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AMS 335/ECO 355 Game Theory
Fall 2010
Exercise of 1.3 Mixed Strategy Equilibrium
Zhen Xu
Page
1
of
3
Exercise 1.3.1
the Prisoners’ Dilemma
Table 1 shows Aumann version of the Prisoner's Dilemma, where the units of the
payoff are thousands of dollars. Find the maxmin strategies and the mixed strategy
Nash equilibrium if any.
Table 1 The Prisoner's Dilemma
Player 2
Cooperate
Defect
Player
1
Cooperate
3, 3
0, 4
Defect
4, 0
1, 1
We know from the practice in chapter 1.1 Normal Form Game that both players have
dominant strategy
Defect
and the game has a unique pure strategy Nash equilibrium
(
Defect
,
Defect
).
We can also discuss the game by assuming that the two players prepare for the worst,
that is, choose a
maxmin
strategy, which maximizes the player’s worst payoff against
all possible choices of the opponent. For the above game, the worst scenario for
Player 1 is that the opponent chooses
Defect
, thus Player 1 will also choose
Defect
in
order to better off the worst case. Since this is a symmetric game, Player 2 has the
same maxmin strategy choice –
Defect
.
Suppose Player 1 players
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 Fall '10
 Xu
 Game Theory

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