One-Dimensional Bargaining with Markov Recognition Probabilities

Abstract

People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal.

One-dimensional bargaining

“…Cardona and Ponsatí (2007) show that stationary subgame perfect equilibria in pure strategies are unique in a game where the proposers rotate in a fixed sequence, provided that each player's utility function is symmetric around the peak and the acceptance rule is a quota rule. Herings and Predtetchinski (2010) establish the uniqueness result in a model where the identity of the proposer follows a general Markov process, assuming tent-shaped utility functions and the unanimity acceptance rule.…”

“…Various results on one-dimensional bargaining have been previously obtained in Banks and Duggan (2000), Cho and Duggan (2003), Kalandrakis (2006), Cardona and Ponsatí (2007), Herings and Predtetchinski (2010), Imai and Salonen (2000), Compte and Jehiel (2010). Banks and Duggan (2000) consider bargaining in a situation where the alternatives are represented by points in a general compact convex set.…”

“…The question of uniqueness of stationary subgame perfect equilibria in the one-dimensional bargaining game is addressed in Cho and Duggan (2003), Cardona and Ponsatí (2007), Herings and Predtetchinski (2010). Cho and Duggan (2003) derive the uniqueness of subgame perfect equilibria in pure stationary strategies assuming that the utility functions are quadratic and the acceptance rule is proper and strong.…”

“…In this paper not only do we show that equilibria are asymptotically unique, but we also provide a description of the limit by means of a characteristic equation. A characterization of the limit of equilibria is also given in Herings and Predtetchinski (2010), but this result only applies in a game with the unanimity acceptance rule and the tent-shaped utility functions. In the case of time-invariant recognition probabilities the characterization of Herings and Predtetchinski (2010) follows as a corollary to our main result.…”

“…A characterization of the limit of equilibria is also given in Herings and Predtetchinski (2010), but this result only applies in a game with the unanimity acceptance rule and the tent-shaped utility functions. In the case of time-invariant recognition probabilities the characterization of Herings and Predtetchinski (2010) follows as a corollary to our main result. Imai and Salonen (2000) introduce the concept of representative Nash bargaining solution for the situation of two-sided bargaining.…”