Consider a housing market (I, H, R), where I = {1,2,3,4}, H = {h(1), h(2), h(3),...
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Consider a housing market (I, H, R), where I = {1,2,3,4}, H = {h(1), h(2), h(3), h(4)}, where agent i EI owns house h(i) € H, and players' preferences are as follows: R₂ R3 R₁ h(3) h(3) h(2) h(2) R₁ h(2) h(4) h(4) h(4) h(3) h(1) h(1) h(1) h(3) h(1) h(2) h(3) h(4) (a) Consider matching μ = {(1, h(2)), (2, h(1)), (3, h(4)), (4, h(3))}. Is μ individually rational? Is μ core stable? Is u Pareto optimal? μ (b) Compute the matching that is the result of the Gale's top trading cycles (TTC) rule at preferences R = (R₁, R2, R3, R₁), i.e., find TTC(R), and show that it is core stable. (c) Suppose that agent 4 misreports her preferences by reporting R₁ : h(3) P₁ h(1) P₁ h(2) P₁ h(4). Compute the result of the TTC rule under this misreporting (while other agents still report their true preferences), i.e., compute TTC(R) when the preference profile is R = (R₁, R₂, R3, R₁). Is agent 4 made better off with her misreporting? How can you conclude? Consider a housing market (I, H, R), where I = {1,2,3,4}, H = {h(1), h(2), h(3), h(4)}, where agent i EI owns house h(i) € H, and players' preferences are as follows: R₂ R3 R₁ h(3) h(3) h(2) h(2) R₁ h(2) h(4) h(4) h(4) h(3) h(1) h(1) h(1) h(3) h(1) h(2) h(3) h(4) (a) Consider matching μ = {(1, h(2)), (2, h(1)), (3, h(4)), (4, h(3))}. Is μ individually rational? Is μ core stable? Is u Pareto optimal? μ (b) Compute the matching that is the result of the Gale's top trading cycles (TTC) rule at preferences R = (R₁, R2, R3, R₁), i.e., find TTC(R), and show that it is core stable. (c) Suppose that agent 4 misreports her preferences by reporting R₁ : h(3) P₁ h(1) P₁ h(2) P₁ h(4). Compute the result of the TTC rule under this misreporting (while other agents still report their true preferences), i.e., compute TTC(R) when the preference profile is R = (R₁, R₂, R3, R₁). Is agent 4 made better off with her misreporting? How can you conclude?
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Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
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