Two buyers wish to buy a horse from a seller. Both buyers are willing to pay at most v > 0 for the horse. Each buyer must bid a real number bi > 0 at the same time. The horse attributed to the buyer who makes the higher bid. Note that however, both buyers must pay their bids (if the bids are equal, each buyer gets the horse with probability 0.5). (a) Formulate this situation as a strategic game (b) Show that this game does not have a pure strategy Nash equilibrium (c) Solve for a Nash equilibrium

Two buyers wish to buy a horse from a seller. Both buyers are willing to pay at most v > 0 for the horse. Each buyer must bid a real number bi > 0 at the same time. The horse attributed to the buyer who makes the higher bid. Note that however, both buyers must pay their bids (if the bids are equal, each buyer gets the horse with probability 0.5). (a) Formulate this situation as a strategic game (b) Show that this game does not have a pure strategy Nash equilibrium (c) Solve for a Nash equilibrium

Principles of Microeconomics

7th Edition

ISBN:9781305156050

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter22: Frontiers Of Microeconomics

Section: Chapter Questions

Problem 6PA

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Suppose that the University of Alabama and Clemson are making spending decisions for theupcoming year. Assume that Alabama is currently spending $15 million on their recruiting andfacilities, and Clemson is spending $10 million. Each team has an additional $5 million to spendor keep as profits. If they both choose to not spend the additional $5 million then Alabama hasa 60% chance of getting the highest quality quarterback recruit to commit to them (getting thecommitment of the player is the goal). However, if they both choose to spend the additional $5million then there is a 57% chance that Alabama gets the high quality quarterback to commit. IfAlabama spends the additional $5 million but Clemson doesn’t then there is a 67% chanceAlabama gets the recruit. However, if Alabama does NOT spend the additional $5million butClemson does then there is a 50% change either team gets the recruit’s commitment. Setup thepayoff matrix and label the players, their strategies, and their payoffs, and…
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