A COALITION APPROACH TO THE MANAGEMENT OF HIGH SEAS FISHERIES IN THE PRESENCE OF EXTERNALITIES

ABSTRACT. The current paper extends the coalition approach of the management of high seas fisheries to the presence of externalities. The coalition approach is set within the framework of a two‐stage game in which the payoffs depend on the entire coalition structure and are determined through a partition function. The relationship between the presence of externalities and the stability of the coalition structures is explored. The equilibrium coalition structures of the game are also examined. The application of the game to the Northern Atlantic bluefin tuna shows a typical picture of the high seas fisheries: the simultaneous presence of strong externalities in the coalition structures and the absence of stability of the grand coalition. A fundamental conclusion of this paper is that, generally, in order to guarantee the stability of the cooperative agreements it is not sufficient to implement a fair sharing rule for the distribution of the returns from cooperation. Stability requires a legal regime preventing the players that engage in noncooperative behavior from having access to the resource.     

The collective value: a new solution for games with coalition structures

In this study, we provide a new solution for cooperative games with coalition structures. The collective value of a player is defined as the sum of the equal division of the pure surplus obtained by his coalition from the coalitional bargaining and of his Shapley value for the internal coalition. The weighted Shapley value applied to a game played by coalitions with coalition-size weights is assigned to each coalition, reflecting the size asymmetries among coalitions. We show that the collective value matches exogenous interpretations of coalition structures and provide an axiomatic foundation of this value. A noncooperative mechanism that implements the collective value is also presented.     

Accessibility and stability of the coalition structure core

This article shows that, for any transferable utility game in coalitional form with a nonempty coalition structure core, the number of steps required to switch from a payoff configuration out of the coalition structure core to a payoff configuration in the coalition structure core is less than or equal to $(n^2+4n)/4$ , where $n$ is the cardinality of the player set. This number improves the upper bounds found so far. We also provide a sufficient condition for the stability of the coalition structure core, i.e. a condition which ensures the accessibility of the coalition structure core in one step. On the class of simple games, this sufficient condition is also necessary and has a meaningful interpretation.     

Negotiation,preferences over agreements,and the core

We analyze conditions under which negotiated agreements are efficient from the point of view of every possible coalition of negotiators. The negotiators have lexicographic preferences over agreements they reach. Their utility is the first criterion. The coalition reaching an agreement is the second criterion. In the analyzed non-cooperative discrete time bargaining game Γ the players bargain about the choice from the sets of utility vectors feasible for coalitions in a given NTU game (N, V). If Γ has a Markov perfect equilibrium, then the set of equilibrium utility vectors in Markov perfect equilibria in it equals the core of (N, V). I thank an anonymous referee, an anonymous Associate Editor, and the Editor for their comments that helped me to improve the paper. The research reported in this paper was supported by the Grant VEGA 1/1223/04 of the Ministry of Education of the Slovak Republic.     

Share functions for cooperative games with levels structure of cooperation

In a standard TU-game it is assumed that every subset of the player set N can form a coalition and earn its worth. One of the first models where restrictions in cooperation are considered is the one of games with coalition structure of Aumann and Drèze (1974). They assumed that the player set is partitioned into unions and that players can only cooperate within their own union. Owen (1977) introduced a value for games with coalition structure under the assumption that also the unions can cooperate among them. Winter (1989) extended this value to games with levels structure of cooperation, which consists of a game and a finite sequence of partitions defined on the player set, each of them being coarser than the previous one.     

On coalition formation: a game-theoretical approach

This paper deals with the question of coalition formation inn-person cooperative games. Two abstract game models of coalition formation are proposed. We then study the core and the dynamic solution of these abstract games. These models assume that there is a rule governing the allocation of payoffs to each player in each coalition structure called a payoff solution concept. The predictions of these models are characterized for the special case of games with side payments using various payoff solution concepts such as the individually rational payoffs, the core, the Shapley value and the bargaining set M₁ ⁽ⁱ⁾. Some modifications of these models are also discussed.     

On the Structural Stability of Values for Cooperative Games

It is generally assumed that any set of players can form a feasible coalition for classical cooperative games. But, in fact, some players may withdraw from the current game and form a union, if this makes them better paid than proposed. Based on the principle of coalition split, this paper presents an endogenous procedure of coalition formation by levels and bargaining for payoffs simultaneously, where the unions formed in the previous step continue to negotiate with others in the next step as “individuals,” looking for maximum share of surplus by organizing themselves as a partition. The structural stability of the induced payoff configuration is discussed, using two stability criteria of core notion for cooperative games and strong equilibrium notion for noncooperative games.

