Problem description
The prisoner’s dilemma is a classic problem in game theory, in which two prisoners have a secret theft, and each prisoner can choose to deny it or confess it during the interrogation. A situation is a situation in which two prisoners give their own strategy, and then in terms of permutations and combinations of situations
- Resist, resist
- Confess, resist
- Resist, confess
- Frank, frank
If they both resist and they don’t confess they each get one year, if they both confess they each get three years, if one confesses and the other one resists, the one who confesses gets five years and the one who confesses gets released.
Player:
Two prisoners
strategy
Resistance or confession
Utility function matrix
| resist | frank | |
|---|---|---|
| resist | 1, 1 | 5, 0 – |
| frank | 0,-5 | -3,-3 |
Everyone will choose the maximization strategy to maximize their own benefits, so the maximization strategy for prisoners is to serve the shortest time. For this purpose, what is the rational strategy?
When making A strategy for prisoner (A), the strategic choice of another prisoner (B) should also be taken into account. Then prisoner B’s choice has two possibilities: resistance or confession, which is called prisoner B. If prisoner B confesses, prisoner A will serve 3 years in prison if he confesses, and 5 years if he refuses. So A’s best option is to plead guilty.
Assume that prisoner A chooses the resistance situation and prisoner B chooses to confess, and the payoff is 0. When prisoner A chooses to confess, prisoner B will also choose to confess and gain to maximize the payoff.
For prisoner A, no matter what strategy prisoner B makes, confession is the dominant strategy of prisoner A. Neither prisoner can increase his benefit by unilaterally changing his strategy, so neither has an incentive to deviate from the strategy mix.
Dominant strategy
When one Strategy is always more effective than all others, we call it a Dominant Strategy.
Dominant strategy Nash equilibrium
The Nash equilibrium achieved when the optimal response of all participants is to choose their dominant strategy is called the dominant strategy Nash equilibrium.