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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 …