Uniqueness of Coalitional Equilibria

We provide an existence and a uniqueness result for coalitional equilibria of a game in strategic form. Both results are illustrated for a public good game and a homogeneous Cournot-oligopoly game.Existence and uniqueness of coalitional equilibrium, Game in strategic form

Hierarchical Cooperation for Operator-Controlled Device-to-Device Communications: A Layered Coalitional Game Approach

Device-to-Device (D2D) communications, which allow direct communication among mobile devices, have been proposed as an enabler of local services in 3GPP LTE-Advanced (LTE-A) cellular networks. This work investigates a hierarchical LTE-A network framework consisting of multiple D2D operators at the upper layer and a group of devices at the lower layer. We propose a cooperative model that allows the operators to improve their utility in terms of revenue by sharing their devices, and the devices to improve their payoff in terms of end-to-end throughput by collaboratively performing multi-path routing. To help understanding the interaction among operators and devices, we present a game-theoretic framework to model the cooperation behavior, and further, we propose a layered coalitional game (LCG) to address the decision making problems among them. Specifically, the cooperation of operators is modeled as an overlapping coalition formation game (CFG) in a partition form, in which operators should form a stable coalitional structure. Moreover, the cooperation of devices is modeled as a coalitional graphical game (CGG), in which devices establish links among each other to form a stable network structure for multi-path routing.We adopt the extended recursive core, and Nash network, as the stability concept for the proposed CFG and CGG, respectively. Numerical results demonstrate that the proposed LCG yields notable gains compared to both the non-cooperative case and a LCG variant and achieves good convergence speed.Comment: IEEE Wireless Communications and Networking Conference 201

Concept Lattices and Convexity of Coalitional Game Forms

The concept lattice of a coalitional game form is introduced and advocated as a structural classificatory tool. The basic properties of such lattices are studied. Sufficient concept-latticial properties for convexity of the underlying coalitional game form are identified. Spectral issues concerning widths and lengths of concept lattices of convex CGFs are also addressed

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

Spatial Pillage Game

A pillage game is a coalitional game as a model of Hobbesian anarchy. The spatial pillage game introduces a spatial feature into the pillage game. Players are located in regions and can travel from one region to another. The players can form a coalition and combine their power only within their destination regions, which limits the exertion of the power of each coalition. Under this spatial restriction, a coalition can pillage less powerful coalitions without any cost. The feasibility of pillages between coalitions determines the dominance relation that defines stable states in which powers among the players are endogenously balanced. With the spatial restriction, the set of stable states changes. However, if the players have forecasting ability, then the set of stable states does not change with the spatial restriction. Core, stable set, and farsighted core are adopted as alternative solution concepts.allocation by force, coalitional games, pillage game, spatial restriction, stable set, farsighted core

Coalitional Equilibria of Strategic Games

Let N be a set of players, C the set of permissible coalitions and G an N-playerstrategic game. A profile is a coalitional-equilibrium if no coalition permissible coalition in C has a unilateral deviation that profits to all its members. Nash-equilibria consider only single player coalitions and Aumann strong-equilibria permit all coalitions to deviate. A new fixed point theorem allows to obtain a condition for the existence of coalitional equilibria that covers Glicksberg for the existence of Nash-equilibria and is related to Ichiishi's condition for the existence of Aumann strong-equilibria.Fixed point theorems, maximum of non-transitive preferences, Nash and strong equilibria, coalitional equilibria

On Game Formats and Chu Spaces

It is argued that virtually all coalitional, strategic and extensive game formats as currently employed in the extant game-theoretic literature may be presented in a natural way as discrete nonfull or even-under a suitable choice of morphisms- as full subcategories of Chu (Poset 2).