Question

Let α1, α2 ∈ R. Consider the following version of
prisoners’ dilemma (C

means “Confess” and N means “Do not confess”):

2

C N

1

C 0, 0 α1, −2

N −2, α2 5, 5

Suppose that the two players play the above stage game infinitely
many times. Departing

from our in-class discussion, however, we assume that for each i ∈
{1, 2}, player i discounts

future payoffs at rate δi ∈ (0, 1), allowing δ1 and δ2 to
differ.

(a) (10 points) The stage game above would be a proper prisoners’
dilemma only if

C is a strictly dominant strategy for each player. Find the
conditions on α1 and α2 under

which this is true.

(b) (30 points) Assume, from now on, that the conditions identified
in part (a) are

satisfied. Using grim trigger strategies, show that under
appropriate assumptions on δ1

and δ2, it is possible to obtain a repeated play of (N, N) as the
outcome of a subgame

perfect equilibrium

Answer #1

on and Vlad are two players in an indefinitely repeated
Prisoners Dilemma Game. Let the
probability that the game continues one more round be “q”.
Assume both players are risk neutral
and have a common per-period discount rate of “d”.
1. From this information alone, what must be true about the
range of possible values for d and q?
2. Is mutual defection a Nash Equilibrium (NE)? If so, under
what conditions is mutual
defection a NE? (HINT: Consider Don’s...

Consider the following market entry game. There are two firms :
firm 1 is an incumbent monopolist on a given market. Firm 2 wishes
to enter the market. In the first stage, firm 2 decides whether or
not to enter the market. If firm 2 stays out of the market, firm 1
enjoys a monopoly profit of 2 and firm 2 earns 0 profit. If firm 2
decides to enter the market, then firm 1 has two strtegies : either...

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