N-person Cooperative Game Research Articles

Syntax- und Semantikkoordination im Dialog

‘Coordination’ as used here is understood in the following way: Agents solve problems in on-going dialogue under mutual control and according to stable, well-understood patterns. In task-oriented dialogue the social frame for coordination is fixed. The need for coordination among agents arises because of differences in information, the dominant dialogue pattern ‘directive — reply’, and because of incompatibilities with respect to speakers’ ontologies, language variation and agents’ focus management. We discuss three dialogue examples showing coordination in some detail. In all of them the coordination problem is solved via a side sequence. Side sequences can be implemented either as autonomous dialogue contributions or they can be fused into the utterances they start from. Grammars treating ‘syntax-in-dialogue’ and, above all, side sequences, have to meet several constraints: They must describe various forms of extraposition to the right and long distance dependencies, produce and analyse by increments, and shift from production to reception and vice versa. All these patterns will be of relevance for the man-machine-interaction focused upon in the research unit „Situated Artificial Communicators“. It is suggested to set up the theory of grammar needed to accomplish all that within a theory of n-Person Cooperative Games.

Approximate Core Allocation for Binpacking Games

A binpacking game is a cooperative N-person game, where the set of players consists of k bins of size 1 and n items of sizes a1,..., an. The value of a coalition of bins and items is the maximum total size of items in the coalition that can be packed into the bins of the coalition. Our main result asserts that for every $\epsilon > 0$, there exist $\epsilon$-approximate core allocations provided k is large enough. Moreover, for every fixed $\delta > 0$, the smallest $\epsilon$ for which the $\epsilon$-approximate core of a given binpacking game is nonempty can be computed in polynomial time with error at most $\delta$, provided k is sufficiently large. We furthermore derive more specialized results for some subclasses of binpacking games.

The Organizational Economics of Risk Pooling

The need to share or pool risk is an important economic determinant of cooperation among firms, but the economic theory of risk pooling has been clouded by an error made in a seminal paper in the 1960s. Even into this decade, writers on risk and insurance have asserted that the market mechanism cannot bring a risk pool to an economically efficient outcome, concluding therefore that the risk pool must be analyzed as an n-person cooperative game. This paper describes clearly the economic structure of a risk pool and shows how the market mechanism can function to solve the organizational problem of a risk pool. This analysis reveals a twin interpretation of risk pooling, both as a competitive market and as a centrally administered cooperative organization. One significant feature of organized risk pooling is that the centralized solution is not incentive compatible, meaning that self-interested participants could misrepresent their attitude toward risk and skew the allocation of risk in their favor. However, there are economic conditions that mitigate the incentive incompatibility and tend to restore efficiency to the centralized pooling solution.

Probabilistic Values on Convex Geometries

A game on a convex geometry is a real-valued function defined on the family L of the closed sets of a closure operator which satisfies the finite Minkowski-Krein-Milmanproperty. If L is the Boolean algebra 2N, then we obtain an n-person cooperative game. We will extend the work of Weber on probabilistic values to games on convex geometries. As a result, we obtain a family of axioms that give rise to several probabilistic values and a unique Shapley value for games on convex geometries.

NETWORK EXCHANGE AS A COOPERATIVE GAME

This paper presents parallels between network exchange experiments and N-person cooperative games with transferable utility, to show how game theory can assist network exchange researchers, not only in predicting outcomes, but in properly specifying the scope of their models. It illustrates how utility, strategy and c-games, concepts found in game theory, could be used by exchange theorists to help them reflect on their models and improve their research design. One game theoretic solution concept, the kernel, is compared to recent network exchange algorithms as an illustration of how easy it is to apply game theory to the exchange network situation. It also illustrates some advantages of using a game theory solution concept to model network exchange.

