Applied Game Theory in Politics
In game theory, Nash equilibrium is a concept that occurs when all players in a game choose the best strategy for themselves given the strategies chosen by the other players. It is named after the mathematician John Nash, who developed the concept in his 1950 paper 'Equilibrium Points in N-Person Games.'
To understand Nash equilibrium, it is important to first understand the concept of dominant strategies. A dominant strategy is a strategy that is always the best choice for a player, regardless of what the other players do. Once all players in a game have identified their dominant strategies, the game is said to be in a dominant strategy equilibrium. However, not all games have a dominant strategy equilibrium.
In cases where there is no dominant strategy, players must consider the strategies chosen by the other players when making their own choices. Nash equilibrium occurs when each player's strategy is the best response to the strategies chosen by the other players. In other words, no player can improve their outcome by changing their strategy, given the strategies chosen by the other players.
For example, consider the game of rock-paper-scissors. If both players choose rock, they will tie. If both choose paper, they will tie. If both choose scissors, they will tie. However, if one player chooses rock and the other chooses scissors, the player who chose rock wins. If one player chooses paper and the other chooses rock, the player who chose paper wins. And if one player chooses scissors and the other chooses paper, the player who chose scissors wins. In this game, there is no dominant strategy, but there is a Nash equilibrium in which each player chooses rock, paper, or scissors with equal probability.
Nash equilibrium is an important concept in political science because it can help predict the outcomes of political decisions. By analyzing the strategies of each player in a political decision-making process, analysts can identify the Nash equilibrium and predict the likely outcome of the decision.
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