they are newly introduced to the graph or shifted from
another partition.

With the whales discussed in section III-E, we perform a similar analysis with
the Bow-tie model and these events to see how the overall patterns of the
network compare to the patterns of just the transactions involving the whales.
Also, by looking at the changing amount of SAND held by different addresses
over time, we identified if there were whales that bailed on SAND and thus
stopped being whales and whether their transaction patterns revealed anything
about the graph. Also, as mentioned previously, we identify which categories
within the Bow-tie model these whales exist within and discuss the
implications of those classifications. In addition, we use the average degree
of the network and the whales as a point of analysis.

##  V Results

###  V-A Bow-tie Model

Our complete network has a total of $659,248$ nodes. When we split the network
into the components of the bow-tie model, we find that most of the network
falls into the SCC and OUT partitions. The SCC accounts for $390,531$ nodes
($\sim 59.25\%$) while the OUT accounts for $264,501$ nodes ($\sim 40.13\%)$.
The IN only accounts for $4,071$ nodes ($\sim 0.62\%$). The IN TENDRILS, OUT
TENDRILS, and OTHER groups account for 7, 136, and 2 nodes respectively. We
found the TUBES partition to be empty.

Figure 1: Diagram of our Network in the Bow-tie Model

Since most user transactions in _The Sandbox_ involve some transaction in
response, we don’t see many addresses in the IN category. It mostly consists
of inactive or bot addresses and addresses approving the use of the SAND token
for the trade-in of another contract. On the other hand, the OUT group holds
more investors than normal users. One would have to interact with _The
Sandbox_ to get anything from its game aspect, so this makes sense. Then, in
the SCC, we have the bulk of it making up _The Sandbox_ ’s gaming community.
These primary users drive the value of SAND by actually using it to play in
_The Sandbox_.

###  V-B _The Sandbox_ Support

After calculating the number of transactions per day for the entire range of
our dataset, we plotted the values for the 30 days before and after the dates
attributed to each “support event” in figure 2. We did the same for the total
value of the transactions each day in figure 3. Both graphs show short-lived
spikes in transactions and value but no long-lasting effects after these
spikes stabilize. The two exceptions to this are deadmau5 and Warner Music
Group. However, the consistent increase in daily interactions after deadmau5’s
support is likely attributed to the simultaneous GameFi boom. On the other
hand, Warner Music Group’s effect is not so easily written off. Nevertheless,
the rest of the support events quickly returned to the norm, meaning they
failed to attract a consistent user base.

Figure 2: Graph showing the number of daily transactions in the 30 days before
and after each support event explored. Figure 3: Graph showing the total value
of transactions daily in the 30 days before and after each support event
explored.

To take a closer look at these results, we have graphed the data for deadmau5,
Warner Music Group, and Square Enix in figures 4, 5, and 6, respectively.
Here, we have split the transactions based on whether they belong to the bow-
tie model’s SCC, OUT, or IN groups.

Figure 4: Stacked bar graph showing the number of transactions per day in the
30 days before and after October 29, 2021, when deadmau5’s project was
released. The transactions are split into three groups depending on whether
they are part of the SCC, OUT, or IN groups of the bow-tie model.

In the deadmau5 graph, figure 4, there is an initial spike in SCC transactions
followed by a dip that stays well above the number of transactions each day
throughout the previous month. This indicates a reliable increase in activity.
There has also been a noticeable increase in the number of transactions
belonging to the OUT group. It is not as significant as the SCC’s but still
significant relative to its previous values. This indicates an increase in
investors. The IN group does not have a noticeable change in activity, which
could be attributed to its small size. However, we do have to keep in mind
that this support event coincided with the widespread boom of the GameFi
market.

Figure 5: Stacked bar graph showing the number of daily transactions in the 30
days before and after January 27, 2022, when Warner Music Group’s project was
released. The transactions are split into three groups depending on whether
they are part of the SCC, OUT, or IN groups of the bow-tie model.

There is a similar pattern in the Warner Music Group’s graph, figure 5. There
is an increase in activity in the SCC and the OUT groups without anything
noticeable in the IN group. However, the increase in OUT transactions is less
noticeable since the previous month’s values are higher than they were with
deadmau5. Regardless, this again indicates an increase in the active user base
and investors. Additionally, this effect cannot be as easily attributed to
another event, so it is likely due to the Warner Music Group’s efforts in _The
Sandbox_.

Figure 6: Stacked bar graph showing the number of daily transactions in the 30
days before and after February 28, 2022, when Square Enix’s project was
released. The transactions are split into three groups depending on whether
they are part of the SCC, OUT, or IN groups of the bow-tie model.

We use Square Enix’s support to represent the rest of the support events, as
they all had similarly unspectacular results. In the Square Enix graph, figure
6, there is a very short-lived spike in SCC transactions followed by an
immediate return to normalcy. The OUT and IN transactions are not noticeably
affected. The other support events saw similar results666More data and graphs
showing these results can be generated or found in the GitHub repository
linked in the Resource Contributions. except for The Smurfs, which had no
effect, likely due to how early into _The Sandbox_ ’s life they supported it.
Therefore, Warner Music Group is the exception rather than the rule, and most
of these events did not have a long-lasting effect on the activity in _The
Sandbox_.

###  V-C _The Sandbox_ Scandals

We created similar graphs of the number of transactions and the total value of
transactions for our scandals in figures 7 and 8. In both graphs, we do not
see any long-lasting effects due to the CEO’s Twitter account being hacked or
the Employee’s computer being hacked and used to send phishing emails. In the
value graph, the same applies to the SEC naming SAND unregistered security and
the Ronin Hack. However, the effects of these scandals are more noticeable in
the transactions graph, with the Ronin Hack having long-term effects.

Figure 7: Graph showing the number of transactions per day in the 30 days
before and after each of the scandals explored. Figure 8: Graph showing the
total value of transactions each day in the 30 days before and after each of
the scandals explored.

Similarly to what we did for the support events, we have graphed the data for
the Ronin Hack, SEC naming SAND a security, and the CEO’s Twitter account
being hacked in figures 9, 10, and 11, respectively. Once again, we split the
transactions based on whether they belong to the bow-tie model’s SCC, OUT, or
IN groups.

