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Consider the following all-pay auction.
There is an object that is worth K to n bidders.   Each bidder i  submits a bid b(i).  The highest
bidder wins the object while every bidder, not just the winner, pays his bid.  ( In case of a tie,   a winner is chosen randomly among those who submit the hightest bid with equal probability.)   
  Bidder i`s payoff is K-b(i) if he wins, and -b(i) otherwise.
  Find a symmetric mixed strategy Nash equilibrium in which each bidder chooses his bid  following a cdf F with support [0 , K].

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关键词：博弈论 Probability equilibrium following otherwise 博弈论

in a mixed strategy nash equilibrium, every action within the support generates the same expected payoff, and then you can also calculate the winning probability given other players mixed strategy F
given these facts, you can solve for F(z) for any z in [0,K]