Coalition Of Players Research Articles

Elephant in the Room: How to Assess the Vote-weighting System in the Council of the EU

The article emphasises the complementarity of research based on voting power theory with the analysis of the structure of blocking. Combining both methods enables a more comprehensive assessment of the vote weighting system in the Council of the EU, in particular the impact of changes in the voting system on the position of individual Member States and the power balance in this institution. I make two contributions to the existing literature. Firstly, the study develops a non-random voting model, dedicated to QMV in the Council, which abandons the assumption that each coalition of players is equally likely and takes into account the role of the European Commission as an agenda-setter. This not only allows us to exclude many coalitions that are only theoretically possible, but also to analyse the blocking structure from the perspective of different states or coalitions in the Council. Secondly, it shows that the application of blocking structure analysis provides novel insights into the Council’s voting system. Unlike the a priori voting power approach, such analysis does not focus on distribution of winning power in the Council, but on the Member States’ ability to build minimal blocking coalitions. Hence, it complements the application of mathematical indices of voting power in the assessment of the voting system in this institution.

Post-Brexit council: winners and losers after the UK’s withdrawal from the EU

ABSTRACT This paper examines the impact of Brexit on the voting system in the Council. For this purpose, the study is developing a new voting model which abandons the assumption that each coalition of players is equally likely. The analysis focuses on the structure of blocking for the voting game. I find that for seven most populous Member States, Brexit has had profound effects on their ability to build minimal blocking coalitions in the Council when QMV is used. The Germany’s ability to build the smallest blocking coalitions has increased dramatically. The position of Italy and Spain, and consequently that of the Mediterranean states, has also been strengthening. Moreover, France has become a pivotal player in the disputes between the North and the South. These findings have important implications for institutional design, negotiations between Member States in the Council and the European Commission’s legislative influence as an agenda-setter.

Altruistic behavior and international environmental agreements: a differential game approach

AbstractIn the last three decades International Environmental Agreements (IEAs) have been widely analyzed. Classic models predict that only coalitions formed by a few countries can be stable, generating a rich literature devoted to solving the small coalition puzzle. The fundamental idea behind the great part of the literature is that players are selfish: to achieve a large stable coalition it is necessary to design an agreement that includes a credible system of incentives or punishments. The aim of this model is to study the effects, on equilibrium strategies and on the stability of an IEA, of players that do not look only at their own interests, but that take care of the wellness of the other players in coalition. Following the approach of the Paris Agreement in 2015, countries that join the coalition do not decide emissions collectively, but each of them sets their own emissions. The model is the usual two-step game: first the players have to choose whether they want to join the coalition or not, in the second step they solve a Nash differential game to find the optimal emissions. The stability of the coalition is studied in two cases: (i) with the classic internal and external stability, (ii) defining an altruistic stability condition.

A coalitional differential game of vaccine producers

The paper proposes a game-theoretic model of competition and cooperation of vaccine producers. Various versions of players' cooperation (partial and full) have been studied. The differential game has an infinite duration. For each possible coalition of players, the profits and production quantities of its members are determined. An stability analysis of possible coalition structures, as well as coalitions that are most attractive to customers has been made.

A Coalitional Differential Game of Vaccine Producers

The paper proposes a game-theoretic model of competition and cooperation, including partial cooperation, of vaccine producers. Various versions of players’ cooperation (partial and full) have been studied. The differential game has an infinite duration. For each possible coalition of players, the profits and production quantities of its members are determined. An stability analysis of possible coalition structures, as well as coalitions that are most attractive to customers has been made.

