145,935 research outputs found
Stationary consistent equilibrium coalition structures constitute the recursive core
We study coalitional games where the proceeds from cooperation depend on the entire coalition structure. The coalition structure core (Kóczy, GEB, 2007) is a generalisation of the coalition structure core for such games. We introduce a noncooperative, sequential coalition formation model and show that the set of equilibrium outcomes coincides with the recursive core. In order to extend past results to games that are not totally balanced (understood in this special setting) we introduce subgame-consistency that requires perfectness in relevant subgames only, while subgames that are never reached are ignored.partition function, externalities, implementation, recursive core, stationary perfect equilibrium, time consistent equi- librium
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 -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
-core of our coalitional game not to be empty with zero forcing
transmission. Since, the -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
Cooperative Games with Lattice Structure
A general model for cooperative games with possibly restricted and hierarchically ordered coalitions is introduced and shown to have lattice structure under quite general assumptions. Moreover, the core of games with lattice structure is investigated. Within a general framework that includes the model of classical cooperative games as a special case, it is proved algorithmically that monotone convex games have a non-empty core. Finally, the solution concept of the Shapley value is extended to the general class of cooperative games with restricted cooperation. It is shown that several generalizations of the Shapley value that have been proposed in the literature are subsumed in this model
Stationary Consistent Equilibrium Coalition Structures Constitute the Recursive Core
We study coalitional games where the proceeds from cooperation depend on the entire coalition structure. The coalition structure core (Kóczy, 2007) is a generalisation of the coalition structure core for such games. We introduce a noncooperative, sequential coalition formation model and show that the set of equilibrium outcomes coincides with the recursive core. In order to extend past results to games that are not totally balanced (understood in this special setting) we introduce subgame-consistency that requires perfectness in relevant subgames only, while subgames that are never reached are ignored.Partition Function, Externalities, Implementation, Recursive Core, Stationary Perfect Equilibrium, Time Consistent Equilibrium
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
Comments on: Games with a permission structure - A survey on generalizations and applications 2
In the field of cooperative games with restricted cooperation, various restrictions on coalition formation are studied. The most studied restrictions are those that
arise from restricted communication and hierarchies. This survey discusses several
models of hierarchy restrictions and their relation with communication restrictions.
In the literature, there are results on game properties, Harsanyi dividends, core stability, and various solutions that generalize existing solutions for TU-games. In this
survey, we mainly focus on axiomatizations of the Shapley value in different models
of games with a hierarchically structured player set, and their applications. Not only
do these axiomatizations provide insight in the Shapley value for these models, but
also by considering the types of axioms that characterize the Shapley value, we learn
more about different network structures. A central model of games with hierarchies
is that of games with a permission structure where players in a cooperative transferable utility game are part of a permission structure in the sense that there are players
that need permission from other players before they are allowed to cooperate. This
permission structure is represented by a directed graph. Generalizations of this model
are, for example, games on antimatroids, and games with a local permission structure. Besides discussing these generalizations, we briefly discuss some applications,
in particular auction games and hierarchically structured firms
The Cost of Stability in Coalitional Games
A key question in cooperative game theory is that of coalitional stability,
usually captured by the notion of the \emph{core}--the set of outcomes such
that no subgroup of players has an incentive to deviate. However, some
coalitional games have empty cores, and any outcome in such a game is unstable.
In this paper, we investigate the possibility of stabilizing a coalitional
game by using external payments. We consider a scenario where an external
party, which is interested in having the players work together, offers a
supplemental payment to the grand coalition (or, more generally, a particular
coalition structure). This payment is conditional on players not deviating from
their coalition(s). The sum of this payment plus the actual gains of the
coalition(s) may then be divided among the agents so as to promote stability.
We define the \emph{cost of stability (CoS)} as the minimal external payment
that stabilizes the game.
We provide general bounds on the cost of stability in several classes of
games, and explore its algorithmic properties. To develop a better intuition
for the concepts we introduce, we provide a detailed algorithmic study of the
cost of stability in weighted voting games, a simple but expressive class of
games which can model decision-making in political bodies, and cooperation in
multiagent settings. Finally, we extend our model and results to games with
coalition structures.Comment: 20 pages; will be presented at SAGT'0
Game theoretic contribution to horizontal cooperation in logistics
International audienceHorizontal cooperation in logistics was proved globally advantageous, but we see only few realizations until now. The main obstacle to the successful implementation of horizontal cooperation is the absence of appropriate cooperation decision making model, consisting of the detailed cooperation process, the optimization model, and the stable-and-fair gain sharing mechanism. In this paper, we propose a practical cooperation decision making model for the realization of horizontal logistics cooperation scheme. This model is a decision process integrating an optimization tool and a game-theoretic approach to find a feasible allocation rule, and stable coalitions related to coalition structures issue. We propose a weighted allocation rule that takes bargaining power, contribution and core stability into account, and generalize it in games with coalition structure. Then we investigate related stability issue under two different cooperation patterns. At the end, we present a case study of France retail supply network, which verifies the cooperation model we proposed
The Harsanyi set for cooperative TU-games
A cooperative game with transferable utilities, or simply a TU-game, describes a situation in which players can obtain certain payos by cooperation. A solution mapping for these games is a mapping which assigns to every game a set of payo distributions over the players in the game. Well-known solution mappings are the Core and the Weber set. In this paper we consider the mapping assigning to every game the Harsanyi set being the set of payo vectors obtained by all possible distributions of the Harsanyi dividends of a coalition amongst its members. We discuss the structure and properties of this mapping and show how the Harsanyi set is related to the Core and Weber set. We also characterize the Harsanyi mapping as the unique mapping satisfying a set of six axioms. Finally we discuss some properties of the Harsanyi Imputation set, being the individally rational subset of the Harsanyi set. Key words: TU-games, Core, Harsanyi Set, Weber Set, Shapley value, Selectope. JEL-code: C71.
Solution Concepts for Cooperative Games with Circular Communication Structure
We study transferable utility games with limited cooperation between the agents. The focus is on communication structures where the set of agents forms a circle, so that the possibilities of cooperation are represented by the connected sets of nodes of an undirected circular graph. Agents are able to cooperate in a coalition only if they can form a network in the graph. A single-valued solution which averages marginal contributions of each player is considered. We restrict the set of permutations, which induce marginal contributions to be averaged, to the ones in which every agent is connected to the agent that precedes this agent in the permutation. Staring at a given agent, there are two permutations which satisfy this restriction, one going clockwise and one going anticlockwise along the circle. For each such permutation a marginal vector is determined that gives every player his marginal contribution when joining the preceding agents. It turns out that the average of these marginal vectors coincides with the average tree solution. We also show that the same solution is obtained if we allow an agent to join if this agent is connected to some of the agents who is preceding him in the permutation, not necessarily being the last one. In this case the number of permutations and marginal vectors is much larger, because after the initial agent each time two agents can join instead of one, but the average of the corresponding marginal vectors is the same. We further give weak forms of convexity that are necessary and sufficient conditions for the core stability of all those marginal vectors and the solution. An axiomatization of the solution on the class of circular graph games is also given.Cooperative game;graph structure;average tree solution;Myerson value;core stability;convexity
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