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QUESTION 24. Consider the following two-player game. The players simultaneously
draw one sample each from a continuous random variable X,
which follows Uniform[0, 100]. After observing the value of her own sample,
which is private information (that is, opponent does not observe it), players
simultaneously and independently choose one of the following: SW AP,
RET AIN. If both the players choose SW AP then they exchange their initially
drawn numbers. Otherwise, if at least one person chooses RET AIN,
both of them retain their numbers. A player earns as many Rupees as the
number she is holding at the end of the game.
Find the probability that the players will exchange their initially drawn numbers
The answer is 0.
However, what if we consider the following possibility.
Individuals A and B draw very low numbers, but they dont know what the other person has drawn. Now, what they draw is so low that they think it is worthwhile to take a risk and take the bundle of the other. Would (Swap,Swap) not be an equilibrium?
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