Values of games over Boolean player sets

In this paper, we study new classes of value operators for coalitional games with players organized into a boolean algebra. Coalitional games are cooperative models in which players can form coalitions to maximize profit. The basic solution concepts in such game scenarios are value operators, which assign a unique real value to every player, reflecting thus selected principles of economic rationality. Some value concepts were extended beyond the classic coalitional model where every coalition of players can form. In particular, the extension of Shapley value exists for coalitional games in which players are partially ordered, and the feasible coalitions are the corresponding down-sets. Interestingly, this game-theoretic framework was employed in the method called Information Attribution. This method aims to solve the information decomposition problem, which asks for a particular additive decomposition of the mutual information between the input and target random variables. In such information-theoretic games, the players are predictors, and their set has the natural structure of a boolean algebra. Motivated by the original problem, we consider coalitional games where the players form a boolean algebra, and the coalitions are the corresponding down-sets. This more general approach enables us to study various value solution concepts in detail. Namely, we focus on the classes of values that can represent alternatives to the solution of the information decomposition problem, such as random-order values or sharing values. We extend the axiomatic characterization of some classes of values that were known only for the standard coalitional games.

Directed communication in games with directed graphs

AbstractWe introduce a novel concept of directed communication and a related connectedness in directed graphs, and apply this to model certain cooperation restrictions in cooperative games. In the literature on communication in directed networks or directed graphs, one can find different notions of connectedness, and different ways how directed communication restricts cooperation possibilities of players in a game. In this paper, we introduce a notion of connectedness in directed graphs that is based on directed paths. We assume that a coalition of players in a game can only cooperate if these players form a directed path in a directed communication graph. We define a restricted game following the same approach as Myerson for undirected communication situations, and consider the allocation rule that applies the Shapley value to this restricted game. We characterize this value by extended versions of the well-known component efficiency, fairness and balanced contributions axioms. Moreover, using the new notion of connectedness, we apply this allocation rule to define network centrality, efficiency and vulnerability measures for directed networks.

Programming models-based method for deriving profits allocation scheme with interval-valued cooperative games

Owing to the fact that the payoff of grand coalition is limited to players’ allocation, what is more, other players will not satisfy with the allocation scheme if one of the possible coalitions allocate too much. Based on this fact, it is better to pursuit the allocation scheme of all players in coalition are as close to the coalition’s payoff as possible. In contrast, if the allocation scheme of all players in coalition is far from the coalition’s payoff, this will lead to the instability of the coalition. To address this issue, several linear programming models are constructed for taking into account the players in the coalition with compromise limit constraints. First, the profits allocation model with undominated nonnegative excess vector is extended to interval-valued fuzzy environments. Second, several linear programming models are constructed respectively considering without and with coalitions’ compromise limit constraints. Third, an illustrative example in conjunction with comparative analyses is employed to demonstrate the validity and applicability of the proposed models. Finally, the relationship of the models is discussed between without and with coalitions’ compromise limit constraints.

Sharing congestion management costs among system operators using the Shapley value

With energy generation becoming increasingly decentralized, the need for congestion management across grid voltage levels is also increasing. To enable fair sharing of congestion costs among grid operators, these costs must be allocated to congested grid elements. We propose using the Shapley value for this purpose. The Shapley value is a cooperative game theory concept that was developed to share a total surplus generated by a coalition of players between the players based on their marginal contributions to the coalition. We apply this concept to share the costs of congestion management between grid elements based on their contributions to overall congestion management costs. To reduce the computational complexity of the Shapley value, we introduce two novel simplification approaches and compare them to existing methods using a numerical example based on CIGRE benchmark grids. The first method exploits the fact that the characteristic function for the congestion costs is obtained from an optimal power flow computation (i.e., a constrained optimization problem). It utilizes knowledge about which constraints are non-binding in the optimization to derive the values of related coalitions without calculating them. The second method takes advantage of the fact that the congestion management cost-allocation game is monotone and derives the values of coalitions based on this property. Both methods are implemented and compared to sampling. Using the first method, we are able to reduce computational complexity to less than 20% of that of the original problem while maintaining exact results. Our second approach is not dependent on detailed knowledge of the underlying optimization problem and can reduce the computational time by almost half with exact results and much further when compromising precision. While the methods are presented through an application example, they can be applied to other games with similar properties.