Least Cores and Nucleoli in a Multi-Commodity Game

In a multi-commodity game, we consider e-cores, least cores and nucleoli, which are originally defined in a conventional n-person cooperative game in characteristic function form. First we review the definition of a multi-commodity game and the concept of the core, and then introduce concepts of e-cores and least cores. Employing excess functions in the multi-commodity game, the cores, the ε-cores and the least cores are redefined, and nucleoli are defined. To compute solutions, we classify excess functions into two categories and give two instances for each category, and briefly mention the difference among them. We develop computational methods for obtaining a point in each of the least cores under some assumptions and illustrate one of the methods with a numerical example. Finally we refer to methods for obtaining a point in each of the nucleoli.

New mathematical properties of the Banzhaf value

A new axiomatic characterization of the Banzhaf value for a cooperative n-person game with transferable utilities is given, by using a new potential function. In the space of all games with a fixed set of players a potential basis has been found, which allows an explicit representation of all games with an apriori given Banzhaf value.

Meaningful and Meaningless Solutions for Cooperative N-person Games

<p>Game values often represent data that can be measured in more<br />than one acceptable way (e.g. monetary amounts). We point out that<br />in such a case a statement about cooperative n-person game model<br />might be "meaningless" in the sense that its truth or falsity depends on<br />the choice of an acceptable way to measure game values. In particular<br />we analyze statements about solution concepts such as the core, stable<br />sets, the nucleolus, the Shapley value (and its generalizations).</p><p>Keywords: Cooperative n-person Games, Measurement, Sensitivity<br />Analysis.</p>

Dual representation of cooperative games based on fenchel-moreau conjugation

A dual representation for n-person cooperative games with transferable utility, called the indirect function, is introduced and studied. It contains the same information as the characteristic function since there are simple formulas for obtaining each from the other. Indirect functions are characterized as certain nonincreasing polyhedral convex functions; their relations with the associated characteristic functions are analyzed by means of Fenchel-Moreau generalized conjugation theory. Many concepts in the theory of cooperative games can be easily expressed in terms of indirect functions. In the case of monotone games, the relationship between characteristic and indirect functions takes a simpler form

Bargaining in n -person cooperative games with linearly distributed, transferable utility

Coalitional aspects of bargaining are investigated. Binary trees describe coalition structures; at a vertex the payoffs are distributed linearly according to parameters for the two sets. The parameter for a player-set is assumed to be the sum of the parameters in that set. These values are the subject of bargaining. The criteria for the results of bargaining are formulated, thus determining a bargaining point(s) in the space R of the parameters. R can be divided into regions in which a particular tree is maximal. In completely essential 3-player games these regions are simply connected; the bargaining point is where these regions meet. The solutions for 4- and n -player games present immense problems. Our solutions are compared with other solution concepts. We show that in the 3-player game our solution is monotonic but not completely coalitionally monotonic.

A lexicographical solution concept in an n-person cooperative fuzzy game

Abstract In this paper, a new solution concept in an n -person cooperative fuzzy game with sidepayment is proposed. We first define an excess with respect to a player in a fuzzy game with sidepayment. Usually, the concept of an excess is defined for each coalition. In contrast however, we define an excess of a player by summing up all the excess of a coalition to which he belongs. By considering a payoff vector which minimizes the excess of a player in the lexicographical order, we proposed a new solution concept in a fuzzy game as well as in a nonfuzzy game. Then, we further consider the problem to extend a nonfuzzy game into a fuzzy game. Such an extension can be described by the mappings from a characteristic function in a nonfuzzy game into a characteristic function in a fuzzy game. An illustrative numerical example of the proposed solution concept to some extended fuzzy games is also presented.

Game-Theory Models for Exchange Networks: Experimental Results

The goal of current exchange-network literature is to develop algorithms, loosely based on rational choice, that predict how resources are distributed through exchange networks and which positions have power to accumulate resources. These objectives closely resemble those of N-person cooperative games with transferable utility, which are based on formal explicit models of rational choice. Experimentally, power is exhibited when a position can amass a favorable proportion of available resources by negotiating a division with another network member. Game-theory solution concepts that address the question of power in networks are introduced and compared to network-exchange models to evaluate the effectiveness of the game-theory solutions and those of exchange theory in predicting results observed in experiments. Experimental data show that there is a utility in incorporating game theory into the discussion of exchange in negatively connected networks. Furthermore, the use of game theory leads to a more comprehensive understanding of many processes to which exchange theory is insensitive.

