# Angry Madness Payoff Detail-Game Theory For Managers-Handout, Exercises for Game Theory

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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 ...
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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)

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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)

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