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econ100_winter2010_lecture19_topost

econ100_winter2010_lecture19_topost - Consider the game...

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Consider the game below… 5,5 10,10 10,10 5,5 Player 1 Player 2 S1 S2 S1 S2
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Consider each player’s best strategy in turn: Player 1: If player 2 chooses S1, best strategy is to choose S2 If player 2 chooses S2, best strategy is to choose S1 (NO Dominant Strategy for player 1)
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Player 2: If player 1 chooses S1, best strategy is to choose S2 If player 1 chooses S2, best strategy is to choose S1 The combinations of strategies (by player1, player2) (S1,S2) and (S2,S1) are said to be Nash Equilibria NE means that each player is choosing best response, given what the other player is doing
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Nash Eqilibrium A pair of strategies (Si,Sj) is a Nash Equilbrium if: 1. Si is player 1’s best response, assuming that player 2 chooses Sj AND 2. Sj is player 2’s best response, assuming that player 1 chooses Si
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What is a Nash Equilbrium in this game? 5,5 10,10 4,6 5,5 Player 1 Player 2 S1 S2 S1 S2
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First, consider (S1,S1). S1 is the best player 1 can do, IF player 2 chooses S1 BUT S1 is NOT the best player 2 can do if player 1 chooses S1, so (S1,S1) is NOT a NE Next, consider (S1,S2). S1 is the best player 1 can do, IF player 2 chooses S2 AND S2 is the best player 2 can do, IF player 1 chooses S1, so (S1,S2) is a NE
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Can show that other combinations of strategies (S2,S1), (S2,S2) are NOT NE in above game Why is NE thought of as an equilibrium/likely outcome, or solution of the game?
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