5,715 research outputs found
Computational Aspects of Extending the Shapley Value to Coalitional Games with Externalities
Until recently, computational aspects of the Shapley value were only studied under the assumption that there are no externalities from coalition formation, i.e., that the value of any coalition is independent of other coalitions in the system. However, externalities play a key role in many real-life situations and have been extensively studied in the game-theoretic and economic literature. In this paper, we consider the issue of computing extensions of the Shapley value to coalitional games with externalities proposed by Myerson [21], Pham Do and Norde [23], and McQuillin [17]. To facilitate efficient computation of these extensions, we propose a new representation for coalitional games with externalities, which is based on weighted logical expressions. We demonstrate that this representation is fully expressive and, sometimes, exponentially more concise than the conventional partition function game model. Furthermore, it allows us to compute the aforementioned extensions of the Shapley value in time linear in the size of the input
Coalitional Games for Transmitter Cooperation in MIMO Multiple Access Channels
Cooperation between nodes sharing a wireless channel is becoming increasingly
necessary to achieve performance goals in a wireless network. The problem of
determining the feasibility and stability of cooperation between rational nodes
in a wireless network is of great importance in understanding cooperative
behavior. This paper addresses the stability of the grand coalition of
transmitters signaling over a multiple access channel using the framework of
cooperative game theory. The external interference experienced by each TX is
represented accurately by modeling the cooperation game between the TXs in
\emph{partition form}. Single user decoding and successive interference
cancelling strategies are examined at the receiver. In the absence of
coordination costs, the grand coalition is shown to be \emph{sum-rate optimal}
for both strategies. Transmitter cooperation is \emph{stable}, if and only if
the core of the game (the set of all divisions of grand coalition utility such
that no coalition deviates) is nonempty. Determining the stability of
cooperation is a co-NP-complete problem in general. For a single user decoding
receiver, transmitter cooperation is shown to be \emph{stable} at both high and
low SNRs, while for an interference cancelling receiver with a fixed decoding
order, cooperation is stable only at low SNRs and unstable at high SNR. When
time sharing is allowed between decoding orders, it is shown using an
approximate lower bound to the utility function that TX cooperation is also
stable at high SNRs. Thus, this paper demonstrates that ideal zero cost TX
cooperation over a MAC is stable and improves achievable rates for each
individual user.Comment: in review for publication in IEEE Transactions on Signal Processin
Incentives and Stability of International Climate Coalitions: An Integrated Assessment
This paper analyses the incentives to participate in and the stability of international climate coalitions. Using the integrated assessment model WITCH, the analysis of coalitionsâ profitability and stability is performed under alternative assumptions concerning the pure rate of time preference, the social welfare aggregator and the extent of climate damages. We focus on the profitability, stability, and âpotential stabilityâ of a number of coalitions which are âpotentially effectiveâ in reducing emissions. We find that only the grand coalition under a specific sets of assumptions finds it optimal to stabilise GHG concentration below 550 ppm CO2-eq. However, the grand coalition is found not to be stable, not even âpotentially stableâ even through an adequate set of transfers. However, there exist potentially stable coalitions, but of smaller size, which are also potentially environmentally effective. Depending on the assumptions made, they could achieve up to 600 ppm CO2-eq. More ambitious targets lead to the collapse of the coalition.Climate Policy, Climate Coalition, Game Theory, Free Riding
Computing optimal coalition structures in polynomial time
The optimal coalition structure determination problem is in general computationally hard. In this article, we identify some problem instances for which the
space of possible coalition structures has a certain form and constructively prove that the problem is polynomial time solvable. Specifically, we consider games with an ordering over the players and introduce a distance metric for measuring the distance between any two structures. In terms of this metric, we define the property of monotonicity, meaning that coalition structures closer to the optimal, as measured by
the metric, have higher value than those further away. Similarly, quasi-monotonicity means that part of the space of coalition structures is monotonic, while part of it is non-monotonic. (Quasi)-monotonicity is a property that can be satisfied by coalition
games in characteristic function form and also those in partition function form. For a setting with a monotonic value function and a known player ordering, we prove that the optimal coalition structure determination problem is polynomial time solvable
and devise such an algorithm using a greedy approach. We extend this algorithm to quasi-monotonic value functions and demonstrate how its time complexity improves from exponential to polynomial as the degree of monotonicity of the value function increases. We go further and consider a setting in which the value function is monotonic and an ordering over the players is known to exist but ordering itself is unknown. For this setting too, we prove that the coalition structure determination problem is polynomial time solvable and devise such an algorithm
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