Nash bargaining solution under externalities

We define a Nash bargaining solution (NBS) of partition function games. Based on a partition function game, we define an extensive game, which is a propose–respond sequential bargaining game where the rejecter of a proposal exits from the game with some positive probability. We show that the NBS is supported as the expected payoff profile of any stationary subgame perfect equilibrium (SSPE) of the extensive game such that in any subgame, a coalition of all active players forms immediately. We provide a necessary and sufficient condition for such an SSPE to exist. Moreover, we consider extensions to the cases of nontransferable utilities, time discounting and multiple-coalition formation.     

The generalized Nash bargaining solution and Incentive Compatible Mechanisms

In this paper I analyze whether the generalized Nash solution which has been defined by Harsanyi and Selten for bargaining problems with incomplete information can be characterized in the mechanism framework introduced by Myerson.I show that the solution is uniquely determined by a set of axioms in the case of independently distributed types. It can be seen that the axioms given by Harsanyi and Selten cannot be used if the types are not independently distributed.     

On the sensitivity matrix of the Nash bargaining solution

In this note we provide a characterization of a subclass of bargaining problems for which the Nash solution has the property of disagreement point monotonicity. While the original d-monotonicity axiom and its stronger notion, strong d-monotonicity, were introduced and discussed by Thomson (J Econ Theory, 42: 50–58, 1987), this paper introduces local strong d-monotonicity and derives a necessary and sufficient condition for the Nash solution to be locally strongly d-monotonic. This characterization is given by using the sensitivity matrix of the Nash bargaining solution w.r.t. the disagreement point d. Moverover, we present a sufficient condition for the Nash solution to be strong d-monotonic.     

The ordered field property and a finite algorithm for the Nash bargaining solution

This note proves that the two person Nash bargaining theory with polyhedral bargaining regions needs only an ordered field (which always includes the rational number field) as its scalar field. The existence of the Nash bargaining solution is the main part of this result and the axiomatic characterization can be proved in the standard way with slight modifications. We prove the existence by giving a finite algorithm to calculate the Nash solution for a polyhedral bargaining problem, whose speed is of orderBm(m-1) (m is the number of extreme points andB is determined by the extreme points).     

The Nash solution of a maintenance-production differential game

A simple two-person nonzero-sum differential game between the maintenance crew of a firm and the production department of the same firm is considered. It is assumed that preventive maintenance decelerates the decrease in quality of a machine, whereas the production activities set by the firm reduces the quality of the machine. Due to the special structure of the game a system of two differential equations for the non-cooperative Nash solution trajectories can be derived. This provides a possibility to obtain qualitative insights into the structure of the solution paths by phase diagram methods without solving the necessary optimality conditions explicitly.For small salvage values of the machine, it is shown that the optimal maintenance expenditures decrease over time whereas the optimal production rate increases monotonically.Moreover, another interpretation of the differential game analyzed is given as a conflict situation between a firm polluting the environment by producing an output and a governmental agency cleaning up the pollution.     

An exponential differential game which admits a simple Nash solution

This paper deals with a class ofN-person nonzero-sum differential games where the control variables enter into the state equations as well as the payoff functionals in an exponential way. Due to the structure of the game, Nash-optimal controls are easily determined. The equilibrium in open-loop controls is also a closed-loop equilibrium. An example of optimal exploitation of an exhaustible resource is presented.The helpful comments of Professor Y. C. Ho and Dipl. Ing. E. Dockner are gratefully acknowledged.     

Sufficient conditions for Nash bargaining in differential games

Sufficient conditions for Nash bargaining in differential games are given. These conditions are compared with the sufficient conditions given by Liu (Ref. 1).     

Nash equilibria in optimal reinsurance bargaining

We introduce a strategic behavior in reinsurance bilateral transactions, where agents choose the risk preferences they will appear to have in the transaction. Within a wide class of risk measures, we identify agents’ strategic choices to a range of risk aversion coefficients. It is shown that at the strictly beneficial Nash equilibria, agents appear homogeneous with respect to their risk preferences. While the game does not cause any loss of total welfare gain, its allocation between agents is heavily affected by the agents’ strategic behavior. This allocation is reflected in the reinsurance premium, while the insurance indemnity remains the same in all strictly beneficial Nash equilibria. Furthermore, the effect of agents’ bargaining power vanishes through the game procedure and the agent who gets more welfare gain is the one who has an advantage in choosing the common risk aversion at the equilibrium.     

Commitments to threat strategies in Nash bargaining

Nash's two-person bargaining model consists of two stages: threat strategies and utility demands are chosen in the first and second stages respectively. Here players commit to play the threat strategies chosen in the first stage for the case where disagreement occurs in the second stage. Whether a player commits or not to play a threat strategy, however, is voluntary in principle. This leads to some possible extensions of Nash's model so that players' commitment choices are taken into account. In this paper, we consider three extensions. In the two person case, these three extensions give essentially the same result as that given by Nash. This is not the case for more than two players; the result depends upon an extension. In one extension, Nash's result always holds for more than two players. In the other two extensions, however, we give a three person example where not all players choose commitments in equilibrium.     

