Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
TARK '01 Proceedings of the 8th conference on Theoretical aspects of rationality and knowledge
Exponentially Many Steps for Finding a Nash Equilibrium in a Bimatrix Game
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Marginal contribution nets: a compact representation scheme for coalitional games
Proceedings of the 6th ACM conference on Electronic commerce
The complexity of computing a Nash equilibrium
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems - Volume 2
Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations
Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
Extremal behaviour in multiagent contract negotiation
Journal of Artificial Intelligence Research
Pure Nash equilibria: hard and easy games
Journal of Artificial Intelligence Research
Complexity results about Nash equilibria
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Designing incentives for Boolean games
The 10th International Conference on Autonomous Agents and Multiagent Systems - Volume 1
The parameterized complexity of k-flip local search for SAT and MAX SAT
Discrete Optimization
Taxation search in boolean games
Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems
| Hi-index | 0.00 |
Boolean games are a compact and expressive class of games, based on propositional logic. However, Boolean games are computationally complex: checking for the existence of pure Nash equilibria in Boolean games is Εp/2-complete, and it is co-NP-complete to check whether a given outcome for a Boolean game is a pure Nash equilibrium. In this paper, we consider two possible avenues to tractability in Boolean games. First, we consider the development of alternative solution concepts for Boolean games. We introduce the notion of k-bounded Nash equilibrium, meaning that no agent can benefit from deviation by altering fewer than k variables. After motivating and discussing this notion of equilibrium, we give a logical characterisation of a class of Boolean games for which k-bounded equilibria correspond to Nash equilibria. That is, we precisely characterise a class of Boolean games for which all Nash equilibria are in fact k-bounded Nash equilibria. Second, we consider classes of Boolean games for which computational problems related to Nash equilibria are easier than in the general setting. We first identify some restrictions on games that make checking for beneficial deviations by individual players computationally tractable, and then show that certain types of socially desirable equilibria can be hard to compute even when the standard decision problems for Boolean games are easy. We conclude with a discussion of related work and possible future work.