Chess and its Relation to Game Theory
For centuries, Chess has maintained its status as one of the most popular games in the world. It is known for its complexity, strategic nature, and game knowledge that players must thoroughly understand in order to become a viable competitor.
But it is, in fact, the strategic nature of Chess that makes it such an incredible target for game theorists. In game theory, players make decisions based on the expected outcomes of their strategies. In doing so, players are able to choose the option that maximizes their chances of winning. Chess players must make strategic decisions based on the positions of their pieces on the board relative to that of their opponent’s pieces. They must try to anticipate their opponent’s strategy in order to deploy the move that is most likely to lead to a victory.
One concept from game theory that is particularly relevant to Chess is the Nash equilibrium. In which each player has made the best decision they can given the decisions of the other players. More rigidly, the players reach an equilibrium if there is no move that either player could make that leads to a better payoff than the current position. In Chess, players seek to find Nash equilibria to maximize their payoff in the game. In the short term, this may be sacrificing a knight to take an opponent’s rook. In the long term, it is picking a strategy that leads to checkmate.
Another concept from game theory relevant to Chess is the prisoner’s dilemma, a scenario in which two players must agree to cooperate or betray each other. In Chess, we see this most clearly when one player is trying to anticipate their opponent’s decision. At that moment, the opponent is also trying to figure out the player’s strategy. Both parties must decide whether to attack each other’s pieces or defend their own.
Overall, the strategic nature of Chess is related to game theory through several concepts we have learned about in this course. Players can use these concepts to gain a more fundamental understanding of the system underlying the game to improve the likelihood of victory.