     

Coalition formation in the presence of continuing conflict

This paper studies endogenous coalition formation in a rivalry environment where continuing conflict exists. A group of heterogeneous players compete for a prize with the probability of winning for a player depending on his strength as well as the distribution of strengths among his rivals. Players can pool their strengths together to increase their probabilities of winning as a group through coalition formation. The players in the winning coalition will compete further until one individual winner is left. We show that in any equilibrium there are only two coalitions in the initial stage of the contest. In the case of three players, the equilibrium often has a coalition of the two weaker players against the strongest. The equilibrium coalition structure with four players mainly takes one of the two forms: a coalition of the three weaker players against the strongest or a coalition of the weakest and strongest players against a coalition of the remaining two. Our findings imply that the rivalry with the possibility of coalition formation in our model exhibits a pattern of two-sidedness and a balance of power. We further study the impact of binding agreements by coalition members on equilibrium coalition structures. Our analysis sheds some light on problems of temporary cooperation among individuals who are rivals by nature.     

Sequential Formation of Coalitions Through Bilateral Agreements in a Cournot Setting

We study a sequential protocol of endogenous coalition formation based on a process of bilateral agreements among the players. We apply the game to a Cournot environment with linear demand and constant average costs. We show that the final outcome of any subgame perfect equilibrium of the game is the grand coalition, provided the initial number of firms is high enough and they are sufficiently patient.This research was partially conducted while the first authors were visiting the Department of Economics of the Norwegien School of Economics and Business Administration (Bergen).     

On implementation via demand commitment games

A simple version of the Demand Commitment Game is shown to implement the Shapley value as the unique subgame perfect equilibrium outcome for any n-person characteristic function game. This improves upon previous models devoted to this implementation problem in terms of one or more of the following: a) the range of characteristic function games addressed, b) the simplicity of the underlying noncooperative game (it is a finite horizon game where individuals make demands and form coalitions rather than make comprehensive allocation proposals and c) the general acceptability of the noncooperative equilibrium concept. A complete characterization of an equilibrium strategy generating the Shapley value outcomes is provided. Furthermore, for 3 player games, it is shown that the Demand Commitment Game can implement the core for games which need not be convex but have cores with nonempty interiors. Received March 1995/Final version February 1997     

Edgeworth equilibrium in a model of interregional economic relations

We introduce an analog of an Edgeworth equilibrium for a class of multiregional economic systems. We analyze the game-theoretic aspects of the coalition stability of regional development plans and establish a quite general existence theorem for an Edgeworth equilibrium. We discuss the questions of coincidence of the set of these equilibria with the fuzzy core and the set of theWalrasian equilibria of the multiregional systemin question.Our methods rest on a systematic accounting for the polyhedrality of the sets of balanced coalition plans.     

Noncooperative formation of coalitions in hedonic games

We study a bargaining procedure of coalition formation in the class of hedonic games, where players’ preferences depend solely on the coalition they belong to. We provide an example of nonexistence of a pure strategy stationary perfect equilibrium, and a necessary and sufficient condition for existence. We show that when the game is totally stable (the game and all its restrictions have a nonempty core), there always exists a no-delay equilibrium generating core outcomes. Other equilibria exhibiting delay or resulting in unstable outcomes can also exist. If the core of the hedonic game and its restrictions always consist of a single point, we show that the bargaining game admits a unique stationary perfect equilibrium, resulting in the immediate formation of the core coalition structure.     

Stable profit sharing in a patent licensing game: general bargaining outcomes

By considering coalition structures formed by an external licensor of a patented technology and oligopolistic firms, we investigate licensing agreements that can be reached as bargaining outcomes under those coalition structures. The following results hold in a generalized patent licensing game. The core for a coalition structure is always empty, unless the grand coalition forms. We give a necessary and sufficient condition for the nonemptiness of the core (for the grand coalition). If the number of licensees that maximizes licensees’ total surplus is greater than the number of existing non-licensees, each symmetric bargaining set for a coalition structure is a singleton, and the optimal number of licensees that maximizes the licensor’s revenue is uniquely determined. The authors wish to thank the chief editor, anonymous referees, and participants in the 10th DC (Japan), the 3rd ICMA, and the 17th Stony Brook conference for helpful comments and suggestions. Thanks are extended to Ryo Kawasaki for editing English. They are partially supported by the MEXT Grant-in-Aid for 21 Century COE Program, Grant-in-Aid 18730517 (Watanabe), and Grant-in-Aid 16310107 (Muto).     

不确定条件下n人非合作博弈均衡点集的通有稳定性

基于经典博弈模型的Nash均衡点集的通有稳定性和具有不确定参数的n人非合作博弈均衡点的概念,探讨了具有不确定参数博弈的均衡点集的通有稳定性.参照Nash均衡点集稳定性的统一模式,构造了不确定博弈的问题空间和解空间,并证明了问题空间是一个完备度量空间,解映射是上半连续的,且解集是紧集（即usco（upper semicontinuous and compact-valued）映射）,得到不确定参数博弈模型的解集通有稳定性的相关结论.     

