On bargaining partner selection when communication is restricted

Abstract. This paper analyzes the optimal selection of a bargaining partner when communication among players is restricted by an exogenously given graph. If players are equally patient, bargaining agreements are immune to players' locations, and the selection of a bargaining partner is not an issue. In contrast, when players differ in their discount factors, both location and impatience matter for bilateral agreements and partner selection becomes an issue. We show that selecting the most impatient neighbor is an equilibrium strategy whenever two players having a common neighbor share their most impatient neighbor. This condition is always satisfied by stratified graphs with no more than three strata. In the absence of this condition, cyclically-stratified graphs with no more than three strata also admit this equilibrium selection rule.

[1]  Antoni Calvó-Armengol.  A note on three-player noncooperative bargaining with restricted pairwise meetings , 1999 .

[2]  A. Shaked,et al.  Involuntary Unemployment as a Perfect Equilibrium in a Bargaining Model (Now published in Econometrica, vol.52, (1984), pp.1351-1364.) , 1984 .

[3]  M. Slikker,et al.  Network formation models with costs for establishing links , 2000 .

[4]  József Sákovics,et al.  Randomly available outside options in bargaining , 2001 .

[5]  Xavier Martinez-Giralt,et al.  Selecting Negotiation Processes with Health Care , 2000 .

[6]  A. Shaked,et al.  An Outside Option Experiment , 1989 .

[7]  R. Kranton,et al.  A Theory of Buyer-Seller Networks , 2001 .

[8]  József Sákovics,et al.  Rubinstein bargaining with two-sided outside options , 1998 .

[9]  A. Rubinstein.  Perfect Equilibrium in a Bargaining Model , 1982 .

[10]  Margarida Corominas Bosch.  On Two Sided Network Markets , 1999 .

[11]  Antoni Calvó-Armengol,et al.  Bargaining power in communication networks , 2001, Math. Soc. Sci..

[12]  Philippe Jehiel,et al.  Negative Externalities May Cause Delay in Negotiation , 1995 .

[13]  M. Jackson,et al.  A Strategic Model of Social and Economic Networks , 1996 .

[14]  Torben Tranæs,et al.  Sequential bargaining in a market with one seller and two different buyers , 1991 .

[15]  Antoni Calvó-Armengol,et al.  Bargaining Power in Communication Networks ¤ Mathematical Social Sciences, forthcoming , 1999 .

[16]  P. Jehiel,et al.  On the Role of Outside Options in Bargaining with Obstinate Parties , 2002 .

[17]  Roger B. Myerson,et al.  Graphs and Cooperation in Games , 1977, Math. Oper. Res..

[18]  B. Moldovanu,et al.  Resale Markets and the Assignment of Property Rights , 1999 .

[19]  Philippe Jehiel,et al.  Cyclical Delay in Bargaining with Externalities , 1995 .

[20]  Kalyan Chatterjee,et al.  Rubinstein Auctions: On Competition for Bargaining Partners , 1998 .

[21]  R. Aumann,et al.  The Shapley value: Endogenous formation of links between players and of coalitions: an application of the Shapley value , 1988 .

[22]  Leonard M. Adleman,et al.  Proof of proposition 3 , 1992 .

[23]  Stef Tijs,et al.  Link formation in cooperative situations , 1998, Int. J. Game Theory.