A non-cooperative interpretation of bargaining sets

This paper provides a non-cooperative interpretation for bargaining sets concepts in economic environments. We investigate the implementability of the Aumann-Maschler and Mas-Colell bargaining sets, and provide mechanisms whose subgame perfect equilibrium outcomes realize these sets. These mechanisms, in contrast to general mechanisms suggested in the implementation literature, have a natural structure closely related to that of the rationale underlying the bargaining sets. Furthermore, the strategy sets consist mainly of allocations and coalitions (thus avoiding any reference to preference parameters) and are finite dimensional. Received: 17 February 1997 / Accepted: 2 February 1999     

Multi-agent bilateral bargaining and the Nash bargaining solution

This paper studies a bargaining model where n   players negotiate how to share a pie through (n−1)$(n-1)$ bilateral bargaining sessions. In each session, two players bargain for a partial agreement that specifies who exits and who moves on to the next session (if there is any) via the alternating-proposal framework of Rubinstein [Rubinstein, A., 1982. Perfect equilibrium in a bargaining model. Econometrica 50, 97–109]. We consider two bargaining procedures under which the subgame perfect equilibrium outcomes converge to the Nash [Nash, J., 1950. The bargaining problem. Econometrica 18, 155–162] bargaining solution for the corresponding bargaining problem as the players’ discount factor goes to one. Hence, the model studied here provides a non-cooperative foundation for the Nash cooperative bargaining solution in the multilateral case.     

A noncooperative approach to the Mas-Colell bargaining set

We propose an extensive form game to give a noncooperative interpretation of the Mas-Colell bargaining set for transferable utility games. Based on the objection and counterobjection in the sense of the Mas-Colell bargaining set, a bilateral negotiation is designed in our model. We show that the equilibrium outcomes of our extensive form game coincide with the Mas-Colell bargaining set in the supperadditive environments.     

A note on van Damme's mechanism

We consider (two-person) bargaining games and we assume that the agents want to apply two possibly different bargaining solutions. A mechanism is a function which assigns an allocation to every bargaining game and every pair of bargaining solutions. Examining van Damme's mechanism (1986) from a cooperative point of view we see that it fails to satisfy Pareto-optimality. By modifying it we propose a new mechanism yielding the same conclusions as the original while enjoying some additional desirable properties. Received: 8 August 1998 / Accepted: 15 October 1998     

Stable and efficient bargaining networks

Abstract. We examine a bargaining game among players connected by a network, where successively potential partners negotiate over terms of a project. For any network structure and ordering of selection of bargaining partners, there is a unique subgame perfect equilibrium outcome which coincides with the standard Rubinstein split. Based on this, we derive expected payoffs for players as a function of the network. We the characterize the pairwise stable and efficient bargaining networks. These two sets do not always coincide and in many situations pairwise stable networks are over-connected. Received: 10 April 2001 / Accepted: 17 January 2002 I am indebted to Matthew Jackson for suggesting this paper. I also thank Bernard Caillaud, Sanjeev Goyal, and the seminar participants at Universidad de Alicante, Universidad Carlos III de Madrid, CEMFI (Madrid), Universitat Autònoma de Barcelona, Erasmus University of Rotterdam, Universitat Pompeu Fabra (Barcelona) and CERAS (Paris) for helpful comments. This paper was written while at Universitat Pompeu Fabra and CERAS. Financial support from the Spanish Ministry of Education through research grant DGESIC PB96-0302, and from the Ecole Nationale des Ponts et Chaussées, Paris is gratefully acknowledged. All errors are of course mine.     

Learning in a multilateral bargaining experiment

This paper analyzes data from an investigation of a majoritarian bargaining experiment. A learning model is proposed to account for the evolution of play in this experiment. It is also suggested that an adjustment must be made to account for the panel structure of the data. Such adjustments have been used in other fields and are known to be important as unadjusted standard errors may be severely biased downward. These results indicate that this adjustment also has an important effect in this application. Furthermore, an efficient estimator that takes into account heterogeneity across players is proposed. A unique learning model to account for the paths of play under two different amendment rules cannot be rejected with the standard estimator with adjusted standard errors, however it can be rejected using the efficient estimator. The data and the estimated learning model suggest that after proposing “fair” divisions, subjects adapt and their proposals change rapidly in the treatment where uneven proposals are almost always accepted. Their beliefs in the estimated learning model are influenced by more than just the most recent outcomes.     