A Family of Position Values for Directed Communication Situations

In this paper, we define a family of values for directed communication situations that are inspired by the position value. We use the concept of directed communication and related connectedness in directed graphs, under which a coalition of players in a game can only cooperate if these players form a directed path in a directed communication graph. By defining an arc game, which assesses the worth of coalitions of (directed) arcs in generating worth, we allocate the Shapley value payoff of each arc over the nodes incident with this arc, where we allow the head and tail to obtain a different share in this arc payoff. However, the way that the arc payoff is shared over its head and tail is uniform over all arcs. We characterize these values by connection efficiency and a modification of the classical balanced link contributions property for undirected communication situations, discriminating between the roles of the nodes as head and tail.

Word Sense Disambiguation using Cooperative Game Theory and Fuzzy Hindi WordNet based on ConceptNet

Natural Language is fuzzy in nature. The fuzziness of Hindi language was captured in the Fuzzy Hindi WordNet (FHWN) . FHWN assigned membership values to fuzzy relationships by consulting experts from various domains. However, these membership values need to be corrected. In the proposed work, we compute the membership values of fuzzy semantic relations using ConceptNet. Later, we perform WSD of Hindi text using cooperative game theoretic approach. We used the Shapley Value centrality measure where we predict which coalition of players (word senses) proves to be the most beneficial. We tested and compared our algorithm with the existing state-of-the-art approaches of Hindi on three datasets and results are better on all the three datasets. One more notable aspect is that the results are quite stable even if the fuzzy membership values of fuzzy graphs changes.

Dynamic Games with Incomplete Knowledge in Metric Spaces

We describe a model of a discrete time dynamic system with active elements (players) and states in a metric space. Each state is associated with the common utility value and player shares. Coalitions of players can change the system state, but each move requires their expenses. The players may have only restricted and local knowledge about the system. We define the concept of an equilibrium state in this dynamic game and present iterative algorithms that create feasible trajectories tending to equilibrium states under rather general conditions.

Tensor approximation of cooperative games and their semivalues

We propose an algorithm to approximate the semivalues of general transferable-utility cooperative games that involve a large set of players 1,…,|N| and possibly depend on uncertain parameters. We first encode the game's utility function using a low-rank tensor decomposition, namely the tensor train (TT) model, which requires a limited number of function evaluations. The TT format casts the utility as a compressed tensor of shape 2|N| and makes it possible to efficiently work with the exponentially-sized set of all possible coalitions of players. Given a game compressed in this manner, the proposed algorithm obtains arbitrary semivalues without incurring additional error, in particular the Shapley values and Banzhaf-Coleman indices, which are two of the most important allocation rules in cooperative game theory. Our algorithm takes O(|N|R2) operations per semivalue, where R is the game's TT rank. We show experimentally that many classical games can be compressed at low error with a moderate TT rank, making our algorithm more sample-efficient than Monte Carlo-based estimation. We also give a theoretical bound for the error of the semivalues obtained through our algorithm. Last, when the game depends on randomly distributed parameters, we are able to compute the expected semivalues efficiently.

The equal-surplus Shapley value for chance-constrained games on finite sample spaces

Many interactions from linear production problems, financial markets, or sequencing problems are modeled by cooperative games where payoffs to a coalition of players is a random variable. For this class of cooperative games, we introduce a two-stage value as an ex-ante agreement among players. Players are first promised their prior Shapley shares which are exactly their respective shares by the Shapley value of the expectation game. The final payoff vector is obtained by equally re-allocating the surplus when a realization of the random payoff of the grand coalition is observed. In support of the tractability of the newly introduced value called equal-surplus Shapley value, we provide a simple and compact formula. Depending on which probability distributions over the sample spaces are admissible, we present several characterization results of the equal-surplus Shapley value. This is achieved by using some classical axioms together with some other appealing axioms such as the independence of local duplication which simply requires that individual shares in a game remain unchanged when only certain events are duplicated in the sample space of a coalition without altering the probability of observing the others.

