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Chapter-5

Chapter-5 - Chapter 5 n-Player Games Players have the same...

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Chapter 5: n-Player Games Players have the same strategy sets. First cover symmetric games (identical payoff functions), then cover asymmetric games. The force of tipping : the tendency of a player to be increasingly attached to a strategy when more players choose it. The force of congestion : The more people use a strategy, the less attractive it is. Players have the same strategy sets. First cover symmetric games (identical payoff functions), then cover asymmetric games. The force of tipping : the tendency of a player to be increasingly attached to a strategy when more players choose it. The force of congestion : The more people use a strategy, the less attractive it is.

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A game is symmetric when: 1) all players have the same strategy sets; 2) players receive the same payoff when they choose the same strategy; 3) if you switch two players' strategies, then their payoffs switch as well. In a symmetric game, if a strategy profile is a Nash equilibrium then so is a strategy profile that has players swap strategies. A game is symmetric when: 1) all players have the same strategy sets; 2) players receive the same payoff when they choose the same strategy; 3) if you switch two players' strategies, then their payoffs switch as well. In a symmetric game, if a strategy profile is a Nash equilibrium then so is a strategy profile that has players swap strategies. Symmetric Games
The Sneetches There are n sneetches; n is odd. With the arrival of McBean’s Star-Off and Star-On machines, each sneetch decides what to do with his belly: with a star or without a star. Whatever is rarer is prized. Let m be the number of sneetches having star bellies. - If m < n/2, those have stars get payoff 1 and blank bellies get 0. - If m > n/2, those have no stars get payoff 1 and star bellies get 0. There are n sneetches; n is odd. With the arrival of McBean’s Star-Off and Star-On machines, each sneetch decides what to do with his belly: with a star or without a star. Whatever is rarer is prized. Let m be the number of sneetches having star bellies. - If m < n/2, those have stars get payoff 1 and blank bellies get 0. - If m > n/2, those have no stars get payoff 1 and star bellies get 0.

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The Sneetches 2 2 2 2 Payoff to a Sneetch What's on the sneetch's belly? Total number of sneetches with stars ( ) Payoff Star 1 Star 0 Nothing 0 Nothing 1 n n n n m m m m m < < < < Table 5.1 “Then they yelled at the ones who had stars at the start, ’We're exactly like you! You can't tell us apart. We're all just the same, now, you snooty old smarties! And now we can go to your frankfurter parties.’” “Then they yelled at the ones who had stars at the start, ’We're exactly like you! You can't tell us apart. We're all just the same, now, you snooty old smarties!
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Chapter-5 - Chapter 5 n-Player Games Players have the same...

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