| Mamoru Kaneko (Waseda University Tokyo). |
| Undecidability: prediction/decision making in games |
| Abstract We study various aspects of prediction/decision making in a 2-person finite game. When a player adopts the same criterion as himself for a prediction criterion about the other's decision making, it leads to an infinite regress. This is described in an axiomatic manner in a fixed-point extension of the epistemic logic KD^2. For a game satisfying the interchangeability condition, the criterion can make a positive or negative recommendation for each strategy. However, for a game without interchangeability, it may make no recommendation for a given strategy. For example, for a Battle of the Sexes, neither strategy is recommended positively or negatively. Formally, it is given as an incompleteness theorem on the axiomatic description of prediction/decision making in the fixed-point extension of KD^2. Since this involves various new conceptual issues, we touch some (indirectly) related problems so as to have a full interpretation of our undecidability result. References: Hu, T.-W, and M. Kaneko, (2014), Undecidability: Prediction/Decision Making in Games. To appear. Hu, T.-W, M. Kaneko, and N.-Y. Suzuki (2014), Small Infinitary Epistemic Logics and Some Fixed-Point Logics. Kaneko, M., (2002), Epistemic logics and their game theoretical applications: Introduction. Economic Theory 19, 7-62. Kaneko, M., and N.-Y. Suzuki, (2002), Bounded interpersonal inferences and decision making, Economic Theory 19 (2002), 63-103. Kaneko, M., (2004), Game Theory and Mutual Misunderstanding, Springer, Heidelberg. Kaneko, M., and J. J. Kline, (2008), Inductive Game Theory: A Basic Scenario, Journal of Mathematical Economics 44, (2008), 1332--1363. |