N-Person cooperative games with transferable utility: I. The formation of coalitions

We consider the way that players and subcoalitions bargain with each other to form the grand coalition before play occurs. A digraph can be used to describe a particular coalition structure and it is argued that there exists an imputation for each structure. It is shown that there exists at least one subcoalition which loses if a coalition breaks up. So the ‘optimal’ structure consists of indissoluble coalitions, and the resulting digraphs are trees. Arguments are presented for a preference rule which says that for three subcoalitions, two will prefer to join together and then join with the third rather than all three joining together simultaneously. The optimal tree is thus a binary tree.

N-Person cooperative games with transferable utility: II. Side-payment distribution and equilibrium coalition trees for indissoluble coalitions

We suggest a general rule for the distribution of side-payments. With specific values the rule can be used to calculate the imputation for any given coalition structure (tree). An equilibrium structure is defined as that structure in which no coalition can benefit by a move which does not disturb the structure of the other players. It is shown that, for a linear rule, there is always an equilibrium tree and methods of finding such trees are discussed.

MERGER ACTIVITY AND MANAGERIAL COMPENSATION

A theoretical monopolistic economy is developed to explain relationships between merger activity and managerial compensation packages. In this economy, managers are assigned to and compensated by firms based on models established in “n” person cooperative game theory. Compensation packages offered to managers of potential acquiring firms are studied with respect to their impact on managers' willingness to initiate profitable merger bids. The model explains why overall merger returns decrease as the size of the target firm relative to the bidding firm increases. Model results are consistent with numerous other empirical findings regarding merger profit distributions.

Lexicographic optimality in the multiple objective linear programming: The nucleolar solution

In this paper we study the problem of multiple objective linear programming (MOLP). We introduce a new solution concept which is related to that of the nucleolus of n-person cooperative game theory. We prove that a general MOLP problem always has a solution in the new sense. The points in the nucleolus are efficient in the classic way. We prove existence and at the same time we introduce a constructing algorithm for computing it.

N人協力ゲームにおけるファジィ決定に基づく解の概念

n人協力ゲームにおけるファジィ決定に基づく解の概念

Consideration of Fairness form n-Person Cooperative Game

Consideration of Fairness form n-Person Cooperative Game

On finding the nucleolus of an n-person cooperative game

Kohlberg (1972) has shown how the nucleolus for ann-person game with side-payments may be found by solving a single minimization LP in case the imputation space is a polytope. However the coefficients in the LP have a very wide range even for problems with 3 or 4 players. Therefore the method is computationally viable only for small problems on machines with finite precision. Maschler et al. (1979) find the nucleolus by solving a sequence of minimization LPs with constraint coefficients of either −1, 0 or 1. However the number of LPs to be solved is o(4 n ). In this paper, we show how to find the nucleolus by solving a sequence of o(2 n ) LPs whose constraint coefficients are −1, 0 or 1.

A cost allocation method for facilities siting with fixed-charge cost functions

Abstract The fixed-charge plant location problem determines the sites at which to place central treatment facilities as well as the assignments of communities to those facilities. We show here that the mathematical programming dual of a special version of the plant location model provides cost allocations to the communities which satisfy the core conditions of an n-person cooperative game. These cost allocations are faulted- because they may fail to provide equity among the participants. A new methodology is proposed, the Separable Costs Opening Cost method (SCOC), to allocate costs among the participants once the optimal set of facilities and coalitions has been determined. The SCOC is guaranteed to determine allocations which are insidexhe core and hence increase the fairness of the allocation.