Sequential bargaining with common values

We study the alternating-offers bargaining problem of assigning an indivisible and commonly valued object to one of two players who jointly own this object. The players are asymmetrically informed about the object’s value and have veto power over any settlement. There is no depreciation during the bargaining process which involves signalling of private information. We characterise the perfect Bayesian equilibrium outcome of this game which is unique if offers are required to be strictly increasing. Equilibrium agreement is reached gradually and non-deterministically. The better informed player obtains a rent.     

A note on the multiple partners assignment game

In the assignment game of Shapley and Shubik [Shapley, L.S., Shubik, M., 1972. The assignment game. I. The core, International Journal of Game Theory 1, 11–130] agents are allowed to form one partnership at most. That paper proves that, in the context of firms and workers, given two stable payoffs for the firms there is a stable payoff which gives each firm the larger of the two amounts and also one which gives each of them the smaller amount. Analogous result applies to the workers. Sotomayor [Sotomayor, M., 1992. The multiple partners game. In: Majumdar, M. (Ed.), Dynamics and Equilibrium: Essays in Honor to D. Gale. Mcmillian, pp. 322–336] extends this analysis to the case where both types of agents may form more than one partnership and an agent's payoff is multi-dimensional. Instead, this note concentrates in the total payoff of the agents. It is then proved the rather unexpected result that again the maximum of any pair of stable payoffs for the firms is stable but the minimum need not be, even if we restrict the multiplicity of partnerships to one of the sides.     

A note on the structural stability of the equilibrium manifold

In a smooth pure exchange economy with fixed total resources we investigate whether the smooth selection property holds when endowments are redistributed across consumers through a continuous (non-local) redistribution policy. We show that if the policy is regular then there exists a unique continuous path of equilibrium prices which support it.     

The efficiency of training and hiring with intrafirm bargaining

This paper demonstrates that firms hire and train workers efficiently in a matching and intrafirm bargaining economy when the Hosios condition holds and returns to scale are constant. This conclusion stands in contrast to the prevailing view that training costs are a source of inefficiency in imperfect labor markets. The efficiency of the competitive economy relies on the ability of large firms to take into account the negative impact of the training rate on the wages negotiated inside the firm through intrafirm bargaining: untrained workers accept a wage reduction in compensation for potential training that is accessible only following employment. This intrafirm bargaining process solves efficiency problems associated with training costs that would otherwise lead to inefficient hiring and training decisions. This conclusion holds true for both specific and general human capital.     

A trade without collective bargaining

The contract cleaning industry has hitherto managed to avoid the establishment of collective bargaining machinery. Will this situation be remedied in the light of the N.B.P.I, report, pressure from the unions concerned and the T.U.C. ?     

A correction to uniqueness in “Competitive Bidding and Proprietary Information”

In this note I show that there is a mistake in the proof of uniqueness in Engelbrecht-Wiggans, Milgrom and Weber’s seminal “Competitive Bidding and Proprietary Information” and provide a correct proof.     

A bargaining set for roommate problems

Since stable matchings may not exist, we propose a weaker notion of stability based on the credibility of blocking pairs. We adopt the weak stability notion of Klijn and Massó (2003) for the marriage problem and we extend it to the roommate problem. We first show that although stable matchings may not exist, a weakly stable matching always exists in a roommate problem. Then, we adopt a solution concept based on the credibility of the deviations for the roommate problem: the bargaining set. We show that weak stability is not sufficient for a matching to be in the bargaining set. We generalize the coincidence result for marriage problems of Klijn and Massó (2003) between the bargaining set and the set of weakly stable and weakly efficient matchings to roommate problems. Finally, we prove that the bargaining set for roommate problems is always non-empty by making use of the coincidence result.     

Pure strategy equilibria in games with countable actions

In this paper, we extend the Radner–Rosenthal theorem with finite action spaces on the existence of a pure strategy equilibrium for a finite game to the case that the action space is countable and complete. We also prove the existence of a pure strategy equilibrium for a game with a continuum of players of finite types and with a countable and complete action space. To work with the countably infinite action spaces, we prove some regularity properties on the set of distributions induced by the measurable selections of a correspondence with a countable range by using the Bollobás–Varopoulos extension of the marriage lemma.     

A note on redistribution

A consequence of income redistribution may well be to make everyone (including lower-income groups to which redistribution takes place) worse off after a period of years. Possibly income redistribution might gain consent because of risk aversion. The paper also draws attention to the tendency for people to be more concerned about poverty close at hand rather than far away.