Figure 9: Stacked bar graph showing the number of transactions per day in the
30 days before and after March 23, 2022, when the Ronin Hack occurred. The
transactions are split into three groups depending on whether they are part of
the SCC, OUT, or IN groups of the bow-tie model.

In the Ronin Hack graph, figure 9, there is a delayed spike in SCC and OUT
transactions followed by a dip that drops slightly below the previous days.
The reason for the delay is that the Ronin hack took about a week to be
noticed. This result indicates that the initial spike was due to users and
investors jumping ship since there are fewer daily transactions after the
spike. The long-lasting effect of this scandal is clear despite _The Sandbox_
not being directly affected by the Ronin Hack.

Figure 10: Stacked bar graph showing the number of daily transactions in the
30 days before and after June 6, 2023, when the SEC named SAND an unregistered
security. The transactions are split into three groups depending on whether
they are part of the SCC, OUT, or IN groups of the bow-tie model.

In the SEC graph, figure 10, there is a massive spike in SCC transactions a
few days after the event, but there is not much of a change in the number of
daily transactions afterward. This may seem odd, but it is worth noting that
this event happened far after _The Sandbox_ ’s prime, so its user base was
barely active. This is further evidenced by the lack of a reaction in the OUT
group, which indicates that most of the investors in the OUT group who would
have been scared off by this event had already left.

Figure 11: Stacked bar graph showing the number of transactions per day in the
30 days before and after May 26, 2023, when the Twitter account of the CEO of
_The Sandbox_ was hacked and used to post a crypto scam. The transactions are
split into three groups depending on whether they are part of the SCC, OUT, or
IN groups of the bow-tie model.

We use the CEO’s Twitter hacking as a representative for itself and the
Employee computer hacking since they had similar results777More data and
graphs showing these results can be generated or found in the GitHub
repository linked in the Resource Contributions.. In figure 11, the hack has
no noticeable effect on the activity in _The Sandbox_. Like with the SEC
event, it is important to consider that this scandal occurred well after the
prime of _The Sandbox_ , so the user base was already at its weakest point,
with the users left not being shaken by these sorts of scandals.

###  V-D Change in Bow-Tie Model Over Time

In figure 12, we graph the changes in the categories of the bow-tie model over
time in our Sandbox network. We also include future addresses not yet involved
in the network to illustrate when new addresses will be introduced. Note that
addresses cannot leave the SCC once they have entered it. The groups other
than the SCC and OUT are small throughout the graph.

The SCC grows steadily between events, but we see three significant jumps
after Adidas, Steve Aoki, and the SEC hearing. The Adidas jump can likely be
attributed to the GameFi boom. The Steve Aoki jump from the OUT group could,
in part, be attributed to the lasting effects of the Ronin hack, causing
members of the OUT group to sell their investments to members of the SCC. In
contrast, the new addresses that entered the SCC could be attributed to new
users taking advantage of the dropping value of SAND. The influx of addresses
from the OUT to the SCC after the SEC hearing is likely a result of investors
selling their investments, often to members of the SCC.

The growth of the OUT is less consistent than that of the SCC, partly because
the OUT can lose members while the SCC cannot. Nevertheless, there are several
significant increases in new OUT addresses. The first is after Adidas, which,
like with the SCC, can be attributed to the GameFi boom and, thus, a
significant increase in investors. We see a decent increase in new OUT
addresses after the Warner Music Group support, which matches what we saw in
our closer analysis of this event in figure 5, where we saw a slight increase
in OUT activity. We see a similar pattern between the Ronin Hack and Steve
Aoki as we did with the SCC, which once again indicates that investors may
have been hoping the effect of the Ronin Hack was just a dip that would be
recovered from888https://cryptoquant.com/asset/sand/chart/market-data/price-
volume?market=spot&exchange=all_exchange&window=DAY&sma=0&ema=0&metricScale=linear.
After the Gucci Vault event, there is a surprisingly significant increase in
the OUT group. Although this does match a spike in OUT transactions before the
Gucci Vault event present in the data999This data and graphs are available in
the GitHub repository in Resource Contributions., this cannot be attributed to
the Gucci Vault event since it occurred afterward. There is also another
surprising increase in the OUT between the Care Bears event and the Employee’s
computer being hacked. This is likely due to a slight increase in value that
SAND saw between these two
events101010https://cryptoquant.com/asset/sand/chart/market-data/price-
volume?market=spot&exchange=all_exchange&window=DAY&sma=0&ema=0&metricScale=linear
which attracted investors again. It is difficult to attribute this increase to
either of these two events since they did not cause any significant increases
in OUT group activity111111This data and graphs are available in the GitHub
repository in Resource Contributions..

Overall, the SCC’s growth is more consistent than the surprisingly
unpredictable OUT. It is generally difficult to attribute the significant
increases in addresses to the events explored in this paper since the
increases generally do not match the increases in activity that resulted from
these events except for the Warner Music Group support.

Figure 12: Sankey graph showing the change in the Bow-Tie model of the network
over time ten days after each of the events explored, combining both the
support events and scandals.

###  V-E Whales

Figure 13: Graph showing the number of daily transactions involving current
Sandbox whales in the 30 days before and after each event explored. Figure 14:
Graph showing the total value of daily transactions involving current Sandbox
whales in the 30 days before and after each event explored.

We found 2,464 whales invested in _The Sandbox_ as of October 26, 2023. Of
these whales, 890 are in the SCC, and 1,574 are in the OUT group. However, we
also check to see if any addresses ever met this requirement at some point
during the three years our data covers. There were 33,758 qualifying whales
over time, with 32,174 in the SCC and 1,584 in the OUT group. As we can see,
most of the former whales were in the SCC, which makes sense since the SCC
would be the most likely group of nodes to offload one’s SAND on. We combined
the transaction and value graphs for the support events and scandals in
figures 13 and 14, respectively. We combined the graphs because they show
almost identical patterns to the normal graphs, so the same analysis applies.
This implies that whales are largely involved in most transactions in _The
Sandbox_ , which indicates that some of these whales could function as
resources for _The Sandbox_. To avoid filling this paper with more graphs, we
can see how these patterns will also hold when we include the past whales
since they will just be adding more transactions to a pattern that already
matches the pattern created by the entire network121212All the code to
generate these graphs and the graphs themselves are included in the GitHub
repository linked in the Resource Contributions.. This is further supported by
the average degree of the network compared to the average degree of the
whales. The average degree of the network is about 12.866, 5.395 when we
exclude all whales, while the average degree of whales is 735.520, 151.286 if
we include past whales. This demonstrates that whales interact with
significantly more addresses than normal users.

