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the king of Fireland wishes to sell 10 gallon water. Two rich men join the game, and they are
assumed to be identical (homogenous) players (they are the same in all aspects) and risk-neutral
(each man’s utility is simply his net winnings). The king says that
(1) it is a one-shot game;
(2) these two men simultaneously bid with water;
(3) these two men can only bid with an nonnegative integral multiples of 1 gallon water (which
mean the choice set of each man is {0,1, 2, …, 10,…} (gallon));
(4) the man with the higher bid wins 10 gallon water and pays with his bid;
(5) the loser also pays with his bid;
(6) if two men bid the same, no one wins 10 gallon and they still have to pay with their bid.
(Whether wins or loses, a man has to pay what he bids. )
Question: construct a symmetric mixed-strategy Nash equilibrium, in which each bidder has a
positive probability to bid for every less-than-10-gallon bid.

试了几次都不好做出展示图，求大神解答。

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