1. We'll consider a first-price auction with two players. Each player will submit a bid b; 2 0. Whoever places the highest bid wins the auction and must pay the amount they bid, the loser does not pay anything. If there is a tie, 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 2 values the item at vz = 10. If Player i wins with a bid of b;, their payoff is their valuation minus their bid v; – 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 payoff is 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 denomination of money). What is Player 2's best response to bị > 10?
1. We'll consider a first-price auction with two players. Each player will submit a bid b; 2 0. Whoever places the highest bid wins the auction and must pay the amount they bid, the loser does not pay anything. If there is a tie, 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 2 values the item at vz = 10. If Player i wins with a bid of b;, their payoff is their valuation minus their bid v; – 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 payoff is 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 denomination of money). What is Player 2's best response to bị > 10?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![1. We'll consider a first-price auction with two players. Each player will submit a bid b; 2 0. Whoever places the
highest bid wins the auction and must pay the amount they bid, the loser does not pay anything. If there is a
tie, 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 2
values the item at vz = 10. If Player i wins with a bid of b;, their payoff is their valuation minus their bid
v; – 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 payoff
is 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 denomination
of 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7038cbde-5259-4f1b-ade8-fa8f6320a6eb%2F84b98788-87da-464c-bb95-1ab6c1c81046%2Fxxciup_processed.png&w=3840&q=75)
Transcribed Image Text:1. We'll consider a first-price auction with two players. Each player will submit a bid b; 2 0. Whoever places the
highest bid wins the auction and must pay the amount they bid, the loser does not pay anything. If there is a
tie, 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 2
values the item at vz = 10. If Player i wins with a bid of b;, their payoff is their valuation minus their bid
v; – 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 payoff
is 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 denomination
of 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.
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