##  VI Related Work

The bow-tie model has previously been used to analyze the Steemit blockchain
[26], where they found that the SCC made up a comfortable majority of the
transaction network at 56.3%, similar to our 59.25%. The OUT group was the
second largest at 43.7%, which is also similar to our 40.13%. They found that
the third largest group was the IN, with a significantly lower number of nodes
than in the SCC and OUT groups at 0.016%, like with our 0.62% IN group, and
the rest of the groups were insignificantly small. Overall, the groups of
their bow-tie model were very similar to ours, so this could be a common
pattern seen in more blockchains. They also analyzed the whales of the Steemit
chain and found that they held a significant amount of power, which could also
be a common pattern. It is clear that this analysis strategy has its merits
and could be applied to several different blockchain dApps, as we have been
able to apply similar analysis strategies to _The Sandbox_. We have also
possibly found patterns that could be universal across blockchains, so more
research could be done to see if this pattern holds.

Li et al. use the Steemit blockchain transaction graph to measure how
decentralized it is and analyze its bot activity [27]. Their results reveal
that a few powerful addresses in reality controlled the network, similar to
our analysis of whales in _The Sandbox_. Additionally, they also found
significant bot activity abusing the reward system on Steemit. While this
analysis differs from our paper’s approach, it shows the significant power
that a blockchain’s transaction graph holds for analysis.

Guidi et al. analyzes Decentraland, another popular GameFi project where users
can buy land in the form of NFTs [28]. Here, they analyze how the NFT market
affects the in-game world and how users interact with the game itself. They
find that the profitability of the platform works against its playfulness.
Once again, this paper analyzes a different aspect of a GameFi project,
showing much potential for analysis in these projects.

In [29], Lai et al. analyze the transaction graph of Axie Infinity to discover
player behavior patterns and measure the effect of whales on the game. They
found that, while many users were actively playing the game, there was a
worrying amount of hoarding of game assets by a small number of addresses,
which they believed could threaten the game’s future. This is similar to our
analysis of whales in _The Sandbox_ and their significant influence, and we
additionally once again see the power of the transaction graph.

##  VII Conclusion

In the end, we saw that most support from outside parties received by _The
Sandbox_ did not significantly impact its long-term activity. The only
exceptions found were Warner Music Group and deadmau5, with deadmau5’s
supposed impact likely attributable to the general rise of GameFi that
coincides with their support. This means that these attempts to attract users
via popular traditional brands did not result in any shift in public
perception that legitimized _The Sandbox_ enough to attract a new wave of
consistent activity. DApps hoping to achieve this will have to look to other
strategies. This approach may support this end, but it needs to be part of a
larger plan.

The scandals looked at also had largely insignificant effects on the long-term
activity of _The Sandbox_ other than the Ronin hack, which shook the entire
GameFi space. However, this could be because the other three scandals occurred
after _The Sandbox_ ’s prime when its activity was already very low. This
indicates that the users still involved in _The Sandbox_ at the time of these
scandals were more invested and less likely to be shaken by these scandal
levels. Thus, these users form _The Sandbox_ ’s true core user base that will
survive these perturbations. Our analysis showed that whales are involved in
most transactions in _The Sandbox_ environment and largely drive the overall
activity. We also saw that many whales dropped _The Sandbox_ and stopped being
whales. However, we found that these whales were similarly involved to the
surviving whales regarding _The Sandbox_ ’s activity. This driving force that
whales have is significant since it means that they are largely responsible
for the activity on _The Sandbox_ , so it could be beneficial to target whales
directly when trying to drive up activity in GameFi dApps.

Ultimately, GameFi markets, like DeFi, are very unstable and difficult to
control. Trying to stabilize those markets positively through third-party
support and events is a poor strategy. Viable strategies should instead target
whales directly as they are a small subset of the user base with substantial
sway over the market and, thus, have much more potential to produce
significant results. On the other hand, once a GameFi market has stabilized to
a lower state, it is significantly more resilient to both positive and
negative events. It remains stable, meaning a small but reliable user base has
formed. In combination, this means that whales need to be targeted during
unstable periods, but an invested user base needs to be built up over time for
the future as those users will stick with the game past its prime. Building a
dedicated user base is something that traditional web-based games have
excelled at, so GameFi has a great legacy from which to build. Following this
approach, GameFi dApps can achieve early high success followed by a lower but
stable success in the long term.

##  VIII Resource Contributions

Our research artifacts (code, documentation, and graphs) are shared under the
Apache 2.0 license. We maintain an open-source GitHub repository for all our
artifacts: https://github.com/decentralized-social-media/gameFi.

##  IX Acknowledgements

This work was partially supported by the Algorand Centres of Excellence
program managed by the Algorand Foundation. The opinions expressed in this
publication do not necessarily represent the views of the Algorand Foundation.

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# First Star Formation in the Presence of Primordial Magnetic Fields

Daegene Koh  Kavli Institue for Particle Astrophysics and Cosmology
Stanford University, SLAC National Accelerator Laboratory
Menlo Park, CA 94025  Tom Abel  Kavli Institue for Particle Astrophysics and
Cosmology
Stanford University, SLAC National Accelerator Laboratory
Menlo Park, CA 94025  Karsten Jedamzik  Laboratoire d’Univers et Particules de
Montpellier, UMR5299-CNRS, Université de Montpellier, 34095 Montpellier,
France

