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Two political candidates compete for the presidency, whose value is known to the Incumbent, but not to the Challenger. The Challenger only knows that is
Two political candidates compete for the presidency, whose value is known to the Incumbent, but not to the Challenger. The Challenger only knows that is either 1 or 2 with equal probability. The outcome of the election is independent of the value of the presidency, but it depends on the chosen campaign budgets bI and bC. The probability that the Incumbent wins the presidency is bI+bCbI. Interim expected utilities are, therefore, uI(b,)=bI+bCbIbI,uC(b,)=bI+bCbCbC. Suppose that a minimum budget of 101 is required to participate in the election. Find the pure-strategy Bayesian Nash equilibria of this game. Two political candidates compete for the presidency, whose value is known to the Incumbent, but not to the Challenger. The Challenger only knows that is either 1 or 2 with equal probability. The outcome of the election is independent of the value of the presidency, but it depends on the chosen campaign budgets bI and bC. The probability that the Incumbent wins the presidency is bI+bCbI. Interim expected utilities are, therefore, uI(b,)=bI+bCbIbI,uC(b,)=bI+bCbCbC. Suppose that a minimum budget of 101 is required to participate in the election. Find the pure-strategy Bayesian Nash equilibria of this game
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