Final answer:
a. False; b. False; c. False
Step-by-step explanation:
The question pertains to a classic game theory scenario known as the Prisoner's Dilemma, specifically the incentives and strategies involved when two rational players must make a decision without knowing what the other will choose. In the context of the prisoners A and B, each prisoner can either 'confess' or 'not confess'.
If Prisoner A believes that B will confess, A has an incentive to confess to avoid the worse outcome of eight years in prison. Similarly, if A believes B will not confess, A is still incentivized to confess to possibly serve only one year in prison.
Confessing, therefore, becomes a dominant strategy for both prisoners, leading to an outcome where both prisoners may confess and collectively serve more time than if they had both remained silent.
Similarly, in the scenario of two firms knowing their payoffs in a game, they are likely to choose the dominant strategy that maximizes their individual payoff, even if it is not the best collective outcome.
In games involving cooperation, like the one where players are allowed to communicate, outcomes can deviate from those predicted by traditional game theory as players may coordinate to achieve mutually beneficial results.
In a spinner game with designated payoffs for landing on different colors, the expected value of a single game can be calculated to help players understand what they are likely to gain or lose on average over time by participating in the game.
Your complete question is: Consider the payoff matrix shown above, representing a simultaneous-move game between Player 1 (P 1) and Player 2 (P 2 ), where each player chooses between the strategies A and B. State whether the following statements are true or false. a. If this game is repeated for three periods (finitely repeated-with known end), there can be a subgame perfect equilibrium (SPE) where the (A,A) outcome is observed in the first and the second period, and (B,B) is observed in the third period. b. If this game is repeated for three periods (finitely repeated-with known end), both players choosing A in all three periods, that is observing the (A,A) outcome in all three periods, is a subgame perfect equilibrium (SPE). c. If this game is repeated for three periods (finitely repeated-with known end), both players choosing B in all three periods, that is observing the (B,B) outcome in all three periods, is a subgame perfect equilibrium (SPE).