Economics Game Theory Questions Medium
In game theory, mixed strategy equilibrium refers to a situation where players in a game choose their strategies randomly, rather than deterministically. This concept is used to analyze games where players have uncertainty about the actions of their opponents.
In a mixed strategy equilibrium, each player assigns a probability distribution over their available strategies, indicating the likelihood of choosing each strategy. The probabilities are chosen in such a way that no player has an incentive to deviate from their chosen strategy, given the strategies chosen by the other players.
To determine the mixed strategy equilibrium, we use the concept of expected payoffs. Each player calculates the expected payoff for each strategy, taking into account the probabilities assigned to each strategy by themselves and their opponents. The player then chooses the strategy that maximizes their expected payoff.
In a mixed strategy equilibrium, the expected payoffs for all players are equal. This means that no player can improve their payoff by unilaterally changing their strategy. If any player were to deviate from their chosen strategy, the other players would adjust their strategies accordingly, resulting in no improvement in payoffs for the deviating player.
Mixed strategy equilibrium is a powerful concept in game theory as it allows for the analysis of games where players have uncertainty and can lead to more realistic predictions of behavior in strategic interactions. It also provides a solution concept for games where pure strategy equilibria do not exist.