Consider a hedonic game G = (N, 2) where N = {1,2,3} and players' preferences are...

 

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Consider a hedonic game G = (N, 2) where N = {1,2,3} and players' preferences are as follows: (a) (b) (c) (d) ₁: (1,2,3) 1 {1,2} >1 {1,3} >1 {1}, 2:{1,2} 2 (2,3} {1,2,3} 2 {2}, 3: {1,2,3} {1,3} 3 {2,3} 3 {3}. Does this hedonic game satisfy the common ranking property? Does this game satisfy the top-coalition property? Does this game satisfy the weak top-coalition property? Consider partition = {{1,2}, {3}}. Is individually rational? π Is 7 core stable? Is T (FX-FE) Nash stable stable? Is T FX-AE Nash stable (individually stable)? (e) Consider partition = {{2,3}, {1}}. Is Is core stable? Is (FX-FE) Nash stable stable? Is 7 AX-AE Nash stable (contractually individually stable)? individually rational? Consider a hedonic game G = (N, 2) where N = {1,2,3} and players' preferences are as follows: (a) (b) (c) (d) ₁: (1,2,3) 1 {1,2} >1 {1,3} >1 {1}, 2:{1,2} 2 (2,3} {1,2,3} 2 {2}, 3: {1,2,3} {1,3} 3 {2,3} 3 {3}. Does this hedonic game satisfy the common ranking property? Does this game satisfy the top-coalition property? Does this game satisfy the weak top-coalition property? Consider partition = {{1,2}, {3}}. Is individually rational? π Is 7 core stable? Is T (FX-FE) Nash stable stable? Is T FX-AE Nash stable (individually stable)? (e) Consider partition = {{2,3}, {1}}. Is Is core stable? Is (FX-FE) Nash stable stable? Is 7 AX-AE Nash stable (contractually individually stable)? individually rational?

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ANSWER To analyze the properties of the hedonic game G N with N 123 and the given players preferences lets consider each question separately a The common ranking property states that in any coalition ... View the full answer