Exam 13: Game Theory

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The "Normal-Form" of a game is a description including

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D

Game theory shows that

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D

The result that different auction styles in which the good goes to the winner with the highest valuation of the good generate the same amount of revenue is called

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A

Why is collusion more likely in a repeated game?

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After analyzing his opponent a tennis player decides to serve 10% of his serves to the left,50% of his serves to the right,and 40% of his serves at the body of his opponent.This illustrates a

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If a player has a dominant strategy in a simultaneous-move game,then she is sure to get her best outcome.

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Consider the game below: Consider the game below:    a.Use backward induction to find the subgame perfect Nash equilibrium to the game. b.Model the game with a strategic grid.Find all Nash Equilibrium to the normal-form game.Why is your answer different than in (a)? a.Use backward induction to find the subgame perfect Nash equilibrium to the game. b.Model the game with a strategic grid.Find all Nash Equilibrium to the normal-form game.Why is your answer different than in (a)?

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  -The above figure shows a payoff matrix for two firms,A and B,that must choose between a high-price strategy and a low-price strategy.For firm B, -The above figure shows a payoff matrix for two firms,A and B,that must choose between a high-price strategy and a low-price strategy.For firm B,

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  -The above figure shows the payoff matrix for two firms,A and B,choosing to produce a basic computer or an advanced computer.Now the payoff of the firm who produces a basic computer falls to 10 if the other firm chooses to produce an advanced computer.Then the joint profits -The above figure shows the payoff matrix for two firms,A and B,choosing to produce a basic computer or an advanced computer.Now the payoff of the firm who produces a basic computer falls to 10 if the other firm chooses to produce an advanced computer.Then the joint profits

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Consider two agents simultaneously deciding whether to contribute to a public good - the good is said to be public because,if it is made available,an agent who free-rides by paying nothing gets just as much pleasure from its enjoyment as an agent who paid for it.If at least one agent contributes to the construction of the public good,both agents will enjoy a payoff of four from the public good.To ensure the public good is constructed,player one must pay c1 or player two must pay c2.Assume that c1 < 4 and c2 < 4.If neither contributes,the good is not constructed and neither player gets enjoyment from the project.If one or both players contribute,then the good is constructed and each player enjoys a payoff of four minus the contribution cost if that player has contributed.The grid below shows this: Consider two agents simultaneously deciding whether to contribute to a public good - the good is said to be public because,if it is made available,an agent who free-rides by paying nothing gets just as much pleasure from its enjoyment as an agent who paid for it.If at least one agent contributes to the construction of the public good,both agents will enjoy a payoff of four from the public good.To ensure the public good is constructed,player one must pay c<sub>1</sub> or player two must pay c<sub>2</sub>.Assume that c<sub>1</sub> < 4 and c<sub>2</sub> < 4.If neither contributes,the good is not constructed and neither player gets enjoyment from the project.If one or both players contribute,then the good is constructed and each player enjoys a payoff of four minus the contribution cost if that player has contributed.The grid below shows this:     Assume that the costs are common knowledge to both players. a.Find any pure-strategy Nash Equilibrium(s)to the game. b.Find the Mixed Strategy Nash Equilibrium - the probabilities you find will be functions of the cost parameters. c.If c<sub>1</sub> = c<sub>2</sub> = 1,write out the mixed strategy NE and find the probability that the public good is provided? d.If c<sub>1</sub> = c<sub>2</sub> = 3,write out the mixed strategy NE and find the probability that the public good is provided? Assume that the costs are common knowledge to both players. a.Find any pure-strategy Nash Equilibrium(s)to the game. b.Find the Mixed Strategy Nash Equilibrium - the probabilities you find will be functions of the cost parameters. c.If c1 = c2 = 1,write out the mixed strategy NE and find the probability that the public good is provided? d.If c1 = c2 = 3,write out the mixed strategy NE and find the probability that the public good is provided?

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Explain why it is unwise to bid more than your valuation of the good in a sealed bid second-price auction.

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  -The above figure shows the payoff matrix facing an incumbent firm and a potential entrant.Assuming a fixed cost of entry,the incumbent will deter entry because -The above figure shows the payoff matrix facing an incumbent firm and a potential entrant.Assuming a fixed cost of entry,the incumbent will deter entry because

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  -The above figure shows the payoff matrix for two firms,A and B,selecting an advertising budget.The firms must choose between a high advertising budget and a low advertising budget.Firm A's dominant strategy -The above figure shows the payoff matrix for two firms,A and B,selecting an advertising budget.The firms must choose between a high advertising budget and a low advertising budget.Firm A's dominant strategy

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How can a firm be made better off by limiting its options?

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  -The above figure shows the payoff matrix for two firms,A and B,choosing to produce a basic computer or an advanced computer.How many pure-strategy Nash equilibria are in this game? -The above figure shows the payoff matrix for two firms,A and B,choosing to produce a basic computer or an advanced computer.How many pure-strategy Nash equilibria are in this game?

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  -The above figure shows the payoff for two firms,A and B,that must each choose to produce either an advanced computer or a basic computer.Determine the dominant strategies for each firm (if any)and the Nash equilibria (if any). -The above figure shows the payoff for two firms,A and B,that must each choose to produce either an advanced computer or a basic computer.Determine the dominant strategies for each firm (if any)and the Nash equilibria (if any).

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  -The above figure shows a payoff matrix for two firms,A and B,that must choose between a high-price strategy and a low-price strategy.For firm A, -The above figure shows a payoff matrix for two firms,A and B,that must choose between a high-price strategy and a low-price strategy.For firm A,

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Chess is an example of a

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All normal-form games have at least one dominant strategy.

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  -The above figure shows the payoff matrix facing an incumbent firm and a potential entrant.Assuming a fixed cost of entry,the outcome will be that the incumbent -The above figure shows the payoff matrix facing an incumbent firm and a potential entrant.Assuming a fixed cost of entry,the outcome will be that the incumbent

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