of the agents only depend on a local subset of the agents [@kearns2001graphical]. Graphical games can be generalized in a straightforward manner to assuming vectorial payoffs. Formally, there is a support graph $G=(N,E)$ where each vertex represents an agent, and an agent $i$’s evaluation function only depends on the actions of the agents in his inner-neighbourhood ${\mathcal{N}}(i)=\{j\in N|(j,i)\in E\}$. That is $\bm{u}^i:A^{{\mathcal{N}}(i)}\rightarrow{\mathbb{R}}^d$ maps each local action-profile $\bm{a}^{{\mathcal{N}}(i)}\in A^{{\mathcal{N}}(i)}$ to a multi-objective payoff $\bm{u}^i(\bm{a}^{{\mathcal{N}}(i)})\in{\mathbb{R}}^d$.

An MOGG is a tuple $\left(G=(N,E), \{A^i\}_{i\in N}, {{\mathcal{D}}}, \{\bm{u}^i\}_{i\in N}\right)$. $N$ is the set of agents. $\{A^i\}_{i\in N}$ are their individual action-sets. ${{\mathcal{D}}}$ is the set of all objectives. Every function $\bm{u}^i:A^{{\mathcal{N}}(i)}\rightarrow{\mathbb{R}}^d$ is vector-valued, and its scope is vertex $i$’s neighborhood.

Figure 1 pictures a didactic instance of an MOGG. In the same manner as computing equilibria in graphical games was reduced to junction-tree algorithms [@daskalakis2006computing], it is also possible to exploit a generalized MO junction-tree algorithm [@dubus2009multiobjective; @gonzales2011decision]. However, even though this MO junction-tree algorithm is not in polynomial time (but rather pseudo-polynomial time), it still remains faster than browsing the Cartesian product of action-sets and is tractable on average, as experimented in the appendix. Symmetric games [@jiang2007computing] can also be generalized to MOGs:

In 