Stationary perfect equilibria of an n-person noncooperative bargaining game and cooperative solution concepts

This paper characterizes the stationary (subgame) perfect equilibria of an n-person noncooperative bargaining model with characteristic functions, and provides strategic foundations of some cooperative solution concepts such as the core, the bargaining set and the kernel. The contribution of this paper is twofold. First, we show that a linear programming formulation successfully characterizes the stationary (subgame) perfect equilibria of our bargaining game. We suggest a linear programming formulation as an algorithm for the stationary (subgame) perfect equilibria of a class of n-person noncooperative games. Second, utilizing the linear programming formulation, we show that stationary (subgame) perfect equilibria of n-person noncooperative games provide strategic foundations for the bargaining set and the kernel.     

拟凸对策的解

本文先引入拟凸对策的概念作为凸对策的推广,然后研究这种对策的各种解的性质。我们主要证得,当局中人数小于6或者对策的复盖严格凸时,谈判集与核心重合,核是单点集。另外,存在一个6人拟凸对策,其谈判集与核心不同。     

On the bargaining set, kernel and core of superadditive games

We prove that for superadditive games a necessary and sufficient condition for the bargaining set to coincide with the core is that the monotonic cover of the excess game induced by a payoff be balanced for each imputation in the bargaining set. We present some new results obtained by verifying this condition for specific classes of games. For N-zero-monotonic games we show that the same condition required at each kernel element is also necessary and sufficient for the kernel to be contained in the core. We also give examples showing that to maintain these characterizations, the respective assumptions on the games cannot be lifted. Received: March 1998/Revised version: December 1998     

A bargaining game model for measuring performance of two-stage network structures

Data envelopment analysis (DEA) is a method for measuring the efficiency of peer decision making units (DMUs), where the internal structures of DMUs are treated as a black-box. Recently DEA has been extended to examine the efficiency of DMUs that have two-stage network structures or processes, where all the outputs from the first stage are intermediate measures that make up the inputs to the second stage. The resulting two-stage DEA model not only provides an overall efficiency score for the entire process, but also yields an efficiency score for each of the individual stages. The current paper develops a Nash bargaining game model to measure the performance of DMUs that have a two-stage structure. Under Nash bargaining theory, the two stages are viewed as players and the DEA efficiency model is a cooperative game model. It is shown that when only one intermediate measure exists between the two stages, our newly developed Nash bargaining game approach yields the same results as applying the standard DEA approach to each stage separately. Two real world data sets are used to demonstrate our bargaining game model.     

NEGOTIATING OVER EXTERNALITIES

We present a simple model in which two perfectly informed, risk neutral agents will not negotiate an efficient agreement to lessen the effects of an externality and for which the outcome of negotiation depends on the legal assignment of property rights. The model permits agents to pre-commit themselves to refuse to negotiate particular agenda issues. The result is obtained because we prove that one player is always made strictly worse off from the addition of side-payments to a bargaining game. Along the way, we devise a supporting hyperplane for the n-person Nash bargaining game solution. We also display a simple game which establishes that our main result holds true—for at least some games—for an array of alternative bargaining game solutions such as that of Raiffa, Kalai, and Smorodinski.     

Bargaining and negative externalities

Two important issues in distributive bargaining theory are, first, the conditions under which a negotiation breakdown occurs, and second, what and how source of parties’ bargaining powers influences the properties of a possible agreement. Research based on classic Nash’s demand game has explored both questions by sophisticating the original game a lot. As an attempt to deal with both issues under a simpler framework, we propose a modification of the Nash demand game in which bargainers suffer negative externalities proportional to the share of the surplus captured by their rival. It is shown that the negotiator experiencing a relatively high externality level has greater bargaining power and thus, appropriates a larger proportion of the surplus at stake. However, if externality levels are sufficiently high, bargaining powers become incompatible and a negotiation breakdown emerges from the bargaining process. We compare our results with the previous literature, and argue that they can be especially relevant in negotiations held under highly polarized environments.     

多人多目标资源分配协商对策

资源分配问题,一直是决策分析理论研究的核心问题之一.从对各种经济系统进行决策分析中,可得出一类多人多目标资源分配问题的数学描述如下:     

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 kernel and bargaining set for convex games

It is shown that for convex games the bargaining set? ₁ ⁽ⁱ⁾ (for the grand coalition) coincides with the core. Moreover, it is proved that the kernel (for the grand coalition) of convex games consists of a unique point which coincides with the nucleolus of the game.     

On a dynamic theory for the kernel of ann-person game

In this paper, a dynamic theory for the kernel ofn-person games given byBillera is studied. In terms of the (bargaining) trajectories associated with a game (i.e. solutions to the differential equations defined by the theory), an equivalence relation is defined. The “consistency” of these equivalence classes is examined. Then, viewing the pre-kernel as the set of equilibrium points of this system of differential equations, some topological, geometric, symmetry and stability properties of the pre-kernel are given.