A short proof of convexity of step-out–step-in sequencing games

The Step out–Step in sequencing game is a particular example of a game from the sequencing game framework of Curiel, Perderzoli, and Tijs, where coalitions of players in a queue may reorder themselves to improve the their overall cost, under some restrictions. Musegaas, Borm and Quant proved, in two papers, that a simple greedy algorithm correctly computes the valuation of a coalition, and that the game is convex. These proofs entail rather involved case analyses; in this note, we give short proofs of both results.

New Characteristic Function for Two Stage Games with Spanning Tree

Two-stage n-player games with spanning tree are considered. The cooperative behaviour of players is defined. After the first stage, a specified player leaves the game with a probability that depends on the actions of all players in the first stage. A new approach to the construction of the characteristic function is proposed. In the game, all players are connected with the source directly or indirectly. Assume that the players in coalition N \ S have already connected to the source when the players in coalition S ⊂ N wish to connect to the source. The players in coalition S could connect to the source with the help of the players in coalition N \ S. A new characteristic function is de ned in the game, and the Shapley value is constructed. Several results based on the new characteristic function in the two-stage stochastic game are given.

The Prekernel of Cooperative Games with Alpha-Excess

In this paper, we introduce a new approach to measure the dissatisfaction for coalitions of players in cooperative transferable utility games. This is done by considering affine (and convex) combinations of the classical excess and the proportional excess. Based on this so-called alpha-excess, we defi ne new solution concepts for cooperative games, such as the alpha-prenucleolus and the alpha-prekernel. The classical prenucleolus and prekernel are a special case. We characterize the alpha-prekernel by strong stability and the alpha-balanced surplus property. Also, we show that the payoff vector generated by the alpha-prenucleolus belongs to the alpha-prekernel.

COMMON‐ENEMY EFFECTS: MULTIDISCIPLINARY ANTECEDENTS AND ECONOMIC PERSPECTIVES

AbstractA disparate literature hypothesizes what can broadly be described as the common‐enemy effect: the fact that the interaction with a common enemy (formed by Nature, an individual, or a group) increases cooperation. This review identifies the multidisciplinary antecedents of this effect, and then distinguishes between several strands of literature applying noncooperative game theory to account for it. A first strand argues that the threat posed by a common enemy makes each player's cooperative effort more critical. In a second strand a behavioral common‐enemy effect caused by group interaction is studied experimentally. A third strand models the common‐enemy effect as the formation of a coalition of players against another player in a contest. A fourth strand formalizes the principle that the ‘enemy of my enemy is my friend’, either in a model of social relations, interdependent altruistic preferences, or indirect reciprocity in repeated games. The connections between these strands of literature are investigated, and questions for future research are proposed.

Conventions under Heterogeneous Behavioural Rules

Abstract Strategies of players in a population are updated according to the behavioural rules of agents, where each agent is a player or a coalition of players. It is known that classic results on the stochastic stability of conventions are due to an asymmetry property of the strategy updating process. We show that asymmetry can be defined at the level of the behavioural rule and that asymmetric rules can be mixed and matched whilst retaining asymmetry of the aggregate process. Specifically, we show robustness of asymmetry to heterogeneity within an agent (Alice follows different rules at different times); heterogeneity between agents (Alice and Bob follow different rules); and heterogeneity in the timing of strategy updating. These results greatly expand and convexify the domain of behavioural rules for which results on the stochastic stability of conventions are known.

Strong Nash equilibria and mixed strategies

We study strong Nash equilibriain mixed strategies in finite games. A Nash equilibrium is strong if no coalition of players can jointly deviate so that all players in the coalition get strictly better payoffs. Our main result concerns games with two players and states that if a game admits a strong Nash equilibrium, then the payoff pairs in the support of the equilibrium lie on a straight line in the players’ utility space. As a consequence, the set of games that have a strong Nash equilibrium in which at least one player plays a mixed strategy has measure zero. We show that the same property holds for games with more than two players, already when no coalition of two players can profitably deviate. Furthermore, we show that, in contrast to games with two players, in a strong Nash equilibrium an outcome that is strictly Pareto dominated may occur with positive probability.