國外博弈論課件lecture(13)(已改無錯字)
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【正文】 y 20, 2021 73347 Game TheoryLecture 2 15 Example: Tourists amp。 Natives Bar 2 $2 $4 $5 Bar 1 $2 10 , 10 14 , 12 14 , 15 $4 12 , 14 20 , 20 28 , 15 $5 15 , 14 15 , 28 25 , 25 Payoffs are in thousands of dollars Bar 2 $4 $5 Bar 1 $4 20 , 20 28 , 15 $5 15 , 28 25 , 25 May 20, 2021 73347 Game TheoryLecture 2 16 One More Example ? Each of n players selects a number between 0 and 100 simultaneously. Let xi denote the number selected by player i. ? Let y denote the average of these numbers ? Player i’s payoff = xi – 3y/5 May 20, 2021 73347 Game TheoryLecture 2 17 One More Example ? The normalform representation: ? Players: {player 1, player 2, ..., player n} ? Strategies: Si =[0, 100], for i = 1, 2, ..., n. ? Payoff functions: ui(x1, x2, ..., xn) = xi – 3y/5 ? Is there any dominated strategy? ? What numbers should be selected? May 20, 2021 73347 Game TheoryLecture 2 18 New solution concept: Nash equilibrium Player 2 L C R Player 1 T 0 , 4 4 , 0 5 , 3 M 4 , 0 0 , 4 5 , 3 B 3 , 5 3 , 5 6 , 6 The bination of strategies (B, R) has the following property: ?Player 1 CANNOT do better by choosing a strategy different from B, given that player 2 chooses R. ?Player 2 CANNOT do better by choosing a strategy different from R, given that player 1 chooses B. May 20, 2021 73347 Game TheoryLecture 2 19 New solution concept: Nash equilibrium Player 2 L’ C’ R’ Player 1 T’ 0 , 4 4 , 0 3 , 3 M’ 4 , 0 0 , 4 3 , 3 B’ 3 , 3 3 , 3 , The bination of strategies (B’, R’) has the following property: ?Player 1 CANNOT do better by choosing a strategy different from B’, given that player 2 chooses R’. ?Player 2 CANNOT do better by choosing a strategy different from R’, given that player 1 chooses B’. May 20, 2021 73347 Game TheoryLecture 2 20 Nash Equilibrium: idea ? Nash equilibrium
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