Question B1 Consider a first-price auction between two bidders. Each bidder's private value for the auction is independe
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Question B1 Consider a first-price auction between two bidders. Each bidder's private value for the auction is independe
Question B1 Consider a first-price auction between two bidders. Each bidder's private value for the auction is independent and uniformly distributed over [0, 1]. a) Derive bidder one's probability of winning the auction. Fully explain all steps. [25 marks] b) How would your answer to part (a) change if there was three bidders? Fully explain your answer. [10 marks] c) Write down bidder one's expected payoff and derive her optimal bid as a function of her value. Fully explain all steps. Provide an intuitive interpretation of your answer. [25 marks) d) Graph bidder one's expected payoff from part (c) and identify the optimal bid on this graph (10 marks]