Consider a variant of the ultimatum game we studied in class in which players have fairness considerations. The timing of the game is as usual. First, player 1 proposes the split (100 – x, x) of a hundred dollars to player 2, where x € [0, 100]. Player 2 observes the split and decides whether to accept (in which case they receive money according to the proposed split) or reject (in which case they both get 0 dollars). But now player i's utility equals to her monetary utility minus the disutility from unfairness proportional to the difference in the monetary outcomes. That is, given a final split (m1, m2), let u1(m1, m2) = m1 – B1(m1 – m2)² uj(m1, m2) = m2 – B2(m1 – m2)², where ß1, ß2 are parameters of the game indicating how strongly players care about fairness. Note that the case we considered in class corresponds to B1 = B = 0.
Consider a variant of the ultimatum game we studied in class in which players have fairness considerations. The timing of the game is as usual. First, player 1 proposes the split (100 – x, x) of a hundred dollars to player 2, where x € [0, 100]. Player 2 observes the split and decides whether to accept (in which case they receive money according to the proposed split) or reject (in which case they both get 0 dollars). But now player i's utility equals to her monetary utility minus the disutility from unfairness proportional to the difference in the monetary outcomes. That is, given a final split (m1, m2), let u1(m1, m2) = m1 – B1(m1 – m2)² uj(m1, m2) = m2 – B2(m1 – m2)², where ß1, ß2 are parameters of the game indicating how strongly players care about fairness. Note that the case we considered in class corresponds to B1 = B = 0.
Chapter8: Game Theory
Section: Chapter Questions
Problem 8.7P
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![Consider a variant of the ultimatum game we studied in class in which players have fairness considerations. The timing of
the game is as usual. First, player 1 proposes the split (100 – x, x) of a hundred dollars to player 2, where x € [0, 100]. Player 2
observes the split and decides whether to accept (in which case they receive money according to the proposed split) or reject
(in which case they both get 0 dollars). But now player i's utility equals to her monetary utility minus the disutility from
unfairness proportional to the difference in the monetary outcomes. That is, given a final split (m1, m2), let
u1(m1, m2) = m1 – B1(m1 -– m2)²
u1(m1, m2) = m2 - B2(m1 – m2)²,
where B1, B2 are parameters of the game indicating how strongly players care about fairness. Note that the case we considered
in class corresponds to ß1 = B2 = 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbe960b7b-8746-4256-b957-606edabfae78%2Feccfeaaa-71de-4fe3-856e-a248f0f67050%2Fakqu7of_processed.png&w=3840&q=75)
Transcribed Image Text:Consider a variant of the ultimatum game we studied in class in which players have fairness considerations. The timing of
the game is as usual. First, player 1 proposes the split (100 – x, x) of a hundred dollars to player 2, where x € [0, 100]. Player 2
observes the split and decides whether to accept (in which case they receive money according to the proposed split) or reject
(in which case they both get 0 dollars). But now player i's utility equals to her monetary utility minus the disutility from
unfairness proportional to the difference in the monetary outcomes. That is, given a final split (m1, m2), let
u1(m1, m2) = m1 – B1(m1 -– m2)²
u1(m1, m2) = m2 - B2(m1 – m2)²,
where B1, B2 are parameters of the game indicating how strongly players care about fairness. Note that the case we considered
in class corresponds to ß1 = B2 = 0.
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