Three Problems in Learning Mixed-Strategy Nash Equilibria

By J. Jordan. 1993

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In Game & Decision Theory

Citations in the corpus

OpenSpiel: A Framework for Reinforcement Learning in Games (2019, background): “Game Reference(s) Status Backgammon Wikipedia Breakthrough Wikipedia Bridge bidding Wikipedia Coin Game [56] ∼ Connect Four Wikipedia Cooperative Box-Pushing [62] ∼ Chess Wikipedia First-price Sealed-bid Auction Wikipedia Go Wikipedia Goofspiel Wikipedia Havannah Wikipedia Hex Wikipedia ∼ Kuhn poker”
Analyzing Complex Strategic Interactions in Multi-Agent Systems (2002, background): “Definitive, positive theoretical properties of equilibrium convergence for general games of A agents and S strategies, have not yet been established (Fudenberg & Kreps 1993; Fudenberg & Levine 1993; Jordan 1993).”
Survival of dominated strategies under evolutionary dynamics (2011, methodology): “Our construction relies on the theory of potential games, developed in the normal form context by Monderer and Shapley (1996) and Hofbauer and Sigmund (1998) and in the population game context by Sandholm (2001, 2009).”
Deep Fictitious Play for Finding Markovian Nash Equilibrium in Multi-Agent Games (2019, background): “…when it converges (Robinson (1951); Miyasawa (1961); Milgrom and Roberts (1991); Monderer and Shapley (1996b,a); Berger (2005); Hofbauer and Sandholm (2002)) and when it does not (Shapley (1964); Jordan (1993); Monderer and Sela (1996); Foster and Young (1998); Krishna and Sjöström (1998)).”
Regret Testing: Learning to Play Nash Equilibrium Without Knowing You Have an Opponent (2006, background): “Unfortunately it is difficult to satisfy the latter absolute continuity condition when players do not know their opponents’ payoff functions (Jordan 1991, 1993, Foster and Young 2001, Nachbar 1997, 2005).”
A survey of random processes with reinforcement (2006, background): “pirical distribution. Robinson’s result was extended to non-zero-sum 2 × 2 games by [Miy61], but then shown to fail in general by Shapley [Sha64] (a two-player, three-strategy counterexample; see also[Jor93] for acounterexamplewith dichotomousstrategiesbut three players). There are, however, subclas”
Potential Games (1994, background): “…non-zero-sum games by Miyasawa (1961), Shapley (1964), Deschamps (1973), and lately by Krishna (1991), Milgrom and Roberts (1991), Sela (1992), Fudenberg and Kreps (1993), Jordan (1993), Hofbauer (1994), Krishna and Sjöström (1994), Fudenberg and Levine (1994), Monderer et al. (1994), and others.”
A Counter-example to Karlin's Strong Conjecture for Fictitious Play (2014, background): “s not converge [35]. Since then a lot of research has been devoted to understanding classes of games where ﬁctitious play converges (e.g. [28], [31], [21], [17], [34], [4]) or does not converge (e.g. [22], [15], [30], [12], [25]). Surveys can be found in [24], [14], [20]. Other work has studied the ”