Convex games without side payments

A convex game without side payments is defined and discussed. It is shown that such a game is totally balanced. With a second and more restrictive definition of convexity it is shown that the core coincides with the von Neumann-Morgenstern solution.     

Values of games without side payments

A value forn-person games without side payments is given which coincides with theShapley value for games with side payments, and with theNash value for two-person games.     

Stable bargained equilibria for assignment games without side payments

We consider NTU assignment games, which are generalizations of two-sided markets. Matched pairs bargain over feasible allocations; the disagreement outcome is endogenuously determined, taking in account outside options which are based on the current payoff of other players. An allocation is in equilibrium if and only if each pair is in equilibrium (no player wishes to rebargain). The set of equilibria is not empty and it naturally generalizes the intersection of the core and prekernel of TU assignment games. A set with similar properties does not exist for general NTU games. The main source of technical difficulties is the relatively complicated structure of the core in NTU games. We make a strong use of reduced games and consistency requirements. We generalize also the results obtained by Rochford (1984) for TU assignment games.This is a part of my M.Sc. Thesis written at the Hebrew University, Jerusalem and at the University of Heidelberg. I am deeply indebted to my advisor, Prof. Bezalel Peleg. I wish also to thank Professors Michael Maschler, Avraham Neyman and Terje Lensberg for some helpful discussions, and to Prof. Werner Böge for his hospitality in Heidelberg. Finally, the comments of two anonymous referees greatly improved a preliminary version of this paper.     

Bargaining sets of cooperative games without side payments

In this paper an analogue of the bargaining setM ₁ ⁱ is defined for cooperative games without side payments. An existence theorem is proved for games of pairs, while it is shown by an example that no general existence theorem holds.     

Stable bargaining outcomes in patent licensing: A cooperative game approach without side payments

By formulating negotiations about licensing payments as cooperative games without side payments, we investigate stable bargaining outcomes in licensing a cost-reducing technology of an external patent holder to oligopolistic firms producing a homogeneous product under two policies: fee and royalty. The final bargaining outcome in fee licensing is uniquely determined, because the bargaining set for a coalition structure in which the patent holder can gain the maximum profit is a singleton. Under the royalty policy, the non-empty core for a coalition structure suggests that the patent holder should license his patented technology to all firms. Moreover, royalty licensing may be superior to fee licensing for the patent holder, when licensing is carried out through bargaining.     

The reactive bargaining set for cooperative games

We introduce a new bargaining set for cooperative games in characteristic function form, and investigate its structure and properties. We prove that the new bargaining set is not empty. In fact, we show that it contains the kernel and is contained in the classical bargaining set ${\mathcal{M}^i_1}$ , and we further prove that it consists of the unique symmetric vector for the class of simple majority games.     

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.     

The bargaining set of four-person balanced games

It is well known that in three-person transferable-utility cooperative games the bargaining set ℳⁱ ₁ and the core coincide for any coalition structure, provided the latter solution is not empty. In contrast, five-person totally-balanced games are discussed in the literature in which the bargaining set ℳⁱ ₁ (for the grand coalition) is larger then the core. This paper answers the equivalence question in the remaining four-person case. We prove that in any four-person game and for arbitrary coalition structure, whenever the core is not empty, it coincides with the bargaining set ℳⁱ ₁. Our discussion employs a generalization of balancedness to games with coalition structures. Received: August 2001/Revised version: April 2002     

The core and the bargaining set in glove-market games

In a glove-market game, the worth of a coalition is defined as the minimum, over all commodities in the market, of the total quantity that the coalition owns of each commodity. We identify a subclass of these games for which the core and the bargaining set coincide with the set of competitive equilibrium outcomes. We present examples showing that these solution concepts differ outside that subclass. We also illustrate a peculiar behavior of the bargaining set with respect to replication of a glove-market. These examples provide a simple economic setting in which the merits of the various solution concepts may be discussed and compared.Correspondence with Michael Maschler is gratefully acknowledged.This authors work was partly done while visiting the Department of Mathematics, Massachusetts Institute of Technology. Research supported by the Fund for the Promotion of Research at the Technion.     

