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Some Impossibility Results on the Converse Consistency Principle in Bargaining

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Abstract

We investigate the existence of solutions satisfying converse consistency together with other well-known axioms in the context of bargaining. Our results are negative. First, we show that there is no solution satisfying converse consistency together with Pareto optimality and contraction independence. Second, we show that there is no solution satisfying converse consistency together with Pareto optimality and individual monotonicity.

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Notes

  1. Under the name of independence of irrelevant alternatives.

  2. Vector inequalities\(:\) given \(x, y \in {\mathbb {R}}^N,\) x \(\geqq\) y means \(x_i \ge y_i\) for each \(i \in N,\) \(x \ge y\) means x \(\geqq\) y and \(x \ne y,\) \(x > y\) means \(x_i > y_i\) for each \(i \in N\).

  3. Weak Pareto optimality requires that there should be no feasible alternative at which all agents are strictly better off than at the solution outcome.

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Acknowledgements

I am grateful to William Thomson for his comments. This work was supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF-2016S1A3A2924944).

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Correspondence to Youngsub Chun.

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This is a revised version of my paper entitled “Two impossibility results on the converse consistency principle in bargaining.”

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Chun, Y. Some Impossibility Results on the Converse Consistency Principle in Bargaining. Homo Oecon 37, 59–65 (2020). https://doi.org/10.1007/s41412-020-00099-5

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