A Logic for Strategy Updates

In game theory, strategy for a player is defined as “a set of rules that describe exactly how (...) [a] player should choose, depending on how the [other] players have chosen at earlier moves” [14]. Notice that this definition of strategies is static, and presumably constructed before the game is actually played. For example, consider chess. According to Zermelo’s well-known theorem, chess is determined [22]. Then, why would you play chess if you know you will lose (or won’t win) the game? Clearly, if we have logical omniscience (which we don’t), then it is pointless for the player, who is going to lose, to even start playing the game as she knows the outcome already. If we are not logical omniscient, and have only a limited amount of computational power and memory (which we do), then chess is only a perfect information game for God. Therefore, there seems to be a problem. The static, pre-determined notion of strategies falls short analyzing perfect information games. Because, we, people, do not strategize as such even in perfect information games largely because we are not logically omniscient, and we have limited memory, and computational and deductive power. While people play games, they observe, learn, recollect and update their strategies during the game as well as adopting deontological strategies and goals before the game. Players update and revise their strategies, for instance, when their opponent makes an unexpected or irrational move. Similarly, sometimes external factors may force the players not to make some certain moves. For instance, assume that you are playing a video game by using a gamepad or a keyboard, and in the middle of the game, one of the buttons on the gamepad