Reasoning about strategies and rational play in dynamic games

We discuss a number of conceptual issues that arise in attempting to capture, in dynamic games, the notion that there is "common understanding" among the players that they are all rational.Belief revision, common belief, counterfactual, dynamic game, model of a game, rationality

A logic of hypothetical conjunction

This work was supported by the UK Engineering and Physical Sciences Research Council under the research grants EP/K033042/1 and EP/P011829/1.Peer reviewedPostprin

Subjective expectations in economics: a statistical overview of the main findings

In this writing we provide a brief overview on how in different fields such as statistics, econometrics and experimental psychology, the issue of measuring subjective expectations about future uncertain outcomes has been attacked. In many situations realized observed data come from a decision process in which the decision is made by considering future uncertain outcomes, so that the observed data will depend on future outcome via the probabilistic judgement made by the decision maker. For example the decision to buy a car today will depend on our expectations about future incomes, so that observed data about the number of cars sold will depend on peoples’ expectations about their future incomes. Expectations are not observable so that we need proper statistical methods of inference to treat these type of problems. Here, we provide a very general overview, and we try to summarize different approaches

Three Essays on Epistemic Game Theory

Ph.DDOCTOR OF PHILOSOPH

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

Hypothetical Knowledge and Counterfactual Reasoning

Abstract: Salmet introduced a notion of hypothetical knowledge and showed how it could be used to capture the type of counterfactual reasoning necessary to force the backwards induction solution in a game of perfect information. He argued that while hypothetical knowledge and the extended information structures used to model it bear some resemblance to the way philosophers have used conditional logic to model counterfactuals, hypothetical knowledge cannot be reduced to conditional logic together with epistemic logic. Here it is shown that in fact hypothetical knowledge can be captured using the standard counterfactual operator "> " and the knowledge operator "K", provided that some assumptions are made regarding the interaction between the two. It is argued, however, that these assumptions are unreasonable in general, as are the axioms that follow from them. Some implications for game theory are discussed.

Hypothetical knowledge and counterfactual reasoning

Samet introduced a notion of hypothetical knowledge and showed how it could be used to capture the type of counterfactual reasoning necessary to force the backwards induction solution in a game of perfect information. He argued that while hypothetical knowledge and the extended information structures used to model it bear some resemblance to the way philosophers have used conditional logic to model counterfactuals, hypothetical knowledge cannot be reduced to conditional logic together with epistemic logic. Here it is shown that in fact hypothetical knowledge can be captured using the standard counterfactual operator ">" and the knowledge operator "K", provided that some assumptions are made regarding the interaction between the two. It is argued, however, that these assumptions are unreasonable in general, as are the axioms that follow from them. Some implications for game theory are discussed.Counterfactuals · knowledge · backwards induction solution