Question

According to game theory, what should we expect in a situation where two individuals are interacting over a period of two weeks and both individuals know that they will never interact again once the two weeks are up? Assume the payoff matrix describing these interactions takes on the general form of a prisoner's dilemma payoff matrix.

		The individuals cooperate at first but as time goes on they will defect with increasing regularity
		The individuals will defect for the entire time
		Whether these individuals will cooperate depends whether they start out with cooperation or defection. If they begin with cooperation, then they will cooperate for the entire two weeks. If they begin with defection, then they will defect for the entire two weeks.
		The individuals will cooperate for the entire two weeks

Answer 1

Considering the prisoner's dilema between two prisoners A and B of the same gang,

A / B	B stays silent (Cooperates)	B betrays (Defects)
A stays silent (Cooperates)	(1) Both of them serve 1 year	(2) B will be set free, A serves 3 years
A betrays (Defects)	(3) A will be set free, B serves 3 years	(4) Each serves 2 years

Defection is always a dominant strategy because it results in a better payoff than co-operation, despite the other players' choice (consider options 2,3). A different interpretation of this case will be that each player has a choice between selfish behavior and altruistic behavior, the second one being socially desirable. If one individual defects or betrays, no matter what the other does, it will benefit the former. On the contrary, if one individual remains silent or cooperates,he/she benefits the other individual, no matter what the other does. Mutual defection is the only payoff that turns out to be worse for either player who have unilaterally changed the strategy (consider option 4). The dilemma, at this juncture, is that mutual cooperation yields a better payoff than mutual defection (see option 1). But the strategy to mutually cooperate from a self-interested perspective is irrational.

So again considering the nature of the game, the expected outcome is most likely option 1: The individuals will cooperate at first but as time goes on they will defect with increasing regularity.