Question

A game is a strategic interaction between two players. Each player has their own sets of actions called the strategies. Each strategy comes with a definite outcome, these outcomes are tied to some profit or loss called the payoff. One of the favorite examples of game theory is the Prisoners' dilemma.

In this game, two partners of crime are caught by police and held in different cells being interrogated separately. Both have two options, either to confess or be silent. The payoff they receive is in terms of years in jail. For example, if they both confess they get 12 years in jail and thus the payoff is -12 for each for strategy (confess, confess).

The game table is completed as below

What are the Nash equilibria, if any?

Answer 1

In this game we can see that, when player 1 chooses to be silent, it is best for player 2 to confess, because by doing so player 2 will get 0 years of jail but if he also chooses to be silent, then he will get a 2 years jail. So, the strategy becomes (be silent, confess), where the first payoff is player 1's and the later one is player 2's.

When player 1 chooses to confess, then player 2's best response will be to confess as well as by doing so he will get a 12 years jail while by choosing to be silent he will get a 15 years jail. So the strategy becomes (confess, confess).

When player 2 chooses to be silent, then player 1 will confess as by doing so he will get 0 year of jail. So, here the strategy becomes (confess, be silent).

When player 2 chooses to confess, it is best for player 1 to to confess (as -12 > -15). So, the strategy becomes (confess, confess).

From these above strategies we can see that the Nash equilibrium strategy is (confess, confess) with payoff (-12, -12)