Theory of linear and integer programming
Theory of linear and integer programming
International Journal of Game Theory
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
The Cost of Stability in Coalitional Games
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
On the computational complexity of weighted voting games
Annals of Mathematics and Artificial Intelligence
Computational Aspects of Cooperative Game Theory (Synthesis Lectures on Artificial Inetlligence and Machine Learning)
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We initiate the study of dynamic cooperative games --- cooperative games where the characteristic function may change over time. We introduce two types of algorithmic problems for such games: computing a given solution concept at time t, and checking that a certain function of the game (e.g., the Shapley value of a given player or the value of the least core) remains within given bounds during time interval [t_0, t_1]. We then investigate the complexity of these problems for dynamic weighted voting games, where the weight of each player and the quota are functions of time that are given by low-degree polynomials with integer coefficients. We provide pseudopolynomial algorithms for problems of both types, for a variety of solution concepts. We then use our results to investigate the changes in power distribution in the Council of the European Union over the next 50 years.