Regular ArticleOn the Number of Pure Strategy Nash Equilibria in Random Games
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2021, Theoretical Computer ScienceCitation Excerpt :Random games have been used to rationalize mixed Nash equilibria (Harsanyi [3]), to study their generic properties in normal-form games, and as a tool to understand the complexity of the set of Nash equilibria. Most literature on random games focuses on normal form games and studies properties such as the expected number of Nash equilibria [9,10], the distribution of pure Nash equilibria [2,12,14,11,13,16], or the maximal number of equilibria [8]. Similar to our setting, [1] studies games over binary trees with alternating moves where the payoff at the leaves are drawn i.i.d. according to some distribution; [1] considers a more general scenario where payoff profiles are not necessarily zero-sum.
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2019, Physica A: Statistical Mechanics and its ApplicationsCitation Excerpt :We emphasize, furthermore, that only one strict Nash equilibrium can exist in each row and column. This fact maximizes the number of pure and strict Nash equilibria [29–32]. In the absence of pure Nash equilibrium for the rock–paper–scissors game the Nash theorem [26,33] prescribes the existence of a mixed Nash equilibrium for which the players choose one of their three strategies with the same probabilities (1/3).
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2016, Journal of Economic TheoryCitation Excerpt :These games have been used to rationalize mixed Nash equilibria (Harsanyi, 1973), to study generic properties of normal form games, and as a tool to understand the complexity of the set of Nash equilibria. In particular, the existing literature on random games focuses on normal form games and studies properties such as the expected number of Nash equilibria (McLennan, 2005; McLennan and Berg, 2005), the distribution of pure Nash equilibria (Dresher, 1970; Papavassilopoulos, 1995; Powers, 1990; Rinott and Scarsini, 2000; Stanford, 1995; Takahashi, 2008), or the maximal number of equilibria (McLennan, 1997). In this work we study two-player random extensive form games and focus on the subgame perfect Nash equilibrium (henceforth SPE) of these games.
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