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Optimal bidding function

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Reference no: EM13833880

Problem: Consider a first-price auction with three bidders, whose valuations are independently drawn from a uniform distribution on the interval (0, 30). Thus, for each player i and any fixed number y ∈ (0, 30), y/30 is the probability that player i's valuation vi is below y.

a. Suppose that player 2 is using the bidding function b2(v2) = (3/4)v2, and player 3 is using the bidding function b3(v3) = (4/5)v3. Determine player 1's optimal bidding function in response. Start by writing player 1's expected payoff as a function of player 1's valuation v1 and her bid b1.

b. Disregard the assumption made in part (a). Calculate the Bayesian Nash equilibrium of this auction game and report the equilibrium bidding functions.

Reference no: EM13833880

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