On the Role of Bargaining Power in Nash-in-Nash Bargaining: When More is Less

Posted: 23 Dec 2022

See all articles by Marc Escrihuela‐Villar

Marc Escrihuela‐Villar

University of the Balearic Islands

Walter Ferrarese

Universitat de Les Illes Balears

Alberto Iozzi

Universita degli Studi di Roma

Date Written: December 22, 2022

Abstract

In bargainings, the parties’ bargaining powers (BPs) may determine not only how the surplus is shared (share effect), but also the size of the aggregate surplus (size effect). Since the size effect may be positive or negative, the sign of the effect on a party’s payoff of a change in her BP is in principle undetermined. We first look at a general model with a party (the principal) negotiating with two counterparts. At the Nash-in-Nash solution, we show that the equilibrium payoff of the principal may be decreasing in her BP. Necessary conditions for this to occur are an asymmetric bargaining model and a sufficiently large difference in the way the bargained upon variables affect the principal’s payoff. We then revisit a standard linear vertical industry with one upstream firm, downstream Cournot competition, and public contracts. A negative effect on the upstream firm’s profits deriving from an increase in her BP is always found when the firm has different BPs across the negotiations and final goods are complements. We map these conditions to those characterised in the general model.

Keywords: bargaining power, Nash-in-Nash, vertical relations

JEL Classification: D21, D43, D86

Suggested Citation

Escrihuela Villar, Marc and Ferrarese, Walter and Iozzi, Alberto, On the Role of Bargaining Power in Nash-in-Nash Bargaining: When More is Less (December 22, 2022). CEIS Working Paper No. 550, Available at SSRN: https://ssrn.com/abstract=4309416

Marc Escrihuela Villar

University of the Balearic Islands ( email )

Crtra. Valldemossa, km 7.5
Ed. Jovellanos
Palma de Mallorca, Illles Balears 07122
Spain

Walter Ferrarese

Universitat de Les Illes Balears ( email )

Carretera de Valdemossa km 7.5
Palma de Mallorca, Palma de Mallorca
Spain

Alberto Iozzi (Contact Author)

Universita degli Studi di Roma ( email )

Via Columbia n.2
Rome, rome 00100
Italy
39 06 7259 5923 (Phone)
39 06 204 02 19 (Fax)

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