Economic and Game Theory
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Each of two players receives a ticket on which there is a number in the interval [0,1]. The number is the size of the prize that the player might win. The two prizes are identically and independently drawn from the uniform distribution. Each player, independently and simultaneously decides whether or not they wish to exchange their prizes. If they both agree then the prizes are exchanged. After having the opportunity to switch prizes, the size of all prizes is revealed to everyone and players are paid. Players attempt to maximize their expected prize.
Show that, in Bayesian equilibrium, the highest value prize that players are prepared to exchange is the lowest possible prize.
Why would the players only want to exchange 0 and not anything less than 1/2? Again, I don't want a solution, just some hints.
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