# Concave Game

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Definition 1 (Concave Game) We shall define a concave game as a game in which player i chooses an action xi ∈ mi so that x = (x1, ., xn) ∈ C, where C is a . By requiring appropriate concavity in the payoff functions a concave game is defined. It is proved that there is a unique equilibrium point for every strictly concave . Abstract: We consider the use of no-regret algorithms to compute equilibria for particular classes of convex-concave games. While standard . A matrix game is specified by a payoff matrix P G Rm╚n. Players 1 and 2 have m and n strategies respectively, and each player picks his strategy without . By the classical existence theorem of Debreu (1952), every concave game admits a. Nash equilibrium. Moreover, thanks to the individual concavity of the game's . This paper shows that if a game satisfies the sufficient condition for the existence and uniqueness of a pure-strategy Nash equilibrium provided . The study of 1-convex/1-concave TU games possessing a nonempty core and for which the nucleolus is linear was initiated by Driessen and . We are not aware of a similar Nash equilibrium convergence result for concave games with general convex action spaces and bandit feedback: the analysis of . function is strictly concave and strategy sets are compact then the potential game has. a unique correlated equilibrium, which places probability . Smooth, noncooperative, multistage, concave games are formulated so that a new uniqueness condition—based on the Poincaré-Hopf theorem—can be .

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