The kernel,the bargaining set and the reduced game

We present an example showing that forxK(N, v, B) the section ofK(N, v, B) atx| _{N-B k} may be a proper subset ofK(B _k, v_x, X_k). Further we prove that under appropriate conditions these two sets coincide. For the bargaining set we prove a similar result.We are grateful to an anonymous referee for valuable comments.     

The semireactive bargaining set of a cooperative game

The semireactive bargaining set, a solution for cooperative games, is introduced. This solution is in general a subsolution of the bargaining set and a supersolution of the reactive bargaining set. However, on various classes of transferable utility games the semireactive and the reactive bargaining set coincide. The semireactive prebargaining set on TU games can be axiomatized by one-person rationality, the reduced game property, a weak version of the converse reduced game property with respect to subgrand coalitions, and subgrand stability. Furthermore, it is shown that there is a suitable weakening of subgrand stability, which allows to characterize the prebargaining set. Replacing the reduced game by the imputation saving reduced game and employing individual rationality as an additional axiom yields characterizations of both, the bargaining set and the semireactive bargaining set. Received September 2000/Revised version June 2001     

The pairwise egalitarian solution for the assignment game

In this note we consider the pairwise egalitarian solution (Sánchez-Soriano, 2003) on the domain of assignment games and study its relation with the core. Strengthening the dominant diagonal condition (Solymosi and Raghavan, 2001), we introduce k-dominant diagonal assignment games (k≥1), analyzing for which values of k the pairwise egalitarian solution fulfills the standards of fairness represented by the Lorenz domination and the kernel. We also characterize the Thompson’s fair division point (Thompson, 1981) for arbitrary assignment games.     

Two-person bargaining: An experimental test of the Nash axioms

Tests were carried out on thirty pairs of subjects, using three different sets of conditions, for the purpose of experimentally validatingNash's axioms (and also, incidentally, certain other hypotheses of two-person bargaining). Under validation, it was found that subjects' responses conformed to both thesymmetry andindependence of irrelevant alternatives axioms. On the other hand, the axiom ofinvariance under linear transformations of utility was constantly violated. This may be due to the fact that subjects, whenever possible, try to effect an interpersonal comparison of utility.     

Collective bargaining: A differential game

Earlier differential game models of collective bargaining deal only with the strike phase. The model proposed here allows for negotiations without and with a strike.This paper is based on research supported by NSF under Grant No. GP-24205.     

Labor unions and Nash bargaining using coalition formation games

In this paper we examine the properties of stable coalitions under sequential and simultaneous bargaining by competing labor unions. We do this using the Nash bargaining solution and various notions of stability, namely, Nash, coalitional, contractual and core stability.     

Nash bargaining,Shapley threats,and outside options

We introduce a weighted version of the component efficient χ$\chi$-value [Casajus, A., 2009. Outside options, component efficiency, and stability. Games and Economic Behavior 65 (1), 49–61] for TU games with a coalition structure. We provide characterizations both for a symmetric and for an asymmetric treatment of outside options. Further, the stability of coalition structures is explored. These concepts are applied to apex games.     

Nonsymmetric Nash solutions and replications of 2-person bargaining

A 2-person fixed threat bargaining problem is considered. A full characterization of the solutions which satisfy all of Nash's axioms except for the axiom of symmetry is given. It is also shown that these nonsymmetric Nash solutions are precisely the solutions that arise from symmetric Nash solutions through replications.     

Nash equilibria in the two-player kidney exchange game

Kidney exchange programs have been set in several countries within national, regional or hospital frameworks, to increase the possibility of kidney patients being transplanted. For the case of hospital programs, it has been claimed that hospitals would benefit if they collaborated with each other, sharing their internal pools and allowing transplants involving patients of different hospitals. This claim led to the study of multi-hospital exchange markets. We propose a novel direction in this setting by modeling the exchange market as an integer programming game. The analysis of the strategic behavior of the entities participating in the kidney exchange game allowed us to prove that the most rational game outcome maximizes the social welfare and that it can be computed in polynomial time.     

The Kalai-Smorodinsky bargaining solution with loss aversion

We consider bargaining problems under the assumption that players are loss averse, i.e., experience disutility from obtaining an outcome lower than some reference point. We follow the approach of Shalev (2002) by imposing the self-supporting condition on an outcome: an outcome z in a bargaining problem is self-supporting under a given bargaining solution, whenever transforming the problem using outcome z as a reference point, yields a transformed problem in which the solution is z.We show that n-player bargaining problems have a unique self-supporting outcome under the Kalai-Smorodinsky solution. For all possible loss aversion coefficients we determine the bargaining solutions that give exactly these outcomes, and characterize them by the standard axioms of Scale Invariance, Individual Monotonicity, and Strong Individual Rationality, and a new axiom called Proportional Concession Invariance (PCI). A bargaining solution satisfies PCI if moving the utopia point in the direction of the solution outcome does not change this outcome.