The strategy structure of some coalition formation games

In coalitional games with side payments, the core predicts which coalitions form and how benefits are shared. The predictions however run into difficulties if the core is empty or if some coalitions benefit from not blocking truthfully. These difficulties are analyzed in games in which an a priori given collection of coalitions can form, as the collection of pairs of buyer-seller in an assignment game. The incentive properties of the core and of its selections are investigated in function of the collection. Furthermore the relationships with Vickrey-Clarke-Groves mechanisms are drawn.coalition formation ; assignment ; manipulability ; substitutes ; incremental value ; Vickrey-Clarke-Groves mechanism

The strategy structure of some coalition formation games

In coalitional games with side payments, the core predicts which coalitions form and how benefits are shared. The predictions however run into difficulties if the core is empty or if some coalitions benefit from not blocking truthfully. These difficulties are analyzed in games in which an a priori given collection of coalitions can form, as the collection of pairs of buyer-seller in an assignment game. The incentive properties of the core and of its selections are investigated in function of the collection. Furthermore the relationships with Vickrey-Clarke-Groves mechanisms are drawn.Dans un jeu coopératif à paiements latéraux, le coeur prédit quels arrangements de la société sont stables vis-à-vis des possibilités de blocage par les coalitions. Ces prédictions ne sont pas opérationnelles si tout arrangement est bloqué (le coeur est vide) ou si les coalitions n'ont pas d'incitation à bloquer comme le suppose la théorie. Nous analysons ces difficultés dans des jeux où la collection des coalitions qui peuvent se former est a priori restreinte. C'est par exemple le cas dans un jeu de marché lorsque seules les paires acheteur-vendeur sont essentielles. Les propriétés stratégiques du coeur et de ses sélections sont étudiées en fonction de la collection des coalitions admissibles. De plus, les relations avec les mécanismes de Vickrey-Clarke-Groves sont développées

Formation of coalition structures as a non-cooperative game

Traditionally social sciences are interested in structuring people in multiple groups based on their individual preferences. This pa- per suggests an approach to this problem in the framework of a non- cooperative game theory. Definition of a suggested finite game includes a family of nested simultaneous non-cooperative finite games with intra- and inter-coalition externalities. In this family, games differ by the size of maximum coalition, partitions and by coalition structure formation rules. A result of every game consists of partition of players into coalitions and a payoff? profiles for every player. Every game in the family has an equilibrium in mixed strategies with possibly more than one coalition. The results of the game differ from those conventionally discussed in cooperative game theory, e.g. the Shapley value, strong Nash, coalition-proof equilibrium, core, kernel, nucleolus. We discuss the following applications of the new game: cooperation as an allocation in one coalition, Bayesian games, stochastic games and construction of a non-cooperative criterion of coalition structure stability for studying focal points.Comment: arXiv admin note: text overlap with arXiv:1612.02344, arXiv:1612.0374

Coalitional Games in MISO Interference Channels: Epsilon-Core and Coalition Structure Stable Set

The multiple-input single-output interference channel is considered. Each transmitter is assumed to know the channels between itself and all receivers perfectly and the receivers are assumed to treat interference as additive noise. In this setting, noncooperative transmission does not take into account the interference generated at other receivers which generally leads to inefficient performance of the links. To improve this situation, we study cooperation between the links using coalitional games. The players (links) in a coalition either perform zero forcing transmission or Wiener filter precoding to each other. The $\epsilon$-core is a solution concept for coalitional games which takes into account the overhead required in coalition deviation. We provide necessary and sufficient conditions for the strong and weak $\epsilon$-core of our coalitional game not to be empty with zero forcing transmission. Since, the $\epsilon$-core only considers the possibility of joint cooperation of all links, we study coalitional games in partition form in which several distinct coalitions can form. We propose a polynomial time distributed coalition formation algorithm based on coalition merging and prove that its solution lies in the coalition structure stable set of our coalition formation game. Simulation results reveal the cooperation gains for different coalition formation complexities and deviation overhead models.Comment: to appear in IEEE Transactions on Signal Processing, 14 pages, 14 figures, 3 table

Dynamic club formation with coordination

We present a dynamic model of jurisdiction formation in a society of identical people. The process is described by a Markov chain that is defined by myopic optimization on the part of the players. We show that the process will converge to a Nash equilibrium club structure. Next, we allow for coordination between members of the same club,i.e. club members can form coalitions for one period and deviate jointly. We define a Nash club equilibrium (NCE) as a strategy configuration that is immune to such coalitional deviations. We show that, if one exists, this modified process will converge to a NCE configuration with probability one. Finally, we deal with the case where a NCE fails to exist due to indivisibility problems. When the population size is not an integer multiple of the optimal club size, there will be left over players who prevent the process from settling down. We define the concept of an approximate Nash club equilibrium (ANCE), which means that all but k players are playing a Nash club equilibrium, where k is defined by the minimal number of left over players. We show that the modified process converges to an ergodic set of states each of which is ANCE

Coalitional Approaches to Collusive Agreements in Oligopoly Games.

In this paper we review a number of coalitional solution concepts for the analysis of the stability of cartels and mergers under oligopoly. We show that, although so far the industrial organization and the cooperative game-theoretic literature have proceeded somehow independently on this topic, the two approaches are highly inter-connected. We first consider the basic problem of the stability of the whole industry association of firms under oligopoly and, for this purpose, we introduce the concept of core in games with externalities. We show that different assumptions on the behaviour as well as on the timing of the coalitions of firms yield very di¤erent results on the set of allocations which are core-stable. We then consider the stability of associations of firms organized in coalition structures different from the grand coalition. To this end, various coalition formation games recently introduced by the so called endogenous coalition formation literature are critically reviewed. Again, di¤erent assumptions concerning the timing and the behaviout of firms are shown to yield a wide range of different results.Cooperative Games, Coalitions, Mergers, Cartels, Core, Games with Externalities, Endogenous Coalition Formation.

Coalition Formation and Potential Games

In this paper we study the formation of coalition structures in situations described by a cooperative game. Players choose independently which coalition they want to join. The payoffs to the players are determined by an allocation rule on the underlying game and the coalition structure that results from the strategies of the players according to some formation rule. We study two well-known coalition structure formation rules. We show that for both formation rules there exists a unique component efficient allocation rule that results in a potential game and study the coalition structures resulting from potential maximizing strategy profiles.cooperative game;coalition formation;potential game;potential maximizer

MIMO-OFDM Based Energy Harvesting Cooperative Communications Using Coalitional Game Algorithm

This document is the Accepted Manuscript version. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.In this paper, we consider the problem of cooperative communication between relays and base station in an advanced MIMO-OFDM framework, under the assumption that the relays are supplied by electric power drawn from energy harvesting (EH) sources. In particular, we focus on the relay selection, with the goal to guarantee the required performance in terms of capacity. In order to maximize the data throughput under the EH constraint, we model the transmission scheme as a non-transferable coalition formation game, with characteristic function based on an approximated capacity expression. Then, we introduce a powerful mathematical tool inherent to coalitional game theory, namely: the Shapley value (Sv) to provide a reliable solution concept to the game. The selected relays will form a virtual dynamically-configuredMIMO network that is able to transmit data to destination using efficient space-time coding techniques. Numerical results, obtained by simulating the EH-powered cooperativeMIMO-OFDMtransmission with Algebraic Space-Time Coding (ASTC), prove that the proposed coalitional game-based relay selection allows to achieve performance very close to that obtained by the same system operated by guaranteed power supply. The proposed methodology is finally compared with some recent related state-of-the-art techniques showing clear advantages in terms of link performance and goodput.Peer reviewe