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Nash equilibrium

# Nash equilibrium - Nash equilibrium and Best Response...

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Nash equilibrium and Best Response Functions

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Best response functions and Nash Equilibrium The best response function for any player i , is a function that maps the list of actions by other players into the list of actions that are best responses to what the others did. Sometimes there is only one best response. A Nash equilibrium is a list of actions by the players such that each player’s action is a best response to the actions of the other players.
Using Best response functions to find Nash equilibria With two-person games in which there is a discrete number of strategies, there is a handy way to use the payoff tables. The method of stars.

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Example: The Stag Hunt 2 , 2 0 , 1 1 , 0 1 , 1 Stag Sta g Hare Hare Player 1 Player 2 B1(Stag)= {Stag} B1(Hare)={Hare} B2(Stag)={Stag} B2(Hare)={Hare}
Example: The Stag Hunt 2 , 2 0 , 1 1 , 0 1 , 1 Stag Sta g Hare Hare Player 1 Player 2 B1(Stag)= {Stag} B1(Hare)={Hare} B2(Stag)={Stag} B2(Hare)={Hare}

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B1(Stag)= {Stag} 2 *, 2 0 , 1 1 , 0 1 , 1 Stag Sta g Hare Hare Player 1 Player 2 Put a star next to the payoff (s) to Player 1 from making a best response to each of Player 2’s actions .
B1(Hare)= {Hare} 2 *, 2 0 , 1 1 , 0 1* , 1 Stag Sta g Hare Hare Player 1 Player 2

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Nash equilibrium - Nash equilibrium and Best Response...

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