Unformatted text preview: ways of justifying
Nash equilibrium rely on this ﬂavor:
1 2 Introspection: what I do must be consistent with what you will do given your beliefs about me, which should be consistent with my beliefs about you,... Steady state of a learning or evolutionary process. An alternative justiﬁcation: Nash equilibrium is self-reinforcing
If player 1 is told about player 2’s strategy, in a Nash equilibrium she
would have no incentive to change her strategy. 26 Game Theory: Lecture 2 Nash Equilibrium Role of Conjectures
To illustrate the role of conjectures, let us revisit matching pennies
Player 1 \ Player 2 heads
(−1, 1) (1, −1)
(1, −1) (−1, 1)
Here, player 1 can play heads expecting player 2 to play tails. Player 2
can play tails expecting player 1 to play tails.
But these conjectures are not consistent with each other. 27 Game Theory: Lecture 2 Nash Equilibrium Intersection of Best Responses
Recall the best-response correspondence Bi (s−i ) of player i , Bi (s−i ) ∈ arg max ui (si , s−i ). si ∈Si Equivalent characterization: an action...
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- Spring '10
- Game Theory