###### Abstract

It has been recently claimed that primordial magnetic fields could relieve the
cosmological Hubble tension. We consider the impact of such fields on the
formation of the first cosmological objects, mini-halos forming stars, for
present-day field strengths in the range of $2\times 10^{-12}$ \- $2\times
10^{-10}$ G. These values correspond to initial ratios of Alvén velocity to
the speed of sound of $v_{a}/c_{s}\approx 0.03-3$. We find that when
$v_{a}/c_{s}\ll 1$, the effects are modest. However, when $v_{a}\sim c_{s}$,
the starting time of the gravitational collapse is delayed and the duration
extended as much as by $\Delta$z = 2.5 in redshift. When $v_{a}>c_{s}$, the
collapse is completely suppressed and the mini-halos continue to grow and are
unlikely to collapse until reaching the atomic cooling limit. Employing
current observational limits on primordial magnetic fields we conclude that
inflationary produced primordial magnetic fields could have a significant
impact on first star formation, whereas post-inflationary produced fields do
not.

stars: Population III — (cosmology:) dark ages, reionization, first stars —
stars: magnetic field — magnetohydrodynamics (MHD)

††journal: ApJL††software: Enzo (Bryan et al., 2014), YT (Turk et al., 2011)

##  1 Introduction

Magnetic fields are observed throughout the local Universe, in galaxies, in
clusters of galaxies, as well as very possibly in the extra-galactic medium.
Observations of TeV blazars (Neronov & Vovk, 2010) are most easily explained
by the existence of an almost volume filling magnetic field permeating the
space between galaxies. Recently it has also been shown by Jedamzik & Pogosian
(2020) that magnetic fields of $\sim 0.05\,$nG existant before the epoch of
recombination show good promise to alleviate the $4-5\sigma$ cosmic Hubble
tension and the $\sim 2\sigma$ cosmic $S_{8}$ tension within standard
$\Lambda$CDM. The Hubble tension is the mismatch between the inferred small
present day Hubble constant $H_{0}$ from observations of the cosmic microwave
background radiation by the Planck satellite when assuming $\Lambda$CDM
(Planck Collaboration et al., 2018), and a larger $H_{0}$ inferred by local
observations (Reid et al., 2019; Wong et al., 2019; Pesce et al., 2020). The
$S_{8}$ tension is the difference between the $\Lambda$CDM predicted current
matter fluctuation amplitude on a scale of 8 Mpc $h^{-1}$ and that observed
directly via weak lensing (Abbott et al., 2018; Asgari et al., 2020). It has
been shown that weak magnetic fields induce density fluctuations on small,
sub-Jeans comoving $\sim$ kpc scales before recombination (Jedamzik & Abel,
2013) which would indeed alter the prediction for $H_{0}$ and $S_{8}$ within
$\Lambda$CDM in a favorable way. Such fields necessarily would be of
primordial origin.

There are two conceptually different possibilities for the generation of
primordial magnetic fields (PMFs, hereafter), magnetogenesis during inflation
and post-inflationary generation (often referred to as ”causal” scenarios) as
for example during a first-order electroweak phase transition. Though multiple
proposals exist (cf. to Durrer & Neronov (2013); Subramanian (2016);
Vachaspati (2020) for reviews), there is no preferred candidate. Inflationary
scenarios have to lead to an approximate scale-invariant magnetic spectrum to
be successful, whereas most causal scenarios develop a very blue Batchelor
spectrum, with most magnetic power on small scales (Durrer & Caprini, 2003;
Saveliev et al., 2012). Stringent upper limits on PMFs from observations of
the cosmic microwave background radiation have been placed by Jedamzik &
Saveliev (2019) at ${}_{\sim}^{<}\,10^{-10}$G and ${}_{\sim}^{<}\,2\times
10^{-11}$ for inflationary and causal fields, respectively.

In this Letter, we entertain the idea that a primordial magnetic field indeed
existed and make steps to investigate their impact on first structure
formation. In $\Lambda$CDM structure is built bottom up, marginal differences
in the formation of the first objects could have significant impact for all
subsequent structure formation. Population III stars were formed at z $>$ 20
in mini-halos of mass $\sim 10^{5-6}M_{\odot}$ which gravitational collapse
via $H_{2}$ cooling (Tegmark et al., 1997; Abel et al., 2002). Magnetic fields
are understood to impact present day star formation in a number of ways (McKee
& Ostriker, 2007). Although the exact nature of their impact on Pop III stars
is still yet unknown, there have been a number of somewhat idealized studies
exploring these effects (McKee et al., 2020), including reducing fragmentation
(Sharda et al., 2020), increasing ionization degree (Nakauchi et al., 2019),
and angular momentum transport (Machida & Doi, 2013). Any weak initial field
will be amplified by the small scale dynamo (Xu et al., 2008; Sur et al.,
2010; Schleicher et al., 2011; Turk et al., 2012), but tends to not strongly
alter the initial collapse forming primordial stars.

On the other hand, Sanati et al. (2020) considered the impact of PMFs on the
total matter spectrum and the subsequently formed dwarf galaxies. They ruled
out the highest strengths, (i.e. $0.2-0.5\,$nG for inflationary fields) for a
number of reasons. First, the dwarf galaxies in these cases overproduce stars,
in contrast to local scaling relations. They also produce enough ionizing
photons to reionize the universe prior to z=9, also contradicting numerous
other measurements. The properties of dwarf galaxies depend on the chemo-
dynamical environment that they are embedded within. As a result, these
results cannot be fully interpreted without explicitly resolving the mini-halo
scales where the first objects were formed.

The latter is what we attempt here. In addition, we evolve the matter
perturbations and magnetic fields from the linear regime at high redshift
considering the earliest collapsing object in a fairly large volume. This is
in contrast to Machida & Doi (2013); Nakauchi et al. (2019); McKee et al.
(2020); Sharda et al. (2020) which adopt non-linear initial conditions at
lower redshift. However, we stress that unlike Sanati et al. (2020) we do not
take into account the additional power in the baryon density fluctuations
generated by the magnetic fields themselves (Wasserman, 1978; Kim et al.,
1996; Subramanian & Barrow, 1998). As much as the above mentioned works, our
study can therefore not reach ultimate conclusions but should add an important
element to the discussion. In the following section, we introduce our
simulation setup. Then, in section 3, we describe the results. Finally, we
discuss potential impact and caveats in section 4.

