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Nash equilibrium
Named after John Nash, winner of the Nobel Prize in economics in 1994, Today, Nash equilibrium is widely used in various fields of research, especially in the field of economic science, Nash equilibrium has a very important influence on the economic discipline.
So what is Nash Equilibrium
Game theory is the study of rational behavior, in which each player chooses the most advantageous strategy, the optimal response, based on the opponent’s strategy.
Data structure-Tree and binary tree Introduction This section describes what a tree is and the basic terminology of a tree, what a binary tree is, and the classification and features of binary trees.
| A | A | ||
|---|---|---|---|
| frank | resist | ||
| B | frank | 3, 3 | 0, 5 |
| B | resist | 5, 0 | 1, 1 |
What A classic game theory problem, prisoner’s dilemma, prisoner A and prisoner B, each cell is A situation, A and B give their strategy, and the cell is A and B give their strategy’s utility function. For each combination of utility function values, the first value is the utility function value of A, and the second value is the utility function value of B. If A chooses to confess, B’s prisoner will be sentenced to 5 years if he confesses 3. Since 3 years is less than 5 years, B will choose to confess. Then when A chooses the situation of resistance, B chooses to confess as release, and the resistance is 1 year, so B will choose to confess again.
The same is true for A and B will choose to confess no matter which one B chooses. For player A and player B in the game, no matter what the other player chooses, the confessing strategy is their dominant strategy. The strategy of resistance is called inferior strategy.
Dominant strategy
Generally speaking, in A two-person game, if any two strategies A1 and A2 in A player A’s strategy set are investigated, if the payoff of player A’s strategy A1 is always strictly greater than that of strategy A2, no matter what strategy is adopted by the other party, we can say that strategy A2 is strictly dominated by strategy A1. Or A1 is strictly dominant and A2 is strictly inferior.
If the payoff of player A’s strategy A1 is always strictly greater than or equal to that of player A2, no matter what strategy the other party adopts, we say that strategy A2 is dominated by strategy A1, or strategy A1 is dominant and strategy A2 is inferior.
Dominant policy balancing
In economics, a stable and measurable pattern of interactive behavior. When each player in a game chooses their own dominant strategy, the corresponding game result is the dominant strategy equilibrium.
Dominant policy balancing
Nash equilibrium
A strategy combination consisting of the optimal strategies of all participants. This strategy combination is also known as the Nash equilibrium.
In a Nash equilibrium, each rational player has no individual incentive to change strategy, because no player in the game can gain by unilaterally changing his or her strategy.
Individual rationality does not mean the best result, which can be seen from the Prisoner’s dilemma. It is better for both of them to choose to confess rather than resist.
Cooperative equilibrium
The result of coordinated action by all parties in order to achieve a common payment optimization strategy. Generally speaking, if all the players in the game are able to perform the negotiated strategy, the strategy they choose constitutes cooperative equilibrium.