Determine player 1s optimal bidding function

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Reference no: EM131250064

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/)2 , and player 3 is using the bidding function b₃(₃) = (4/5)³ . 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 ₁ and her bid b₁ .

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

Reference no: EM131250064

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