Also known as non-cooperative game equilibrium, it is an important term in game theory, named after johnf nash. In the process of a game, no matter how the opponent chooses a strategy, one side will choose a strategy, which is called the best response. If the combination of strategies of players in two games constitutes their best response, then this combination is defined as Nash equilibrium.
Before giving the explanation of Nash equilibrium, we must first understand a concept about the best game.
Nash equilibrium describes this situation. If each player's strategy in a situation is the best corresponding to the current strategies of other players, this situation is called Nash equilibrium.
If one player's strategy is the best response to any other player's strategy, then this strategy is the player's dominant strategy.
Under Nash equilibrium, no one in the game will want to change, because whoever changes may be at a disadvantage in the game.
First, let's look at the Nash equilibrium in the prisoner's dilemma. Nash equilibrium in prisoner's dilemma is that both sides confess, which belongs to the dominant strategy.
In fact, whether player 2 resists or confesses, the best response to player 2 is to confess. It can be seen that Nash equilibrium point is not necessarily the optimal solution of the whole. Some people may say, then why is it not good for both sides (boycott, boycott)? The best strategy here is that whatever the opponent does is the best strategy for himself. At the end of maxmin, he will know why they made honest choices. This is a strategy to avoid risks.
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This is a pure strategy Nash equilibrium and a mixed strategy Nash equilibrium. The probability of girls watching dance P and boys watching dance Q is 1-p and 1-q respectively.
The wife's random purpose is to leave her husband no choice. No matter which strategy her husband chooses, her expected income is the same.
Husband gives probability distribution and won't let his wife watch the ball.
As far as I know, my husband prefers watching football.
The strategy choice distribution of player 1 is recorded as, and that of player 2 is recorded as. Assuming that the strategy distribution of player 1 remains unchanged, the utility of player 2' s strategy selection is
Mixed Nash equilibrium of scissors, stone and cloth
Any finite game (with a limited number of players and strategies) has at least one Nash equilibrium, which may be a pure strategy Nash equilibrium (such as scissors, stone and paper), or a mixed strategy equilibrium, and the multiplicity of Nash equilibria (such as the battle of gender).