On the Sensitivity Matrix of the Nash Bargaining Solution

J.C. Engwerda, R.C.M.H. Douven

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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.
Original languageEnglish
Place of PublicationTilburg
Number of pages13
Publication statusPublished - 2005

Publication series

NameCentER Discussion Paper


  • Nash bargaining solution
  • d-monotonicity
  • diagonally dominant Stieltjes matrix


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