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On the Structure of Weakly Acyclic Games ⋆
"... Abstract. The class of weakly acyclic games, which includes potential games and dominancesolvable games, captures many practical application domains. Informally, a weakly acyclic game is one where natural distributed dynamics, such as betterresponse dynamics, cannot enter inescapable oscillations. ..."
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Abstract. The class of weakly acyclic games, which includes potential games and dominancesolvable games, captures many practical application domains. Informally, a weakly acyclic game is one where natural distributed dynamics, such as betterresponse dynamics, cannot enter inescapable oscillations. We establish a novel link between such games and the existence of pure Nash equilibria in subgames. Specifically, we show that the existence of a unique pure Nash equilibrium in every subgame implies the weak acyclicity of a game. In contrast, the possible existence of multiple pure Nash equilibria in every subgame is insufficient for weak acyclicity. 1
Schedulers, Potentials and Weak Potentials in Weakly Acyclic Games
, 2014
"... Abstract. In a number of large, important families of finite games, not only do purestrategy Nash equilibria always exist but they are also reachable from any initial strategy profile by some sequence of myopic singleplayer moves to a better or bestresponse strategy. This weak acyclicity property ..."
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Abstract. In a number of large, important families of finite games, not only do purestrategy Nash equilibria always exist but they are also reachable from any initial strategy profile by some sequence of myopic singleplayer moves to a better or bestresponse strategy. This weak acyclicity property is shared, for example, by all perfectinformation extensiveform games, which are generally not acyclic since even sequences of bestimprovement steps may cycle. Weak acyclicity is equivalent to the existence of a weak potential, which unlike a potential increases along some rather than every sequence as above. It is also equivalent to the existence of an acyclic scheduler, which guarantees convergence to equilibrium by disallowing certain improvement moves. A number of sufficient conditions for acyclicity and weak acyclicity are known.