No prisoners: e-Commerce Uses Game Theory to Capture Consumer Share of Wallet thanks to Nash Equilibrium

It is that time of year again. Christmas shopping must be done and deals are flying in all consumers inboxes. Whilst reading ‘The Bargaining Problem‘ by one of my favourite Mathematician/economist, it got me thinking how we use the Game Theory on a regular basis in eCommerce reflecting on my Christmas shopping behaviour (both as a consumer and retailer). Indeed, the rise and rapid proliferation of technology has forced companies to adapt in order to stay relevant and competitive. Specifically, the consumer retail industry has recently navigated this changing landscape by utilising collected consumer data to make prices dynamic depending on seasonal factors, locations (international businesses) and even the strategies of their competitors. These companies are trying to harness the power of technology to achieve perfect price discrimination, where the seller knows every buyer’s willingness to pay and can therefore maximise retail prices without exceeding the buyer’s walk away price.

John Nash and the Equilibrium Point

John Forbes Nash Jr. (June 13, 1928 – May 23, 2015) was an American mathematician who made fundamental contributions to game theory, differential geometry, and the study of partial differential equations. Nash’s work has provided insight into the factors that govern chance and decision-making inside complex systems found in everyday life.



Game theorists use the Nash equilibrium concept to analyse the outcome of the strategic interaction of several decision makers. In other words, it provides a way of predicting what will happen if several people or several institutions are making decisions at the same time, and if the outcome depends on the decisions of the others. The simple insight underlying John Nash’s idea is that one cannot predict the result of the choices of multiple decision makers if one analyses those decisions in isolation. Instead, one must ask what each player would do, taking into account the decision-making of the others.


Game theory applied to eCommerce

In the context of e-Commerce, the retailer and the consumer are the two players. A game theory graph would illustrate the company’s best response to the consumer’s willingness to pay and the consumer’s response to the retail price the company is offering for the product. There would be no dominant strategy in this game because of the availability of information about other sellers and the access to other sellers the customer has in addition to the connectivity to millions of buyers via the Internet the company has. Either party can forego engaging in this transaction and just find another customer/company to sell/buy to/from. This can be illustrated with the given example (I read couple of articles whilst researching) of how Amazon dropped prices on Black Friday of a Samsung TV from $350 to $250 and decided on this final price using collected data, which allowed them to surpass the competition. Amazon took this a step further by hiking the price of HDMI cables, a complementary product, knowing based on consumer data that people are less likely to shop around in pursuit of the lowest prices for smaller items than bigger ticket items. The customers’ willingness to pay was any price lower than what the competitors were offering, which turned out to be the $250 (implying that no other retailer offered prices that low).

The implications of this show how companies are controlling not only prices but consumers’ perception of prices, thereby using this data to surpass the competition by limiting how consumers perceive the choices they have in front of them. Furthermore, this serves as an illustration of another way we experience a loss of control in our lives. However, another side of the argument says that perfect price discrimination can positively impact consumers, since their prices will be individually tailored. At the same time, this constant changing of prices can end up overwhelming and deterring consumers from purchasing the item all together.

As of now, it is too soon to tell how and if this becomes a normalised practice that we all must adapt to. It definitely is interesting to consider the ripple effects it will have on consumer behaviour in the future in addition to potential consumer protection regulation, as we are operating within a rigged sandbox where companies hold all the cards in their favour through informational advantages.

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Happy Christmas Shopping and bargain hunting

Benoit Mercier