Two numbers are selected uniformly at random from the interval (0,1) and shown to Alice. Alice must select one of these two numbers and show it to Bob. Bob must then guess if Alice has shown him the larger of the two or the smaller of the two. What is the optimal (equilibrium) strategy for the players?
This time Alice does not get control of the two numbers, and Bob is aware of the distribution, but Alice gets to choose what number Bob sees, so who gains the advantage from those changes?
2 comments:
Are we asking for a Nash equilibrium here or what?
I guess so. When I first read the problem it was just asking for the optimal strategy for both. Sean pointed out that optimal is funny since if one side is doing something dumb (eg. Alice always shows the larger number), then it is optimal to also do something dumb (eg Bob always guesses it is the larger number).
So I corrected the problem to look for the equilibrium strategy, but I don't really know if there are types of equilibria or what. Basically, my formal knowledge of game theory is lacking.
Anyway, look, find the optimal strategy (however you define that?).
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