##  2 Simulation Setup

Our exploration involves a set of 5 cosmological simulations using the latest
public version of the adaptive mesh refinement ideal MHD simulation code Enzo
v2.6 (Bryan et al., 2014; Brummel-Smith et al., 2019). Our basic setup is
taken from Koh & Wise (2016) with a nested initial grid focusing on a single
mini-halo in a 250 $h^{-1}$ comoving kpc box. We consider the same physics as
with this earlier study including a nine-species non-equilibrium chemistry
model (Abel et al., 1997), a time-dependent Lyman-Werner background (Wise et
al., 2012), and a radiative self-shielding model (Wolcott-Green et al., 2011).
Our main focus is the evolution of the mini-halo prior to self-collapse and
thus, terminate the simulation when a maximal refinement level of 15 (a
spatial resolution of $\sim 400$ astronomical units) is reached and do not
follow the subsequent star formation and feedback processes.

In contrast to this earlier study, we modify the following parameters. First,
the Jeans length criterion is reduced down to 32 zones per Jeans length. In
studies of magnetic field amplification by gravitational turbulence the
required minimum for this parameter is 30 to capture the small scale dynamo
(Federrath et al., 2011; Turk et al., 2012).

The central variable of interest is the initial magnetic field strength. We
seed the entire simulation domain with a magnetic field initially pointed in
the z-direction. To contextualize the values of the magnetic field strengths
chosen, we refer to the speed ratio $v_{a}/c_{s}$, where $v_{a}$ is the Alfvén
speed, and $c_{s}$ is the sound speed, and choose the following ratios for our
study

  * •

0.03 , 0.30, 0.66, 1.00, 3.00

For brevity, we will, in the rest of the Letter, refer to the ratios $<$1,
$\sim$1, $>$1 as sub-sonic, trans-sonic, and super-sonic ratios respectively.

Figure 1: Density-weighted projection plots of density (top) and temperature
(bottom) of the different runs all spanning 1 kpc wide. From left to right,
the plots are of increasing Alfvén to sound speed ratios corresponding to
0.03, 0.30, 0.66, 1.00, and 3.00 respectively. Each plot is taken from the
final data output produced at the time of collapse except for the right-most
panel which was terminated at a comparable time with the trans-sonic (second
from the right) case at z=12.6.

A speed ratio of 1 then is equivalent to an initial proper B-field strength, B
= $v_{a}*\sqrt{4\pi\rho}$ = 1.32 x $10^{-6}$ G at z = 150, where $\rho$ is the
mean density in the box. This field strength corresponds to a comoving field
strength of 5.79 x $10^{-11}$ G. So the full range of initial comoving field
strengths spans 1.75 x $10^{-12}$ G to 1.73 x $10^{-10}$ G. The comoving
region from which the $\sim 10^{6}M_{\odot}$ halo forms is approximately 10
kpc across and hence is the relevant scale over which we assume the magnetic
field to be initially uniform.

##  3 Results

We analyze the numerical simulations based on full snapshots stored on disk
for every 10 Myrs of the evolution until the highest level of refinement of 15
is reached for the first time at which the simulation is terminated and a
final data output is produced. The exception is the super-sonic ratio of 3.0
in which the strong B-field inhibited the collapse and we terminated the
simulation at z = 12.6.

###  3.1 Central Halo Inspection

Here we show plots comparing the different runs. Figure 1 shows projection
plots of density and temperature of the various runs, each panel spanning 1
kpc across. From left to right, the plots are in order of increasing
$v_{a}/c_{s}$ ratios, shown at the time when the highest refinement level is
reached, corresponding to collapse of the central region. The 0.03 and 0.30
sub-sonic ratio central halos collapse at z = 15, the 0.66 halo at z =14, and
the trans-sonic halo at z =12.7. In comparing the two sub-sonic cases of
ratios 0.03 and 0.30 where the collapse times are similar, we can see that the
extended filament protruding from the central object is less dense in the
greater ratio case. Also the surrounding satellite gas clouds all have
noticeably reduced densities.

As the time of collapse is delayed at higher $v_{a}/c_{s}$ ratios, the central
region has more time to grow both in size as it merges with the nearby sub-
halos and in temperature. In particular, for the trans-sonic case where
$v_{a}\sim c_{s}$, we see an extended temperature cavity where the central
halo has collapsed, surrounded by highly heated gas, with temperatures
reaching several $T\sim 10^{4}$ K. The nearby gas clouds to the left and below
the central halo in the plane of the plot in the leftmost panel have
completely merged with the central halo in the trans-sonic case resulting in
significantly elevated temperatures. By the time these clouds merge in, the
central halo had already been cooled to form a dense core. The infalling gas
then collides with the dense core and is scattered around it producing the
extended sub-structure shown in the plot. In the super-sonic case, we see
continued heating of the central region of the halo while the density remains
quite low and that cooling has not begun even at this late stage.

One significant trend is that the time of collapse is delayed as a function of
increasing speed ratio. The additional magnetic pressure heats the gas and
adds an additional barrier for the gravity to overcome to initiate self-
collapse. This trend is such that already the trans-sonic halo collapses at z
= 12.66 where the magnetic field is contributing to a delay time of $\Delta$z
= 2.5. Following this trend, we estimate that the central halo in the highest
ratio run of 3.0 is unlikely to collapse even until z = 10 and may only
collapse once reaching the atomic cooling limit.

Figure 2 shows the temperature evolution of the highest density point as a
function of redshift for each of the different simulations. As the initial
$v_{a}/c_{s}$ increases, the peak temperature reached by this point also
increases. On the other hand, the minimum temperature reached by this densest
point is lowered by a few 10s of Kelvin as the ratio is increased. This
pattern does not hold true for the ratio of 3 as the object has yet to undergo
collapse, but we would expect it to follow the pattern once it does collapse.
This rise in temperature not only results in delayed collapse, but we also
observe that, once collapse takes place, it is progressively elongated with
increasing $v_{a}/c_{s}$ ratio. In the case of the super-sonic ratio of 3, the
halo has not begun to cool even at the final data dump at z = 12.6.

