ECOS3012 Strategic Behaviour
Tutorial 6
Q1. Find the minmax value for player 1 in the following game
Player 2
L R
Player 1
U -2, 2 1, -2
M 1, -2 -2, 2
D 0, 1 0, 1
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Q2easy Let G be the stage game represented below:
Player 2
L M R
Player 1
u 2, 1 3, 1 6, 5
m 4, 2 6, 0 4, 1
d 6, 4 3, 3 3, 1
Consider three possible outcomes of the infinitely repeated game G(∞,δ ):
outcome 1: (m, L), (u, M), (m, L), (u, M), (m, L), (u, M), …
outcome 2: (u, M), (m, L), (u, M), (m, L), (u, M), (m, L), …
outcome 3: (d, R), (u, R), (d, R), (u, R), (d, R), (u, R), …
For each δ ∈ (0,1) find which outcome each player prefers.
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Q3. Alternative trigger strategies
Suppose that the following prisoners’ dilemma is repeated infinitely.
Prisoner 2
Confess Not Confess
Prisoner 1
Confess 1, 1 5, 0
Not Confess 0, 5 4, 4
Check whether each of the following strategies can constitute a subgame perfect Nash equi-
librium. If so, specify the range of discount factor δ for which the strategy is SPE. If not,
explain why.
1. s1: Play “Not Confess” in the first stage. Also play “Not Confess” if the opponent has
played “Not Confess” in every previous period. Otherwise, play “Confess”. (This is
like the trigger strategy, but the punishment is not triggered by own deviation.)
2. s2 : Play “Not Confess” in the first stage. Also play “Not Confess” if both players
chose “Not Confess” in every previous period except for the last period. Choose
“Confess” otherwise. (This is like the trigger strategy, but the punishment is delayed
by one period.)
3. s3 : Play “Not Confess” in the first stage. Also play “Not Confess” if the opponent
chose “Confess” in at most one period. Choose “Confess” otherwise. (This is like s1
, but one mistake is forgiven.)
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