1. We'll consider a first-price auction with two players. Each player will submit a bid b; 2 0. Whoever places thehighest bid wins the auction and must pay the amount they bid, the loser does not pay anything. If there is atie, then Player 1 wins the auction.Payoffs are determined by who wins the auction. Suppose Player 1 values the item at vi = 20 and Player 2values the item at vz = 10. If Player i wins with a bid of b;, their payoff is their valuation minus their bidv; – bị. The player that loses the auction receives a payoff of 0.For example, if Player 1 bids bị = 1 and Player 2 bids by = 2, then Player l's payoff is 0 and Player 2's payoffis 8 = 10 – 2.(iv) Sketch separate graphs of u2(b1, b2) for the cases b1 = 5, 10, 20.(v) Explain why Player 2 does not have a best response to bị < 10 (assuming there is no smallest denominationof money). What is Player 2's best response to bị > 10?(vi) Explain why Player 2's bid b2 = 10 weakly dominates any higher bid b, > 10.

Answered: 1. We'll consider a first-price auction…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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2. Consider a simultaneous-move auction in which two players simultaneously choose bids which must be in nonnegative integer multiples of one cent. The higher bidder wins a dollar bill. If the bids are equal, neither player receives the dollar. Each player must pay his/her own bid whether or not he or she wins the dollar. Each player's payoff is simply the net winnings. Construct a symmetric mixed-strategy equilibrium in which every bid less than 1.00 has a positive probability.
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