A player's pure strategy is called relevant for an outcome of a game in extensive form with perfect recall if there exists a weakly sequential equilibrium with that outcome for which the strategy is an optimal reply at every information set it does not exclude. The outcome satisfies forward...

This paper describes ways that the definition of an equilibrium among players' strategies in a game can be sharpened by invoking additional criteria derived from decision theory. Refinements of John Nash's 1950 definition aim primarily to distinguish equilibria in which implicit commitments are...

Two assumptions are used to justify selection of equilibria in stable sets. One assumption requires that a selected set is invariant to addition of redundant strategies. The other is a strong version of backward induction. Backward induction is interpreted as the requirement that behavior...

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...