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Peter, Andrew, and James are playing the following game in which the winner is awarded M dollars. Each of the three players receives a coupon and is to decide whether or not to bet on it. If a player chooses to bet, he or she loses the coupon with probability 1/2 and wins an additional coupon with probability 1/2 (thus resulting in two coupons in total). The success of each player in the bet is independent of the results of the bets of the other players. The winner of the prize is the player with the greatest number of coupons.
If there is more than one such player, the winner is selected from among them in a lottery where each has an equal chance of winning. The goal of each player is to maximize the probability of winning the award.
(a) Describe this game as a game in strategic form and find all its Nash equilibria.
(b) Now assume that the wins and losses of the players are perfectly correlated: a single coin flip determines whether all the players who decided to bid either all win an additional coupon or all lose their coupons. Describe this new situation as a game in strategic form and find all its Nash equilibria.
Is it ever a best response for player 1 to choose q1 = 25? - Suppose that player 1 has the belief that player 2 is equally likely to select each of the quantities 6, 11, and 13. - What is player 1's best response?
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Identify which player can benefit from making a strategic move, identify the natu re of the strategic move appropriate for this purpose.
Next suppose that the game being played is the battle of the sexes. In the long run, as the game is played over and over, does play always settle down to a Nash equilibrium? Explain.
You have observed the following returns over time. Suppose that the risk free rate is 6 percent and the market risk premium is 5 percent.
Write down the matrix with payoffs for both players - what is the Nash equilibrium in pure strategies - What is the probability that this person is from ethnicity γ? Provide your answer in fractions and not in decimal places. Failure to do so will ..
Designate the (pure-strategy) Nash equilibria of this game (if it has any). - Compute the mixed-strategy Nash equilibrium of the game.
Assuming the life length of batteries is normally distributed, what is the p-value associated with this test? Place your answer, rounded to 3 decimal places in the blank. For example, 0.0234 would be a legitimate entry.
At most three typographical errors are found on a page, and (c) more than three typographical errors are found on a page.
Discuss the interpretation of the core of this game, taking into account that the definition of v(S) makes assumptions about the behavior of the players outside S.
Four bidders 1, 2, 3, and 4 bid for three items I1, I2, and I3 using VCG auction. We use wjk to denote bidder j's value for item k. What is the payment for each winning bidder
What is the relation between the matrices A and B?- Conduct a similar transformation of the names of the players in the following matrix and write down the new matrix.
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