Preferences, counterfactuals and maximisation : reasoning in game theory
This thesis explores two kinds of foundational issues in game theory. The first is concerned with the interpretation of the basic structure of a game, especially the definitions of outcomes and payoffs. This discussion leads to the second issue; namely the nature of solution concepts and their relation to both explicit and implicit assumptions in game theory concerning hypothetical reasoning. Interpreting utility functions in game theory, I argue that the notion of revealed preferences is ill-suited for counterfactual reasoning and for taking account of the implicit normativity of instrumental rationality. An alternative interpretation is outlined that treats preferences as determinants of choice. Accordingly, outcomes have to be individuated so as to capture everything that matters to an agent. I consider whether this is problematic when properties of outcomes depend on choice processes themselves. Turning to a decision theoretic problem, I question Verbeek's (2001) claim that modal outcome individuation conflicts with axioms of consequentialism. Next, I critically assess Rabin's (1993) model of fairness equilibria. Hypothesising about unilateral deviation is shown to be incompatible with belief-dependent utility definitions. Counterfactuals in games are then analysed more generally. It proves to be crucial for solution concepts whether our formal framework allows us to differentiate between indicative and subjunctive conditionals. Stalnaker's (1996) prima facie counterexample to Aumann's (1995) theorem that common knowledge of rationality implies a subgame perfect equilibrium is questioned on the grounds of a plausibility criterion. Again drawing on what has been established about the structure of a game and the meaning of its elements, Gauthier's (1986) notion of constrained maximisation, an attempt to overcome the non-cooperative equilibrium of the finitely iterated prisoner's dilemma, is shown to be incompatible with orthodox game theoretical methodology. The approach of treating the unit of agency as endogenous is addressed.