A New Epistemic Logic Model of Regret Games

摘要

To many real-life games, the algorithm of Iterated Eliminating Regret-dominated Strategies (IERS) can find solutions that are consistent with experimental observations, which have been proved to be problematic for Nash Equilibrium concept. However, there are a serious problem in characterising the IERS epistemic procedure. That is, the rationality of choosing un-dominated strategies cannot be assumed as the common knowledge among all the players of a game, otherwise the outcome of the IERS cannot be implied. Nevertheless, the common knowledge of rationality among players is an essential premise in game theory. To address these issues, this paper develops a new epistemic logic model to interpret the IERS procedure as a process of dynamic information exchanging by setting the players' rationality as a proper announcement assertion. Finally, we show that under the assumption of rationality common knowledge rather than lower probabilities, our model can successfully solve a well-known traveler dilemma.