Strategy6Handout - 9/18/2008 MAXIMIN MINIMAX 9 soldiers,...

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9/18/2008 1 MAXIMIN MINIMAX ± 9 soldiers, three are 5 feet tall, three are 6 feet tall, three are 7 feet tall 567 Min = 5 ± MAXIMIN = 5 < 7 = MINIMAX 7 5 6 675 Min = 5 Min = 5 Max = 7 Max = 7 Max = 7 A Note About Equilibria ± Some games – ± Get feel for what an equilibrium might be ± Show that if everyone does it, nobody has an incentive to change ± Show everything else isn’t equilibrium: for each other possible strategy profile, somebody has an incentive to change ± Others games – when you’re clueless ± Calculate best responses ± Equilibria occur where best responses cross Continuous Strategy Sets ± Our examples have involved discrete action sets with a small number of possible actions ± Even chess and go are discrete ± We now consider strategy sets that are We now consider strategy sets that are continuous: ± Why? ± So we can use CALCULUS ± Players 1 & 2 take actions 0 3 e π Finding Nash Equilibria ± In general, NE occur where “best response curves” cross Finding Nash Equilibria
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Strategy6Handout - 9/18/2008 MAXIMIN MINIMAX 9 soldiers,...

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