Non-cooperative support for the asymmetric Nash bargaining solution

Abstract

Our work contributes to the game-theoretic analysis of bargaining by providing additional non-cooperative support to the well-known Nash bargaining solution. In particular, in the present paper we study a model of non-cooperative multilateral bargaining with a very general proposer selection protocol and set of feasible payoffs. In each period of the bargaining game, one out of n players is recognized as the proposer according to an irreducible Markov process. The proposer offers a particular element of the convex set of feasible payoffs. If all players accept the offer, it is implemented. If a player rejects the offer, with some probability the negotiations break down and with the remaining probability the next period starts. We show that subgame perfect equilibria in stationary strategies exist and we fully characterize the set of such equilibria. Our main result is that in the limit, as the exogenous risk of breakdown goes to zero, stationary subgame perfect equilibrium payoffs converge to the weighted Nash bargaining solution with the stationary distribution of the Markov proposer selection process as the weight vector.

Bargaining under monotonicity constraints

“…In particular, such results have been demonstrated in Hart and Mas-Colell (1996), Laruelle and Valenciano (2007), Miyakawa (2008), Kultti andVartiainen (2010), andBritz et al (2010) under increasingly weaker conditions.…”

“…We are interested in the uniqueness and the characterization of the limit proposal. The literature on multilateral bargaining with unanimous agreement has shown convergence of bargaining equilibrium proposals to the Nash bargaining solution, see Hart and Mas-Colell (1996), Laruelle and Valenciano (2007), Miyakawa (2008), Kultti and Vartiainen (2010), and Britz et al (2010). Unfortunately, all these papers need differentiability assumptions with respect to the set of feasible alternatives, an assumption that is clearly violated in the presence of monotonicity constraints.…”

Costless Delay in Negotiations

“…Fixed rotating orders of recognized players can be modeled similarly, for example the in…nitely-repeated order 1; : : : ; n is captured by setting i+1 (i; x; r) = 1; where we write i + 1 instead of i + 1 mod n. Markov recognition probabilities are studied in Kalandrakis (2004b), Britz et al (2010) and Predtetchinski (2010, 2012). In this case, the probability of player j being recognized in round t + 1 conditional on player i being the proposer in round t is given by i;j : We obtain Markov recognition probabilities by setting j (i; x; r) = i;j .…”

In Search of an Alternative to Shareholder Value Maximization

“…Obviously, this is no longer a normative issue, but rather, a positive one. A partial answer has recently been provided by Britz, Herings, andPredtetchinski (2010, 2011). Suppose that all the shareholders take part in a repeated bargaining processà la Rubinstein: every round, one shareholder is selected at random to make a proposal; if it is unanimously accepted, the game is over; otherwise, either one begins a new round of bargaining or (with little probability) no-production is implemented.…”