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Suppose that the preferences of two players satisfy the von Neumann-Morgenstern axioms. Player I is indifferent between receiving $600 with certainty and participating in a lottery in which he receives $300 with probability 1 4 and $1,500 with probability 3 4 . He is also indifferent between receiving $800 with certainty and participating in a lottery in which he receives $600 with probability 1/2 and $1,500 with probability 1/2. Player II is indifferent between losing $600 with certainty and participating in a lottery in which he loses $300 with probability 1/7 and $800 with probability 6/7. He is also indifferent between losing $800 with certainty and participating in a lottery in which he loses $300 with probability 1/8 and $1,500 with probability 7/8. The players play the game whose payoff matrix is as follows, where the payoffs are dollars thatPlayer II pays to Player I.
(a) Find linear utility functions for the two players representing the preference relations of the players over the possible outcomes.
The players play a game whose outcomes, in dollars paid by Player II to Player I, are given by the following matrix.
(b) Determine whether the game is zero sum.
(c) If you answered yes to the last question, find optimal strategies for each of the players. If not, find an equilibrium.
Let T = 1. What is the critical value δ1 to support the pair of actions (M,m) played in every period? - Let T = 2. What is the critical value δT to support the pair of actions (M,m) played in every period?
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Does this game have a subgame perfect Nash equilibrium? - Do you think any one of the players has a strategy that guarantees him a win (a payoff of 2)?
Is it possible for him to be indifferent between the sure payment and the lottery? What is the general lesson to learn from this exercise - Is this preference relation rational in the sense defined by the preference theory?
How many twbgames are then: in this game (excluding the game itself)? b. Write down the strategies of the two players. c. Find all pure strategy subgame perfect Nash equilania.
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Econ 521 - Week 2. What is the effect of a technological change that increases firm's unit cost c on the production level? Solve the game using iterated removal of strictly dominated strategies
Is it still true that each player bidding his valuation is a weakly dominant strategy? - Are there other Nash equilibria of this game?
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