Core Solutions in Vector-Valued Games

In this paper, we analyze core solution concepts for vector-valued cooperative games. In these games, the worth of a coalition is given by a vector rather than by a scalar. Thus, the classical concepts in cooperative game theory have to be revisited and redefined; the important principles of individual and collective rationality must be accommodated; moreover, the sense given to the domination relationship gives rise to two different theories. Although different, we show the areas which they share. This analysis permits us to propose a common solution concept that is analogous to the core for scalar cooperative games.     

On the core of cost-revenue games: Minimum cost spanning tree games with revenues

In this paper, we analyze cost sharing problems arising from a general service by explicitly taking into account the generated revenues. To this cost-revenue sharing problem, we associate a cooperative game with transferable utility, called cost-revenue game. By considering cooperation among the agents using the general service, the value of a coalition is defined as the maximum net revenues that the coalition may obtain by means of cooperation. As a result, a coalition may profit from not allowing all its members to get the service that generates the revenues. We focus on the study of the core of cost-revenue games. Under the assumption that cooperation among the members of the grand coalition grants the use of the service under consideration to all its members, it is shown that a cost-revenue game has a nonempty core for any vector of revenues if, and only if, the dual game of the cost game has a large core. Using this result, we investigate minimum cost spanning tree games with revenues. We show that if every connection cost can take only two values (low or high cost), then, the corresponding minimum cost spanning tree game with revenues has a nonempty core. Furthermore, we provide an example of a minimum cost spanning tree game with revenues with an empty core where every connection cost can take only one of three values (low, medium, or high cost).     

Computing solutions for matching games

A matching game is a cooperative game (N, v) defined on a graph G = (N, E) with an edge weighting w: E? \mathbb R₊{w: E\to {\mathbb R}_+}. The player set is N and the value of a coalition S í N{S \subseteq N} is defined as the maximum weight of a matching in the subgraph induced by S. First we present an O(nm + n ² log n) algorithm that tests if the core of a matching game defined on a weighted graph with n vertices and m edges is nonempty and that computes a core member if the core is nonempty. This algorithm improves previous work based on the ellipsoid method and can also be used to compute stable solutions for instances of the stable roommates problem with payments. Second we show that the nucleolus of an n-player matching game with a nonempty core can be computed in O(n ⁴) time. This generalizes the corresponding result of Solymosi and Raghavan for assignment games. Third we prove that is NP-hard to determine an imputation with minimum number of blocking pairs, even for matching games with unit edge weights, whereas the problem of determining an imputation with minimum total blocking value is shown to be polynomial-time solvable for general matching games.     

Non-binding agreements and fairness in commons dilemma games

Usually, common pool games are analyzed without taking into account the cooperative features of the game, even when communication and non-binding agreements are involved. Whereas equilibria are inefficient, negotiations may induce some cooperation and may enhance efficiency. In the paper, we propose to use tools of cooperative game theory to advance the understanding of results in dilemma situations that allow for communication. By doing so, we present a short review of earlier experimental evidence given by Hackett, Schlager, and Walker 1994 (HSW) for the conditional stability of non-binding agreements established in face-to-face multilateral negotiations. For an experimental test, we reanalyze the HSW data set in a game-theoretical analysis of cooperative versions of social dilemma games. The results of cooperative game theory that are most important for the application are explained and interpreted with respect to their meaning for negotiation behavior. Then, theorems are discussed that cooperative social dilemma games are clear (alpha- and beta-values coincide) and that they are convex (it follows that the core is “large”): The main focus is on how arguments of power and fairness can be based on the structure of the game. A second item is how fairness and stability properties of a negotiated (non-binding) agreement can be judged. The use of cheap talk in evaluating experiments reveals that besides the relation of non-cooperative and cooperative solutions, say of equilibria and core, the relation of alpha-, beta- and gamma-values are of importance for the availability of attractive solutions and the stability of the such agreements. In the special case of the HSW scenario, the game shows properties favorable for stable and efficient solutions. Nevertheless, the realized agreements are less efficient than expected. The realized (and stable) agreements can be located between the equilibrium, the egalitarian solution and some fairness solutions. In order to represent the extent to which the subjects obey efficiency and fairness, we present and discuss patterns of the corresponding excess vectors.     

Stability and index of the meet game on a lattice

We study the stability and the stability index of the meet game form defined on a meet semilattice. Given any active coalition structure, we show that the stability index relative to the equilibrium, to the beta core and to the exact core is a function of the Nakamura number, the depth of the semilattice and its gap function.     

Cooperative grey games and the grey Shapley value

This contribution is located in the common area of operational research and economics, with a close relation and joint future potential with optimization: game theory. We focus on collaborative game theory under uncertainty. This study is on a new class of cooperative games where the set of players is finite and the coalition values are interval grey numbers. An interesting solution concept, the grey Shapley value, is introduced and characterized with the properties of additivity, efficiency, symmetry and dummy player, which are straightforward generalizations of the corresponding properties in the classical cooperative game theory. The paper ends with a conclusion and an outlook to future studies.