Figure 2: Plot of temperature at the cell with the highest density as a
function of redshift for all simulations. In the super-sonic case, the central
halo has yet to collapse and is continually heating up as it grows in mass. As
the initial $v_{a}/c_{s}$ ratio increases, the peak temperature reached prior
to cooling is higher, the time to collapse is delayed, and the duration of the
cooling is extended. Figure 3: Radial profiles of density (upper left),
temperature (upper right), HII fraction (lower left), and $\mathrm{H_{2}}$
fraction (lower right) centered about the densest point in the central halo
for ratios of 0.03 (solid) and 1.00 (dashed). The trans-sonic case results in
larger halo which produces the larger extended profile as seen in the density
and temperature plots. Embedded in the HII fraction plot is a projection plot
of the HII fraction weighted by density spanning 10pc centered around the
densest point which highlights the highly asymmetric nature of the collapse.

Figure 3 shows radial profiles centered around the central halo for a sub-
sonic ratio of 0.03 and a trans-sonic ratio of 1.00. As the overall collapse
is delayed, the halo is able to accrete more mass and thus we see a more
extended profile in the density plot (upper left). The temperature profile
(upper right) shows that the temperature in the core for the trans-sonic halo
is a few 10s of K cooler but with a more extended heated tail. Surrounding the
cool inner region is a hot gas which is heated to over 1000 degrees greater in
the trans-sonic halo. As the profile is spherically-averaged, the actual
temperatures in the heated region reach several thousand K. The neutral
$H_{2}$ fraction (lower right) shows a corresponding extended profile for the
trans-sonic case as the gas clouds that harbored the molecular cloud in the
sub-sonic cases has been merged into the central object.

Inspecting the collapsed region in detail shows that the nature of the
collapse itself has changed drastically between the two cases. In the sub-
sonic cases, the central halo undergoes a mostly self-similar spherical
collapse. On the other hand, the collapse in the trans-sonic halo proceeds
along a particular axis along a filamentary structure. This results in a
vastly different substructure particularly noticeable in the HII fraction
profile. The ion fraction shows a pronounced increase by a couple orders of
magnitude in the available ions in the cool region surrounding the central
heated core. Figure 3 also includes a projection of the ion fraction for the
trans-sonic case as weighted by density spanning 10 pc to show the asymmetric
nature of the collapse.

Figure 4: Phase plot of the comoving magnetic field strength against baryon
overdensity within a sphere of 1 kpc surrounding the densest point. The left
shows the sub-sonic ratio of 0.03 while the right shows 1.00. Red line
indicates the average field strength while the dotted line is a
$B\propto\rho^{2/3}$ reference trendline representing the ideal magnetized
spherical collapse. While the sub-sonic case suggests some turbulent
amplification, the trans-sonic halo is not even matching the compressional
amplification. This further suggests that the gravitational collapse is
occurring along the field lines.

###  3.2 Magnetic Field Evolution

We now present the behavior of the magnetic fields in our simulation.

Figure 4 shows a phase diagrams of comoving magnetic field strength vs the
baryon overdensity in a sphere of radius 1 kpc surrounding densest cell in the
trans-sonic run. The red line follows the mass-weighted average magnetic field
strengths. The dotted line shows $B\propto\rho^{2/3}$, where $\rho$ is
density, which is the scaling for the magnetic field amplification in the case
of a ideal spherical collapse, or compressional amplification. In the sub-
sonic scenario, there is still evidence of small scale dynamo driven
amplification shown by the red line growing steeper than the dotted line,
noting that it is muted relative to scenarios where $v_{a}<<$ 1\. On the other
hand, in the trans-sonic case, the collapse is not driving strong
amplification, and in fact the field is even less amplified than expected
during ideal compression. The latter implies that much of the collapse must be
occurring along the field lines, rather than squeezing lines together to drive
amplification. This is supported by the projection plot in Fig. 3, where the
collapse was no longer spherical and had a preferential axis. Furthermore, the
field is effectively saturated having reached corresponding energies
comparable to the kinetic energy in the system. And in fact, in this
particular scenario, the magnetic energy is comparable to the kinetic
component in this entire domain.

Figure 5 shows a projection plot of the plasma $\beta$, which is the ratio of
the thermal pressure to the magnetic pressure for the trans-sonic case. The
magnetic fields are overplotted as streamlines and show that the initial
magnetic field which was initialized in the z-direction is still coherent
across the halo that is formed. Within the halo, the turbulent collapse of the
gas pulls the field lines with it and reorders them.

Figure 5: Projection plot of plasma $\beta$ weighted by density centered
around the central object spanning 1 kpc across in the trans-sonic case. The
streamlines trace the magnetic fields and shows the coherence of the initial
magnetic field oriented in the z-direction over the span of the figure. In a
large fraction of the total region, the magnetic pressure dominates over the
thermal pressure.

Figure 6 shows the $v_{a}/c_{s}$ ratio at the highest density point as a
function of redshift for all the simulations. There is a ceiling for this
ratio in the core of the central halo at $v_{a}/c_{s}\sim$10\. For the sub-
sonic cases, the magnetic field is rapidly amplified to approach this limit.
As the initial field strength is increased, the degree of amplification is
reduced overall and the ratio reaches a plateau. This corresponds again to the
saturation point.

Figure 6: Plot of the $v_{a}/c_{s}$ ratio at the cell with the highest density
as a function of redshift for all simulations. At sub-sonic ratios, the small-
scale dynamo driven amplification rapidly increases this ratio. As the initial
ratio is increased, the amplification is suppressed and the ratio near the
center of the halo stays near $v_{a}/c_{s}\sim$10.

##  4 Conclusions and Discussion

In this Letter, we followed the collapse of the first mini-halos in
cosmological simulations in the presence of primordial magnetic fields of
comoving strengths in the range $\sim 2\times 10^{-12}-2\times 10^{-10}$G. We
find that when fields are of order $5\times 10^{-11}$ G or larger,
corresponding to the Alfvén speed being of the same order or larger than the
sound speed at high redshift $z{}_{\sim}^{>}\,100$, the formation of first
stars in such mini-halos is significantly impacted. In particular,

  * •

With increasing initial magnetic field strength, the collapse of mini-halos
due to the $H_{2}$-cooling is progressively delayed both in duration and final
time of collapse.

  * •

Magnetic field amplification by the small-scale dynamo and by simple flux-
freezing during spherical collapse is increasingly reduced with increasing
field strength.

  * •

At high B-field strengths, $H_{2}$-cooling induced collapse can potentially be
completely suppressed.

