Investigating relaxed probability updating games

Abstract

Digital data is everywhere; it is the backbone of science and our modern society. But data is sometimes incomplete. A complex form of incomplete data is when data is coarse. Many coarse data problems cannot be solved with standard conditioning. The problem can be reformulated as a probability updating game: a zero-sum game between a host and a contestant. An instance of a probability updating game is made from rewriting the Monty Hall problem as a game. It is proved that if the host plays a strategy that satisfies the RCAR condition, it plays worst-case optimally and the probabilities can be updated robustly for the contestant. We study whether RCAR still characterises Nash equilibria when the zero-sum constraint or the one-shot constraint of these games are removed. We found that if RCAR characterises optimality for a zero-sum, one-shot probability updating game, it also characterises optimality for the finitely repeated game. Moreover, we conclude from empirical analysis that if RCAR characterises optimality for a zero-sum probability updating game, it may also characterise optimality for a moderately competitive non-zero-sum game.