Uncertainty Aversion and Equilibrium in Extensive Games

Jörn Rothe

Contributions to game theory and management, Tome 4 (2011), pp. 389-406

Résumé

This paper formulates a rationality concept for extensive games in which deviations from rational play are interpreted as evidence of irrationality. Instead of confirming some prior belief about the nature of non-rational play, we assume that such a deviation leads to genuine uncertainty. Assuming complete ignorance about the nature of non-rational play and extreme uncertainty aversion of the rational players, we formulate an equilibrium concept on the basis of Choquet expected utility theory. Equilibrium reasoning is thus only applied on the equilibrium path, maximin reasoning applies off the equilibrium path. The equilibrium path itself is endogenously determined. In general this leads to strategy profiles differ qualitatively from sequential equilibria, but still satisfy equilibrium and perfection requirements. In the centipede game and the finitely repeated prisoners' dilemma this approach can also resolve the backward induction paradox.

Détail

Keywords: rationality, extensive game, uncertainty aversion, perfect equilibrium, backward induction, maximin, Choquet expected utility theory.