  * •

Magnetic fields lead to asymmetric gravitational collapse and an elevated ion
population in the central few pcs of the mini-halo.

  * •

For all magnetic field strengths investigated, the Alfvén- to sound -speed
ratio in the center of the mini-halos saturates at $v_{a}/c_{s}\sim$10, with
saturation occurring earlier for stronger initial fields.

Our findings could have profound implications for early universe structure
formation and beyond. First of all, the minimum collapse mass scale would be
greatly sensitive to this effect as the magnetic fields suppress collapse in
smaller mini-halos. This can impact the initial mass function of primordial
stars and the resulting chemical evolution of the universe. The presence of
larger pristine gas reservoirs by the time of collapse can result in radically
different star formation scenarios. It can also perhaps more readily
facilitate more exotic formation scenarios such as direct-collapse black
holes.

We caution though, that our study has not included all relevant effects. Apart
from the neglect of ambipolar diffusion, a serious limitation is the neglect
of enhanced baryonic density perturbations induced by the magnetic fields
themselves. When taken into account, it may well be that, rather than being
delayed, star formation may occur earlier than in the no initial magnetic
field counterpart. This is due to the enhanced power on small scales making
mini-halos collapse earlier. However, we believe that most other effects found
in this study should remain and possibly lead to more massive first stars.

To place our findings into context, either inflationary produced PMFs or phase
transition produced PMFs could relieve the Hubble tension. In both cases a
pre-recombination field strength of $\sim 5\times 10^{-11}$G is required.
However whereas in the former scenario this field strength is kept to the
present epoch, in the latter scenario fields are subject to further damping
down to $1\times 10^{-11}$G through the epoch of recombination. Coincidentally
this is approximately the strength required to explain cluster magnetic fields
to be entirely primordial. We may therefore conclude that only inflationary
produced PMFs may influence first structure formation, whereas phase
transition produced fields are too weak to have significant impact.

This work was performed using the open-source Enzo and YT codes, which are the
products of collaborative efforts of many independent scientists from
institutions around the world. Their commitment to open science has helped
make this work possible. This work was supported in part by the U.S.
Department of Energy SLAC Contract No. DE-AC02-76SF00515.

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Copyright is held by the author/owner. Permission to make digital or hard
copies of all or part of this work for personal or classroom use is granted
without fee. Poster presented at the 15th Symposium on Usable Privacy and
Security (SOUPS 2019).

[15pc]  Concept of the Privacy Hat: Muting a smart speaker by placing an
object on top of it.

# Making Privacy Graspable: Can we Nudge Users to use Privacy Enhancing
Techniques?

Christian Tiefenau

Maximilian Häring

Eva Gerlitz

Emanuel von Zezschwitz

University of Bonn  Bonn, Germany<EMAIL_ADDRESS>Fraunhofer FKIE
Bonn, Germany<EMAIL_ADDRESS>Fraunhofer FKIE  Bonn, Germany
<EMAIL_ADDRESS>University of Bonn, Fraunhofer FKIE  Bonn, Germany
<EMAIL_ADDRESS>
###### Abstract

Smart speakers are gaining popularity. However, such devices can put the
user’s privacy at risk whenever hot-words are misinterpreted and voice data is
recorded without the user’s consent. To mitigate such risks, smart speakers
provide privacy control mechanisms like the build-in mute button.
Unfortunately, previous work indicated that such mute buttons are rarely used.
In this paper, we present the Privacy Hat, a tangible device which can be
placed on the smart speaker to prevent the device from listening. We designed
the Privacy Hat based on the results of a focus group and developed a working
prototype. We hypothesize that the specific user experience of this physical
and tangible token makes the use of privacy-enhancing technology more
graspable for the user. As a consequence, we expect that the Privacy Hat
nudges users to more actively use privacy-enhancing features like the mute
button. In addition, we propose the Privacy Hat as a study tool as we
hypothesize that the artifact supports participants in reflecting their
behaviour. We report on the concept, the prototype and our preliminary
results.

###### keywords:

Smart speaker; tangible privacy; privacy hat; iot study platform

###### category:

H.5.m Information interfaces and presentation (e.g., HCI) Miscellaneous

##  1 Introduction

The number of smart speakers like the Amazon Echo [2], the Google Home [6] or
Apple’s HomePod [4] grew 2018 by 39.8% in the US, resulting in an estimated
usage by 66.4 million American households [9]. Since their introduction in
2014, usable security research aimed at understanding usage behavior and risk
perception of smart speaker users. Several studies found that users generally
express little privacy concerns, especially due to an incomplete understanding
of the security risks or resignation [5, 3, 8]. Privacy controls like the mute
button or audio logs seem to be rarely used. One reason for these
circumstances can be that these mechanisms do not align with the users’
privacy control needs. Related work suggests to nudge users with privacy
notices to reflect on decisions, so that they can take informed privacy-
related actions [8]. Following this line of thoughts, we hypothesize that
providing users with a physical and tangible device can help them to a better
understanding of the privacy-topic and furthermore nudge them to reflect on
their daily smart speaker interaction.

[-20pc]  Our prototype in the early stage. Here, we tried using a RFID-tag
scanner in combination with an Arduino.

Closely related to our project is the artistic DIY-concept “Project Alias”
[7]. Users can 3D-print a physical token that is then placed on top of a smart
speaker. The use of white noise disables the speakers’ ability to listen to
the activation word. The device itself serves as a trusted component which can
be activated by an individual hot word. If the hot word is received, “Project
Alias” stops sending white noise and activates the smart speaker for further
interaction. While we acknowledge “Project Alias” as a potential solution, it
does not foster physical interaction with the device itself nor does it
communicate the device’s status.

In contrast, our Privacy Hat is a tangible object that can be placed on top of
a smart speaker to prevent it from listening and was designed to provide
implicit visual feedback on the smart speaker’s state. Since anyone in the
room can observe if the Privacy Hat is placed on the device or not, we expect
that the concept can provide unintrusive but clear privacy notices that may
trigger usage-reflection. To inform the design of Privacy Hat, we performed a
focus group with four smart speaker users. We asked them about their current
smart speaker usage behavior and discussed alternative interaction paradigms
that could support privacy-awareness and trigger the active use of the privacy
control “muting.”

