The problem of finding sufficient conditions for backward induction in games of perfect information is analysed in a syntactic framework with subjunctive conditionals. The structure of the game is described by a logical formula. Two different rationality conditions are formulated, which are...

The literary source of the main ideas in Aumann's article ``Backward Induction and Common Knowledge of Rationality" is exposed and analyzed. The primordial archetypal images that underlie both this literary source and Aumann's work are delineated and are used to explain the great emotive impact...

Aumann has proved that common knowledge of substantive rationality implies the backwards induction solution in games of perfect information. Stalnaker has proved that it does not. Roughly speaking, a player is substantively rational if, for all vertices $v$, if the player were to reach vertex...

A notion of cognitive uncertainty is introduced as an agent's uncertainty about the validity of the results of his own information processing. In order to analyze this notion, a formal model of the agent's information processing is presented. It is shown how cognitive uncertainty may prevent a...

This paper investigates algorithmic computability of simple games (voting games). It shows that (i) games with a finite carrier are computable, (ii) computable games have both finite winning coalitions and cofinite losing coalitions, and (iii) computable games violate any conceivable notion of...