66,140 research outputs found
Spanning connectivity games
The Banzhaf index, Shapley-Shubik index and other voting power indices measure the importance of a player in a coalitional game. We consider a simple coalitional game called the spanning connectivity game (SCG) based on an undirected, unweighted multigraph, where edges are players. We examine the computational complexity of computing the voting power indices of edges in the SCG. It is shown that computing Banzhaf values and Shapley-Shubik indices is #P-complete for SCGs. Interestingly, Holler indices and Deegan-Packel indices can be computed in polynomial time. Among other results, it is proved that Banzhaf indices can be computed in polynomial time for graphs with bounded treewidth. It is also shown that for any reasonable representation of a simple game, a polynomial time algorithm to compute the Shapley-Shubik indices implies a polynomial time algorithm to compute the Banzhaf indices. As a corollary, computing the Shapley value is #P-complete for simple games represented by the set of minimal winning coalitions, Threshold Network Flow Games, Vertex Connectivity Games and Coalitional Skill Games
Complexity of coalition structure generation
We revisit the coalition structure generation problem in which the goal is to
partition the players into exhaustive and disjoint coalitions so as to maximize
the social welfare. One of our key results is a general polynomial-time
algorithm to solve the problem for all coalitional games provided that player
types are known and the number of player types is bounded by a constant. As a
corollary, we obtain a polynomial-time algorithm to compute an optimal
partition for weighted voting games with a constant number of weight values and
for coalitional skill games with a constant number of skills. We also consider
well-studied and well-motivated coalitional games defined compactly on
combinatorial domains. For these games, we characterize the complexity of
computing an optimal coalition structure by presenting polynomial-time
algorithms, approximation algorithms, or NP-hardness and inapproximability
lower bounds.Comment: 17 page
Strategic Payments in Financial Networks
In their seminal work on systemic risk in financial markets, Eisenberg and Noe [Larry Eisenberg and Thomas Noe, 2001] proposed and studied a model with n firms embedded into a network of debt relations. We analyze this model from a game-theoretic point of view. Every firm is a rational agent in a directed graph that has an incentive to allocate payments in order to clear as much of its debt as possible. Each edge is weighted and describes a liability between the firms. We consider several variants of the game that differ in the permissible payment strategies. We study the existence and computational complexity of pure Nash and strong equilibria, and we provide bounds on the (strong) prices of anarchy and stability for a natural notion of social welfare. Our results highlight the power of financial regulation - if payments of insolvent firms can be centrally assigned, a socially optimal strong equilibrium can be found in polynomial time. In contrast, worst-case strong equilibria can be a factor of ?(n) away from optimal, and, in general, computing a best response is an NP-hard problem. For less permissible sets of strategies, we show that pure equilibria might not exist, and deciding their existence as well as computing them if they exist constitute NP-hard problems
Learning Cooperative Games
This paper explores a PAC (probably approximately correct) learning model in
cooperative games. Specifically, we are given random samples of coalitions
and their values, taken from some unknown cooperative game; can we predict the
values of unseen coalitions? We study the PAC learnability of several
well-known classes of cooperative games, such as network flow games, threshold
task games, and induced subgraph games. We also establish a novel connection
between PAC learnability and core stability: for games that are efficiently
learnable, it is possible to find payoff divisions that are likely to be stable
using a polynomial number of samples.Comment: accepted to IJCAI 201
A Comprehensive Survey of Potential Game Approaches to Wireless Networks
Potential games form a class of non-cooperative games where unilateral
improvement dynamics are guaranteed to converge in many practical cases. The
potential game approach has been applied to a wide range of wireless network
problems, particularly to a variety of channel assignment problems. In this
paper, the properties of potential games are introduced, and games in wireless
networks that have been proven to be potential games are comprehensively
discussed.Comment: 44 pages, 6 figures, to appear in IEICE Transactions on
Communications, vol. E98-B, no. 9, Sept. 201
Optimizing flow rates in a queueing network with side constraints
Network Analysis;operations research
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