Ahmed: Causal Decision Theory and Intrapersonal Nash Equilibria

UNIVERSITY SEMINAR ON LOGIC, PROBABILITY, AND GAMES
Causal Decision Theory and Intrapersonal Nash Equilibria
Arif Ahmed (University of Cambridge)
4:15 PM, April 4th, 2014
716 Philosophy Hall, Columbia University

Abstract.  Most philosophers today prefer ‘Causal Decision Theory’ to Bayesian or other non-Causal Decision Theories. What explains this is the fact that in certain Newcomb-like cases, only Causal theories recommend an option on which you would have done better, whatever the state of the world had been. But if so, there are cases of sequential choice in which the same difficulty arises for Causal Decision Theory. Worse: under further light assumptions the Causal Theory faces a money pump in these cases. It may be illuminating to consider rational sequential choice as an intrapersonal game between one’s stages, and if time permits I will do this. In that light the difficulty for Causal Decision Theory appears to be that it allows, but its non-causal rivals do not allow, for Nash equilibria in such games that are Pareto inefficient.

Ojea: Evaluation Games for Many Valued Logics

CUNY SEMINAR IN LOGIC, PROBABILITY, AND GAMES
Evaluation Games for many valued logics
Ignacio Ojea (Columbia University)
4:15 PM, March 28th, 2014
Room 3305, CUNY Graduate Center

Abstract.  Evaluation Games for classical logic are well known. Following early applications of games in model theory, by Ehrenfeucht and Fraisse, Hintikka and Parikh independently proposed a game-theoretic approach as a way of defining the classical semantics. A great deal of the game theoretic approach has been more recently studied by van Bentham. The original idea was to define the truth-value of a wff, in a given model, in terms of the existence of a strategy for one of the players (the “Verifier” and “Falsifier”) in a certain two-person game. These games can be also viewed in terms of pay-offs. Recently I suggested a natural extension of these games to the case of many valued logics, where the notion of a Nash equilibrium plays a crucial role.