Games with Type-Indeterminate Players

The Type Indeterminacy model is a theoretical framework that uses some elements of quantum formalism to model the constructive preference perspective suggested by Kahneman and Tversky. In this paper we extend the TI-model from simple to strategic decision-making. In Part I we introduce TI-games by means of an example. A 2X2 game is investigated. We let the game be preceded by a cheap-talk promise exchange game. We show in a numerical example that in the TI-model the promise stage can have impact on next following behavior when the standard classical model predicts no impact whatsoever. The TI approach differs from other behavioral approaches in identifying the source of the effect of cheap-talk promises in the intrinsic indeterminacy of the players ’ type. In Part II, we formulate some basic concepts for the analysis of games with type indeterminate players. We develop the theory in close connection with the standard approach to game of incomplete information à la Harsanyi. We show an equivalence between static games of incomplete information and static TI-games. We extend this equivalence result to dynamic commuting TI-games. Finally, we develop a new solution concept for non-commuting dynamic TI-games. It differs from the Perfect Bayesian equilibrium by one single property characterizing the updating rule. This property captures the novelty brought about by Type Indeterminacy namely that in addition to affecting payoffs, the action of a player impacts on the profile of types and thus on future actions. We provide an example showing that strategies that form a Perfect Bayesian equilibrium are not part of any Perfect TI-equilibrium