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Full-Text Articles in Physical Sciences and Mathematics
Axiomatic Equilibrium Selection For Generic Two-Player Games, Srihari Govindan, Robert B. Wilson
Axiomatic Equilibrium Selection For Generic Two-Player Games, Srihari Govindan, Robert B. Wilson
Robert B Wilson
We impose three conditions on refinements of the Nash equilibria of finite games with perfect recall that select closed connected subsets, called solutions. A. Each equilibrium in a solution uses undominated strategies; B. Each solution contains a quasi-perfect equilibrium; C. The solutions of a game map to the solutions of an embedded game, where a game is embedded if each player's feasible strategies and payoffs are preserved by a multilinear map. We prove for games with two players and generic payoffs that these conditions characterize each solution as an essential component of equilibria in undominated strategies, and thus a stable …
Axiomatic Theory Of Equilibrium Selection For Games With Two Players, Perfect Information, And Generic Payoffs, Srihari Govindan, Robert B. Wilson
Axiomatic Theory Of Equilibrium Selection For Games With Two Players, Perfect Information, And Generic Payoffs, Srihari Govindan, Robert B. Wilson
Robert B Wilson
Three axioms from decision theory are applied to refinements that select connected subsets of the Nash equilibria of games with perfect recall. The first axiom requires all equilibria in a selected subset to be admissible, i.e.\ each player's strategy is an admissible optimal reply to other players' strategies. The second axiom invokes backward induction by requiring a selected subset to contain a sequential equilibrium. The third axiom requires a refinement to be immune to embedding a game in a larger game with additional strategies and players, provided the original players' strategies and payoffs are preserved, viz., selected subsets must be …
A Decomposition Algorithm For N-Player Games, Robert B. Wilson, Srihari Govindan
A Decomposition Algorithm For N-Player Games, Robert B. Wilson, Srihari Govindan
Robert B Wilson
An N-player game can be decomposed by adding a coordinator who interacts bilaterally with each player. The coordinator proposes profiles of strategies to the players, and his payoff is maximized when players' optimal replies agree with his proposal. When the feasible set of proposals is finite, a solution of an associated linear complementarity problem yields an equilibrium of the approximate game and thus an approximate equilibrium of the original game. Computational efficiency is improved by using vertices of a triangulation of the players' strategy space for the coordinator's pure strategies. Computational experience is reported.