More Detail on How Payoffs are Computed | Massachusetts Institute of Technology - Edubirdie

University:
Massachusetts Institute of Technology
Course:
15.992 | S-Lab: Laboratory for Sustainable Business
Academic year:

2023
Views:

263

Pages:

2
Author:

Samantha Reese

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 First round, Ann yields First round, both yield Anger after First round 50% * $200 0% * $300 0% * $200 50% * 10% * $0 = 100 (Note: Chances we go on to second round = P1 = 50% * 90%.) Second round, Bart yields Second round, Ann yields Second round, both yield Anger after Second round P1 * 25% * $200 P1 * 0% * $300 P1 * 0% * $200 P1 * 75% * 20% * $0 = 22.5 (Note: Chances we go on to third round = P2= 50% * 90% * 75% * 80%.) Third round, Bart yields Third round, Ann yields Third round, both yield Anger after Third round P2 * 75% * $200 P2 * 0% * $300 P2 * 0% * $200 P2 * 25% * 30% * $0 = 40.5 (Note: Chances we go to fourth round = P3 = 50% * 90% * 75% * 80% * 25% * 70%.) Third round, Bart yields Third round, Ann yields Third round, both yield Anger after Third round P2 * 100% * $200 P2 * 0% * $300 P2 * 0% * $200 P2 * 0% * 40% * $0 = 9.45 Bart’s Expected Payoff = 172.45 … Bart would have been better off yielding for sure in Round 1 (which gives guaranteed payoff 200) 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 First round, Ann yields First round, both yield Anger after First round 50% * $300 0% * $200 0% * $200 50% * 10% * $0 = 150 (Note: Chances we go on to second round = P1 = 50% * 90%.) Second round, Bart yields Second round, Ann yields Second round, both yield Anger after Second round P1 * 25% * $300 P1 * 0% * $200 P1 * 0% * $200 P1 * 75% * 20% * $0 = 33.75 (Note: Chances we go on to third round = P2= 50% * 90% * 75% * 80%.) Third round, Bart yields Third round, Ann yields Third round, both yield Anger after Third round P2 * 75% * $300 P2 * 0% * $200 P2 * 0% * $200 P2 * 25% * 30% * $0 = 60.75 (Note: Chances we go to fourth round = P3 = 50% * 90% * 75% * 80% * 25% * 70%.) Third round, Bart yields Third round, Ann yields Third round, both yield Anger after Third round P2 * 100% * $300 P2 * 0% * $200 P2 * 0% * $200 P2 * 0% * 40% * $0 = 14.175 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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