3,320 research outputs found
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
Bounds on the Cost of Stabilizing a Cooperative Game
This is the author accepted manuscript. The final version is available from the AI Access Foundation via the DOI in this record.A key issue in cooperative game theory is coalitional stability, usually captured by the
notion of the core—the set of outcomes that are resistant to group deviations. However,
some coalitional games have empty cores, and any outcome in such a game is unstable. We
investigate the possibility of stabilizing a coalitional game by using subsidies. We consider
scenarios where an external party that 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 this coalition
structure, and may be divided among the players in any way they wish. We define the
cost of stability as the minimum external payment that stabilizes the game. We provide
tight bounds on the cost of stability, both for games where the coalitional values are nonnegative
(profit-sharing games) and for games where the coalitional values are nonpositive
(cost-sharing games), under natural assumptions on the characteristic function, such as
superadditivity, anonymity, or both. We also investigate the relationship between the cost
of stability and several variants of the least core. Finally, we study the computational
complexity of problems related to the cost of stability, with a focus on weighted voting
games.DFGEuropean Science FoundationNRF (Singapore)European Research CouncilHorizon 2020 European Research Infrastructure projectIsrael Science FoundationIsrael Ministry of Science and TechnologyGoogle Inter-University Center for Electronic Markets and AuctionsEuropean Social Fund (European Commission)Calabria Regio
Simple Combinatorial Optimisation Cost Games
In this paper we introduce the class of simple combinatorial optimisation cost games, which are games associated to {0, 1}-matrices.A coalitional value of a combinatorial optimisation game is determined by solving an integer program associated with this matrix and the characteristic vector of the coalition.For this class of games, we will characterise core stability and totally balancedness.We continue by characterising exactness and largeness.Finally, we conclude the paper by applying our main results to minimum colouring games and minimum vertex cover games.Combinatorial optimisation game;core stability;totally balancedness;largeness;exactness
Simple Combinatorial Optimisation Cost Games
In this paper we introduce the class of simple combinatorial optimisation cost games, which are games associated to {0, 1}-matrices.A coalitional value of a combinatorial optimisation game is determined by solving an integer program associated with this matrix and the characteristic vector of the coalition.For this class of games, we will characterise core stability and totally balancedness.We continue by characterising exactness and largeness.Finally, we conclude the paper by applying our main results to minimum colouring games and minimum vertex cover games.
Physical Layer Security: Coalitional Games for Distributed Cooperation
Cooperation between wireless network nodes is a promising technique for
improving the physical layer security of wireless transmission, in terms of
secrecy capacity, in the presence of multiple eavesdroppers. While existing
physical layer security literature answered the question "what are the
link-level secrecy capacity gains from cooperation?", this paper attempts to
answer the question of "how to achieve those gains in a practical decentralized
wireless network and in the presence of a secrecy capacity cost for information
exchange?". For this purpose, we model the physical layer security cooperation
problem as a coalitional game with non-transferable utility and propose a
distributed algorithm for coalition formation. Through the proposed algorithm,
the wireless users can autonomously cooperate and self-organize into disjoint
independent coalitions, while maximizing their secrecy capacity taking into
account the security costs during information exchange. We analyze the
resulting coalitional structures, discuss their properties, and study how the
users can self-adapt the network topology to environmental changes such as
mobility. Simulation results show that the proposed algorithm allows the users
to cooperate and self-organize while improving the average secrecy capacity per
user up to 25.32% relative to the non-cooperative case.Comment: Best paper Award at Wiopt 200
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
Study of a Dynamic Cooperative Trading Queue Routing Control Scheme for Freeways and Facilities with Parallel Queues
This article explores the coalitional stability of a new cooperative control
policy for freeways and parallel queuing facilities with multiple servers.
Based on predicted future delays per queue or lane, a VOT-heterogeneous
population of agents can agree to switch lanes or queues and transfer payments
to each other in order to minimize the total cost of the incoming platoon. The
strategic interaction is captured by an n-level Stackelberg model with
coalitions, while the cooperative structure is formulated as a partition
function game (PFG). The stability concept explored is the strong-core for PFGs
which we found appropiate given the nature of the problem. This concept ensures
that the efficient allocation is individually rational and coalitionally
stable. We analyze this control mechanism for two settings: a static vertical
queue and a dynamic horizontal queue. For the former, we first characterize the
properties of the underlying cooperative game. Our simulation results suggest
that the setting is always strong-core stable. For the latter, we propose a new
relaxation program for the strong-core concept. Our simulation results on a
freeway bottleneck with constant outflow using Newell's car-following model
show the imputations to be generally strong-core stable and the coalitional
instabilities to remain small with regard to users' costs.Comment: 3 figures. Presented at Annual Meeting Transportation Research Board
2018, Washington DC. Proof of conjecture 1 pendin
Coalitional Game Theoretic Approach for Cooperative Transmission in Vehicular Networks
Cooperative transmission in vehicular networks is studied by using
coalitional game and pricing in this paper. There are several vehicles and
roadside units (RSUs) in the networks. Each vehicle has a desire to transmit
with a certain probability, which represents its data burtiness. The RSUs can
enhance the vehicles' transmissions by cooperatively relaying the vehicles'
data. We consider two kinds of cooperations: cooperation among the vehicles and
cooperation between the vehicle and RSU. First, vehicles cooperate to avoid
interfering transmissions by scheduling the transmissions of the vehicles in
each coalition. Second, a RSU can join some coalition to cooperate the
transmissions of the vehicles in that coalition. Moreover, due to the mobility
of the vehicles, we introduce the notion of encounter between the vehicle and
RSU to indicate the availability of the relay in space. To stimulate the RSU's
cooperative relaying for the vehicles, the pricing mechanism is applied. A
non-transferable utility (NTU) game is developed to analyze the behaviors of
the vehicles and RSUs. The stability of the formulated game is studied.
Finally, we present and discuss the numerical results for the 2-vehicle and
2-RSU scenario, and the numerical results verify the theoretical analysis.Comment: accepted by IEEE ICC'1
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