Answer:
This is a simple example of a two-player game known as the Prisoner's Dilemma. The payoffs represent the benefits or costs of different strategies chosen by the players. The equilibrium of the game is the combination of strategies that neither player has an incentive to change given the strategy of the other player.
In this game, both players can choose to either "Cooperate" or "Cheat". The payoffs for each combination of choices are given in the matrix below:
Player 2: Cooperate Player 2: Cheat
Player 1: Cooperate (5,5) (12,2)
Player 1: Cheat (2,12) (9,9)
The dominant strategy for both players is to "Cheat". This means that, regardless of the choice of the other player, each player will do better by choosing "Cheat" rather than "Cooperate".
However, if both players choose "Cheat", they will get a lower payoff than if they both choose "Cooperate". Therefore, there is an incentive for both players to choose "Cooperate" instead of "Cheat". This is the paradox of the Prisoner's Dilemma: even though both players would be better off if they cooperated, the dominant strategy leads to a suboptimal outcome.
The Nash equilibrium of the game is the combination of strategies in which neither player has an incentive to change given the strategy of the other player. In this case, the Nash equilibrium is the combination of "Cheat" and "Cheat" because this is the dominant strategy for both players, and there is no other combination of strategies that both players would prefer. However, the "Cooperate" and "Cooperate" outcome would be a more desirable outcome for both players, but they cannot achieve it without cooperation.