? E XERCISE 280.3 (An exchange game) Each of two individuals receives a ticket on which there is…

? EXERCISE 280.3 (An exchange game) Each of two individuals receives a ticket on which there is an integer from 1 to m indicating the size of a prize she may receive. The individuals’ tickets are assigned randomly and independently; the probabil- ity of an individual’s receiving each possible number is positive. Each individ- ual is given the option to exchange her prize for the other individual’s prize; the individuals are given this option simultaneously. If both individuals wish to ex- change then the prizes are exchanged; otherwise each individual receives her own prize. Each individual’s objective is to maximize her expected monetary payoff. Model this situation as a Bayesian game and show that in any Nash equilibrium the highest prize that either individual is willing to exchange is the smallest possible prize.

 

 

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