Pseudo-games, or abstract economies [4], are optimization problems that are closely related to min-max Stackelberg games, but which are technically not games, as noted by Facchinei and Kanzow [26, 27], because each player's strategy set is not fixed at the outset (i.e., before they have to make a decision), but instead depends on the other players' choices. In this appendix, we formally define two-player, zero-sum pseudo-games,10 and discuss how they differ from min-max Stackelberg games. We also define the equilibrium concept par excellence of pseudo-games, namely generalized Nash equilibrium, and juxtapose its definition with vanilla Nash equilibrium. A two-player, zero-sum pseudo-game comprises two players, with respective payoff functions f(x,y)and f(x,y), and respective strategy spaces given by the correspondences X: Y X and Y: X Y, i.e., set valued mappings that depend on the choice the other player takes. Pseudo-games are closely related to min-max Stackelberg games, as they both comprise agents with the same objectives and the same space of feasible strategy profiles, namely {(x,y) 2 X Y |8 k 2 [K],gk(x,y) 0}.

Thecomputation ofthecompetitiveequilibrium isknownasthemarketequilibrium computation problem, whose unique solution was shown to exist under a general model of the economics in the seminal work of Arrow and Debreu[3].