7 1) Players 1 and 2 must each decide whether or not to carry an umbrella when leaving home. The nature decideswhether it will be sunny or rainy with 50-50 chance. Each player's payoff is -5 if (s)he does not carry an umbrellaand it rains, -2 if (s)he carries an umbrella and it rains, -1 if (s)he carries an umbrella and it is sunny, and 1 if (s)hedoes not carry an umbrella and it is sunny. Player 1 accurately learns about the weather (from the TV) beforeleaving home; player 2 does not, but (s)he can observe player 1l's action before choosing own action.(a) Sketch the extensive form of this game.(b) Show that this game can be solved by elimination of strictly dominated strategies.

In Game theory , the extensive form is away of describing a game using a game tree. It’s simply a…

1) Players 1 and 2 must each decide whether or not to carry an umbrella when leaving home. The natu whether it will be sunny or rainy with 50-50 chance. Each player's payoff is –5 if (s)he does not carry a and it rains, –2 if (s)he carries an umbrella and it rains, -1 if (s)he carries an umbrella and it is sunny, an does not carry an umbrella and it is sunny. Player 1 accurately learns about the weather (from the leaving home; player 2 does not, but (s)he can observe player 1's action before choosing own action. (a) Sketch the extensive form of this game. (b) Show that this game can be solved by elimination of strictly dominated strategies.

1) Players 1 and 2 must each decide whether or not to carry an umbrella when leaving home. The natu whether it will be sunny or rainy with 50-50 chance. Each player's payoff is –5 if (s)he does not carry a and it rains, –2 if (s)he carries an umbrella and it rains, -1 if (s)he carries an umbrella and it is sunny, an does not carry an umbrella and it is sunny. Player 1 accurately learns about the weather (from the leaving home; player 2 does not, but (s)he can observe player 1's action before choosing own action. (a) Sketch the extensive form of this game. (b) Show that this game can be solved by elimination of strictly dominated strategies.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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6. Players 1 and 2 are leaving the house and need to decide whether or not to bring an umbrella. They know there's a 75% chance that it will rain (thanks AccuWeather). If they don't bring an umbrella and it rains they receive a payoff of -7. If they do bring an umbrella and it rains, they receive a payoff of -4. If it doesn't rain, but they bring an umbrella they receive a payoff of -2. Finally, if it doesn't rain and they don't bring an umbrella they receive a payoff of 2. Player 1 learns the weather before they leave the house, but player 2 does not. Player 2 can, however, observe player 1s choice. (a) Represent this game in the extensive form. i. Use backwards induction to solve for the Nash equilibrium (b) Represent this game in the normal form i. Solve for the Nash equilibrium (c) Are the equilibrium strategy profiles the same in a) and b)? Explain why or why not.
Player 2 C D A Player 1 2,3 В 6, —2 | 4, 3 7,8 Select the value corresponding to the probability with which player 2 plays C in the mixed strategy Nash equilibrium: O 1/8 O 1/6 1/5 O 1/4 1/3 1/2 2/3 O 3/4 4/5 O 5/6
Question 5 ave Answer Player 1 has two options: L and R. If Player 1 chooses L, then Player 2 has two options; she can choose A or B. If Player 2 chooses A payoffs are (2; 1) and if she chooses B payoffs are (1; 2). If Player 1 chooses R, then Player 2 has two options; she can choose Y or N. If Player 2 shows Y payoffs are (0; 3) and if she chooses N payoffs are (1; 2). Which of the following statements is true? O A. (L; B,Y ) is a subgame perfect equilibrium of this game O B. (R; B,N ) is a subgame perfect equilibrium of this game O C.(L; A,Y) is a subgame perfect equilibrium of this game O D. (R; B,Y ) is a subgame perfect equilibrium of this game
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a W 3,5 3,4 8,4 0,0 3,3 8,9 y 0,1 5,9 9,8 Describe a strategy for player 1 that dominates x. O (1/3.0. 2/3) 1.0,0) O01.1) to
Two politicians from the same party decide whether to support or oppose the gov- ernment's environmental policy. Politician A prefers that they both support, but Politician B prefers that they both oppose. Both politicians agree that the party should have a coherent position and the worst outcome is that one supports and the other opposes the policy. (a) Formulate this situation as a strategic game - specify the players, actions, and payoffs (you can set-up a table of the actions and payoffs). (b) What are the Nash equilibria of this game? Explain your answer.
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