Jan 20, 2011 - s cover story (AIDS, Budget); Magazines are...

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Nash Equilibrium = (1, 1) and (0, 0) By this we mean that the best payoff for both players is in opposing strategies. In other words, both players will never choose the same strategy because they ʼ ll either be selFsh, or sel±ess but they won ʼ t know if their opponent will do the same. (5, 5) (0, 10) (10, 0) ( U , U ) Nash Equilibrium - Mutual best responses for all players in the game => (U 1 *, U 2 *, U 3 *, U 4 *, U 5 *) Battle of the Sexes W i f e ²ootball Opera ²ootball (1*, 3*) (0, 0) Husband Opera (0, 0) (3*, 1*) Schelling Point: “focal point equilibrium” i.e. Two friends want to meet at NYC. They set a time, but not a place. What will they do? Answer: In a survey, most people said they ʼ d meet at Grand Central Station. Animal Kingdom: Player 2 Concede ²ight - The U if bigger than 0, then the outcome is ( U , U ) Concede - If U is smaller than 0, however, then the outcome Player 1 is either (0, 10) or (10, 0) ²ight Best Response Functions: Back to the example with Time and Newsweek
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Unformatted text preview: s cover story (AIDS, Budget); Magazines are differentiated products, meaning they have loyalties. January 20, 2011 - Lecture 5 45 Nash Equilibrium NBR (Newsweek s Best Response unction) TBR (Time s Best Response unction) P T = 1/2 + (1/2 * P N ) P N = 1/2 + (1/2 * P T ) $ 1.00 $0.90 $1. 10 $1. 10 $ 1.00 $0.90 (+1, -1) (-1, +1) (-1, +1) (+1, -1) (-5*, -5*) (0, -25) (-25, 0) (-1, -1) Pare to Superior (here we see that even though it s in their best interest to Confess, both Bonnie and Clyde could ve gotten a higher payoff if they could somehow agree to Withhold. Matching Pennies Jane Heads Tails Heads- Here there is no Nash Equilibrium because there are John only two possible outcomes: (-1, +1) or (+1, -1) Tails (this could be considered a zero-sum game) Prisoners Dilemma Clyde Confess Withhold Confess Bonnie Withhold January 20, 2011 - Lecture 5...
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Jan 20, 2011 - s cover story (AIDS, Budget); Magazines are...

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