R}}$. For any set ${\mathcal{K}}\subseteq{V}$, let ${\mathcal{K}^*}=\{x \mid {\langle x,y \rangle} \ge 0, \forall
y\in{\mathcal{K}}\}$ be its dual cone. We let ${\Vertv\Vert}_2 = \sqrt{{\langle v,v \rangle}}$, and, if $V$ is of finite dimension with orthonormal basis $\{e_1,\ldots,e_K\}$, let ${\Vertv\Vert}_1 = \sum_{k=1}^K {\vert\alpha_k\vert}$ where $v = \sum_{k=1}^K\alpha_k
e_k$. Typically, we will take ${V}={{\mathbb R}^{K}}$ and use the standard inner product.

Game Theory {#game-theory .unnumbered}
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Matrix games are the canonical tool of game theorists for representing strategic interactions ranging from illustrative toy problems, such as the “Prisoner’s Dilemma" and the “Battle of the Sexes" games, to important negotiations, collaborations, and auctions. Unlike the traditional definition [@osborne1994course], in this work we model games where only the features of the players’ utility are known and not the utilities themselves.

A [****]{} is a tuple ${\Gamma}=({\mathcal N},{\mathcal A},{u^{{\Gamma}}_{{i}}})$ where

-   ${\mathcal N}$ is the finite set of the game’s ${N}$ [****]{},

-   ${\mathcal A}=\times_{{i}\in{\mathcal N}}{A_{{i}}}$ is the set of the game’s [****]{} or [****]{}, where

-   ${A_{{i}}}$ is the finite set of [****]{} or [****]{} for player ${i}$, and

-   ${{u^{{\Gamma}}_{{i}}} : {\mathcal A}\rightarrow {{V}}}$ is the [****]{} for player ${i}$.

We let ${A}=\max_{{i}\in{\mathcal N}}{\vert{A_{{i}}}\vert}$.

Players aim to maximize their [****]{}, a quantity measuring 