Angry Madness Payoff Detail-Game Theory For Managers-Handout, Exercises for Game Theory. Amity Business School
muneb
muneb

Angry Madness Payoff Detail-Game Theory For Managers-Handout, Exercises for Game Theory. Amity Business School

2 pages
1000+Number of visits
Description
Content of Game Theory for Managers course includes ratiinality, prisoner dilemma, Loyal servant, assurance, credibility, stratigic subtitutes, entry, brinkmanship, negotiation, auctions, signaling, reputation etc. This ...
20 points
Download points needed to download
this document
Download the document
Preview2 pages / 2
Download the document
Urn Game

Angry Madness: Payoff Detail Your overall payoff will be determined by averaging your payoff in each of the 9 cases when you and your have M,U = 100, 200, or 400. Your expected payoff in each of these 9 cases is, in turn, calculated by checking every possible way that the game might end.

Bart’s expected payoff when M = $200 for Ann and U = $200 for Bart We add up all of the terms below, which correspond to all ways the game might end: First round, Bart yields 50% * $200 = 100 First round, Ann yields 0% * $300 First round, both yield 0% * $200 Anger after First round 50% * 10% * $0 (Note: Chances we go on to second round = P1 = 50% * 90%.) Second round, Bart yields P1 * 25% * $200 = 22.5 Second round, Ann yields P1 * 0% * $300 Second round, both yield P1 * 0% * $200 Anger after Second round P1 * 75% * 20% * $0 (Note: Chances we go on to third round = P2= 50% * 90% * 75% * 80%.) Third round, Bart yields P2 * 75% * $200 = 40.5 Third round, Ann yields P2 * 0% * $300 Third round, both yield P2 * 0% * $200 Anger after Third round P2 * 25% * 30% * $0 (Note: Chances we go to fourth round = P3 = 50% * 90% * 75% * 80% * 25% * 70%.) Third round, Bart yields P2 * 100% * $200 = 9.45 Third round, Ann yields P2 * 0% * $300 Third round, both yield P2 * 0% * $200 Anger after Third round P2 * 0% * 40% * $0 Bart’s Expected Payoff = 172.45 … Bart would have been better off yielding for sure in Round 1 (which gives guaranteed payoff 200)

docsity.com

Ann’s expected payoff when M = $200 for Ann and U = $200 for Bart We add up all of the terms below, which correspond to all ways the game might end: First round, Bart yields 50% * $300 = 150 First round, Ann yields 0% * $200 First round, both yield 0% * $200 Anger after First round 50% * 10% * $0 (Note: Chances we go on to second round = P1 = 50% * 90%.) Second round, Bart yields P1 * 25% * $300 = 33.75 Second round, Ann yields P1 * 0% * $200 Second round, both yield P1 * 0% * $200 Anger after Second round P1 * 75% * 20% * $0 (Note: Chances we go on to third round = P2= 50% * 90% * 75% * 80%.) Third round, Bart yields P2 * 75% * $300 = 60.75 Third round, Ann yields P2 * 0% * $200 Third round, both yield P2 * 0% * $200 Anger after Third round P2 * 25% * 30% * $0 (Note: Chances we go to fourth round = P3 = 50% * 90% * 75% * 80% * 25% * 70%.) Third round, Bart yields P2 * 100% * $300 = 14.175 Third round, Ann yields P2 * 0% * $200 Third round, both yield P2 * 0% * $200 Anger after Third round P2 * 0% * 40% * $0 Ann’s Expected Payoff = 258.675 … Ann is better off with her strategy than yielding for sure in Round 1 (which gives guaranteed payoff 200)

docsity.com

no comments were posted
Download the document