The object of study in Game Theory is the “game”, which is a formal description of a strategic situation.
In a game, each decision-maker (player) chooses its strategy to maximize its utility, given the other players’ strategies. By “utility” what is meant is a payoff, an interest, or a revenue of some type that reflects the player’s expected outcome, and players are assumed to be “rational”, as in self-interested, with the goal to always maximize their own payoffs. According to von Neumann & Morgenstern, “The aim of all participants in the economic system, consumers as well as entrepreneurs, is money”.
From here, decision models are created in keeping with the rules of the game to reflect the options available to the players, and solutions for best and worst outcomes (consequences) are explored based on possible player strategies.
Parrachino, Zara & Patrone sum up the topic nicely: Games in “Game Theory consist of a modeling part and a solution part. Mathematical models of conflicts and of cooperation provide strategic behavioral patterns, and the resulting payoffs to the players are determined according to certain solution concepts.”
In The Art of Strategy, Dixit and Nalebuff state that a game is “a situation of strategic interdependence: the outcome of your choices (strategies) depends upon the choices of one or more other persons acting purposely,” and that there are four rules a player should follow when choosing moves and consequences:
– Rule 1: Look forward and reason backward.
– Rule 2: If you have a dominant strategy, use it.
– Rule 3: Eliminate dominated strategies from consideration.
– Rule 4: Look for equilibrium, a pair of strategies in which each player’s action is the best response to the other’s.
Decision trees and matrices are often used in Game Theory to describe the choices available to players, but, as said by Will Lissner in his article, ‘Mathematical Theory of Poker Applied to Business Problems’, “The illustration, of course, loses the generality and the rigor of the formula.”
Thanks for reading!