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Player 2 can play tails expecting player 1 to play

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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 tails heads (−1, 1) (1, −1) tails (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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