In addition to the development of the Privacy Hat, we present a smart home
study-framework that enables us to get feedback of the participants’ actual
device usage in the field. This framework will be used to measure the effect
of the Privacy Hat in our participants’ actual smart homes.

We like to note that our concept is not simply a usability-optimized solution
to the privacy-related problems of smart-home users. For this we would have
proposed a concept which supports remote control of such a functionality. On
the contrary, our concept suggests that users have to actively put an object
on top of the device and thus have to physically go to the speaker to perform
the action. We hypothesize that requiring explicit physical interaction makes
the process more tangible, has potential to affect the users’ privacy-related
behavior and helps them to reflect about their behavior. We anticipate that
this tool will give us additional insights into the smart home user’s
reasoning when using privacy-enhancing technology.

###  1.1 Research questions

With the concept and preliminary study presented in this paper, we aim to
explore the following research questions:

  * •

How do users interact with the traditional mute button and what do they think
about it?

  * •

Is a tangible “Mute-Token” perceived beneficial by users?

  * •

Can a tangible “Mute-Token” help gather additional insights on user behavior
and thoughts?

##  2 Privacy Hat

By providing a new mechanism, so that the act of muting the smart device is
transformed into a explicit, physical action, we aim to nudge the user to
reflect on their interaction with the device, especially their muting
behaviour. In our study this mechanism takes the form of the Privacy Hat:
Covering the device with the Privacy Hat (see Figure Making Privacy Graspable:
Can we Nudge Users to use Privacy Enhancing Techniques?) will mute it and give
a new visual representation on the status of the speaker, different to the
usual flashing red LEDs.

[-20pc]  A sketch, how our study-framework looks like. The Raspberry Pi is
placed below the Echo Dot and connected internally to its mute button and LED.
The distance sensor is placed on the side of the platform to detect objects on
top of the device.

To test this concept and before we developed the prototype, we were interested
in users’ opinions towards the idea of using this way to mute a smart speaker
and if it would change their perception towards the device. For this, we
conducted a focus group with four participants who had already used an Amazon
Echo in their households for several tasks, including setting a timer,
listening to music or news and controlling smart home devices like smart bulbs
or outlets. They positively stressed its sound and “human”-like voice while
disliking when they had to talk about the device itself whenever other people
are visiting them in their homes. All of them stated that privacy is important
to them. One participant regularly used the mute button before going to bed
and one mentioned using it when talking about sensitive data.

After introducing them to the principle of the Privacy Hat, we asked them how
they would use such a token and how it would change their perception. They
mentioned, that the positioning of the smart speaker is crucial to this
concept, so that anyone who is entering the room can see it. In addition to
just placing something on top of the device, they presented the idea of
“remote” muting stations that are placed at several places in the room. Also
they could imagine using the token as some kind of authentication token,
placing it the other way around on top of the speaker for specific actions
that require user authentication, for example placing an order. Related to the
design they agreed on using some kind of hat that covers the device completely
to connote a more secure feeling.

##  3 Proposed study design

For an evaluation of the concept, a platform that enables us to track the
muting-behavior of a smart speaker is needed. In the following we will discuss
a prototype and give further details on the upcoming study.

###  3.1 Prototype

We assembled a prototype that uses a Raspberry Pi as the main component. For
the smart speaker we chose a modified Amazon Echo Dot as seen in Figure 1. For
the modification, we soldered a wire to the red status LED of the muting
button to capture the current muting status of the Echo Dot. Another wire was
placed on the contact of the physical mute-button enabling the Raspberry Pi to
trigger it. To sense if something is put on the Echo Dot we tried to integrate
a distance sensor into the Echo Dot itself. However, this did not turn out as
an applicable scenario due to size restrictions. Therefore, we placed the
sensor in a 3D-printed case, that acts as a docking station for the Dot (see
Figure 3.2). A python script on the Raspberry Pi tracks the muting events of
the participants as well as whether the event was triggered by pressing the
button or by putting the Privacy Hat on the device. The way of muting, the
status of the device and the time are then logged.

###  3.2 Directions for Future Work

We are in preparation of a pilot study, that will provide the participants
with a default object to mute the Echo Dot, as proposed by the participants of
our focus group. However, technically every object could be used to provide
this functionality. If this approach turns out to be promising, further
studies can evaluate the "best" and most useful design for such a token. To
test if the proposed prototype can help to answer our research questions, we
plan to conduct a field study that tests both aspects. Over the course of
several weeks, we will gather data and observe muting behavior after
introducing the Privacy Hat. For this, we will hand out modified Amazon Echo
Dots to participants that have not used a smart home speaker before. This way,
we try to ensure that the novelty effect of the device will be nearly the same
for everyone. We want to point out that the novelty effect may benefit our
study design. However, we do not want to measure the behavior of users in the
most realistic scenario but trigger reflection and experimenting.

[-35pc]  Top view of our prototype with the sensor placed on the side.

The current plan of the study spans 4 weeks and is split into two phases that
will each last two weeks to counter the possible novelty effect of introducing
a smart home speaker and a resulting higher frequency in usage. In phase one
we will only be observing the actual usage of the Echo Dot with focus on the
muting-behavior. For the second phase, which will also last two weeks, we will
present the Privacy Hat to the participants as an alternative way to mute the
device. We will still be collecting the muting behavior of our participants to
then evaluate the actual effect of a tangible muting option.

After the two phases we will conduct interviews concerning the participants
general opinion about the concept of the Privacy Hat, which aspects they like
and whether they see potential for improvement. Additionally, we are
interested in the participants’ perceptions regarding privacy, whether these
perceptions change when having a tangible muting option and if they
consciously note a shift in their own muting behaviour. For this, we will ask
for the muting frequency and which events caused them to use the Privacy Hat.

We proposed and discussed the Privacy Hat, an example for a graspable privacy
enhancing technology in smart homes. We argue that this principle can be used
to evaluate privacy perceptions in other scenarios as well. We are confident
that making the usage of IoT devices more tangible is a promising area worth
looking at, since it could help the users to reduce resignation and make them
feel more in control. In addition, the proposed study framework can be used to
track actual user behavior in the field and now enables us to compare the
already self-reported data with empirical measured ones.

## References

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