The reactive bargaining set of some flow games and of superadditive simple games

We prove that the reactive bargaining set coincides with the core of simple flow games, and it essentially coincides with the kernel of simple superadditive games.     

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     

Stakeholder bargaining games

We study bilateral bargaining problems with an interested third party, the stakeholder, that enjoys benefits upon a bilateral agreement. To address the strategic implications of stakeholders over negotiations, we consider a model where two bargainers interact in the presence of a third party that (a) can transfer a share of her benefits to the bargainers but cannot receive a share of the bilateral surplus, and (b) while she may not participate in all periods of the negotiation, she cannot remain entirely inhibited. Our main findings are:(1) the stakeholder’s (reverse) liquidity constraint implies the existence of a multiplicity of stationary subgame perfect equilibria that include outcomes with very asymmetric bilateral agreements, and (2) the partial participation of the stakeholder may be the source of severe inefficiency     

ψ-Stability of a cooperative game without side payments

In the present paper we defineψ-stability for theAumann-Peleg theory of cooperative games without side payments, and we prove some theorems which are analogous to the core theorem byAumann andBurger. These theorems provide foundations of the theory ofψ-stability for cooperative games without side payments in addition to being of interest for their own sake. We also consider the composition of two admissible functionsψ ₁ andψ ₂.     

The core of a cooperative game without side payments

For cooperative games without side payments, there are several types of conditions which guarantee nonemptiness of the core, for example balancedness and convexity. In the present paper, a general condition for nonempty core is introduced which includes the known ones as special cases. Moreover, it is shown that every game with nonempty core satisfies this condition.     

Generalised bargaining sets for cooperative games

Although theM ₁ -bargaining set for games with side payments is known to exist, it frequently contains payoffs which are highly inequitable. For this reason the more restrictedM ₂-bargaining set is of interest. SinceM ₂ is not known to exist in general, this paper introduces anM _*-bargaining set, contained inM ₁ and containingM ₂, and presents an existence theorem. For the class of symmetric, simple games with decreasing returns, theM ₂ -bargaining set is shown to exist, and a fairly severe restriction on payoffs satisfyingM ₂ -stability is obtained.     

The nonemptiness of thef-core of a game without side payments

We prove the nonemptiness of the core of a continuum game without side payments where only small coalitions — ones bounded in absolute size of finite cardinality — are permitted. This result covers assignment games with a continuum of players and includes combinations of several assignment games, such as housing and automobile markets.The authors thank two anonymous referees for many helpful comments. The second author is indebted primarily to the Natural Sciences and Engineering Research Council of Canada for financial support and also the Social Sciences and Humanities Research Council of Canada.     

On the non-emptiness of the one-core and the bargaining set of committee games

We study the committee decision making process using game theory. Shenoy  [15] introduced two solution concepts: the one-core and the bargaining set, and showed that the one-core of a simple committee game is nonempty if there are at most four players. We extend this result by proving that whether the committee is simple or not, as far as there are less than five players, the one-core is nonempty. This result also holds for the bargaining set.     

The reactive bargaining set: Structure, dynamics and extension to NTU games

The reactive bargaining set (Granot [1994]) is the set of outcomes for which no justified objection exists. Here, in a justified objection the objector first watches how the target tries to act (if he has such an option), and then reacts by making a profit and ruining the target's attempt to maintain his share. In this paper we explore properties of the reactive bargaining set, set up the system of inequalities that defines it, and construct a dynamic system in the sense of Stearns' transfer scheme that leads the players to this set. We also extend the definition of the reactive bargaining set toNTU games in a way that keeps it nonempty. To shed light on its nature and its relative ease of computation, we compute the reactive bargaining set for games that played important role in the game theory literature.     

An equitable solution for multicriteria bargaining games

In this paper we study bargaining models where the agents consider several criteria to evaluate the results of the negotiation process. We propose a new solution concept for multicriteria bargaining games based on the distance to a utopian minimum level vector. This solution is a particular case of the class of the generalized leximin solutions and can be characterized as the solution of a finite sequence of minimax programming problems.