Context-dependence: uncertainty and games
|Speaker:||Dr Patrick O'Callaghan, University of Queensland|
|Date:||Thursday 13 June 2013|
|Location:||Streatham Court 0.28|
The Gilboa and Schmeidler (2003) derivation of ``Expected Utility maximisation in the context of a game" seeks to explain experimental evidence from the Ultimatum and Dictator Games, where strategies with strictly dominated monetary payoffs are often played. Preferences feature context-dependence, where each context is a belief or conjecture about the strategy of the opponent and, for each context, preferences are defined on a set of alternatives. A problem with their model arises due to the conditions that are needed to obtain a model of linear context-dependence. This rules out the vast majority of perfectly reasonable preferences. In fact, for low dimensions of uncertainty, there are no preferences satisfying the conditions. In the present paper, a nonlinear model of context-dependence that represents a minimal departure from the linear case is derived: hyperplanes are given up for ``connected separators". Both the strengths and the weaknesses of the nonlinear approach are discussed using simple and familiar examples from choice under uncertainty and game theory. This is work in progress in the sense that, although the model has the potential to provide a preference foundation for the reference-dependent utility function in the Koszegy-Rabin (2006) formalisation of Prospect Theory, the present results only apply to problems with countably many alternatives.