In this note we derive the sensitivity matrix of the Nash bargaining solution w.r.t. the disagreement point d. This first order derivative is completely specified in terms of the Pareto frontier function. We show that whenever one player increases his threatpoint always at least one player will loose utility: i.e. the dual result of Pareto optimality. Furthermore,the dmonotonicity property is easily re-established from this matrix. This matrix also enables us to consider the concept of local strong d-monotonicity. That is,under which conditions on the Pareto frontier function . an infinitesimal increase of di,while for each j = i, dj remains constant,it happens that agent i is the only one who s payoff increases. We show that for the Nash bargaining solution this question is closely related to non-negativity of the Hamiltonian matrix of . at the solution.
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Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number
35.
Find related papers by JEL classification: C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
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