Seminario 22/13: Marc Escrihuela (Universidad de las Islas Baleares). On the role of bargaining power in Nash-in-Nash bargaining: when more may be less

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In many economically relevant situations, the outcome of a negotiation determines not only how the two parties share the surplus generated by their interaction (share effect), but also the aggregate surplus (size effect). We show that, in multilateral negotiations modeled using the Nash-in-Nash solution, the equilibrium payoff of a party may be decreasing in her bargaining power. We show this result in a standard problem in industrial organization, that is the one of a negotiation in a vertical industry over a linear input price. We first show that, in a bilateral monopoly, the upstream firm is better off when she has a larger bargaining power, as the intuition suggests. This result is not always confirmed with downstream competition. We provide examples in which it is possible that a negative size effect outplays a positive share effect, so that a larger bargaining power for the upstream firm may be associated to lower equilibrium profits. Under both quantity and price competition, this unexpected relationship is shown to occur when downstream goods are complements.