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Page 24
player l's payoff is at most her equilibrium payoff. In a game that is not strictly competitive a player's equilibrium
strategy does not in general have these properties (consider, for example, BoS (Figure 16.1)).
• Exercise 24.1
Let
G
be a strictly competitive game that has a Nash equilibrium.
a
. Show that if some of player 1's payoffs in
G
are increased in such a way that the resulting game
G'
is strictly
competitive then
G' has
no equilibrium in which player 1 is worse off than she was in an equilibrium of
G
. (Note
that
G
' may have no equilibrium at all.)
b
. Show that the game that results if player 1 is prohibited from using one of her actions in
G
does not have an
equilibrium in which player l's payoff is higher than it is in an equilibrium of
G
.
c
.Give examples to show that neither of the above properties necessarily holds for a game that is not strictly
competitive.
2.6 Bayesian Games: Strategic Games with Imperfect Information
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This note was uploaded on 09/10/2011 for the course DEFR 090234589 taught by Professor Vinh during the Spring '10 term at Aarhus Universitet, Aarhus.
 Spring '10
 VINH

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