Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
Simple local search problems that are hard to solve
SIAM Journal on Computing
The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Algorithmica
When the players are not expectation maximizers
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
Convergence and approximation in potential games
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Computer Science Review
Risk sensitivity of price of anarchy under uncertainty
Proceedings of the fourteenth ACM conference on Electronic commerce
| Hi-index | 0.00 |
We consider strategic games in which each player seeks a mixed strategy to minimize her cost evaluated by a concave valuationV (mapping probability distributions to reals); such valuations are used to model risk. In contrast to games with expectation-optimizer players where mixed equilibria always exist [15, 16], a mixed equilibrium for such games, called a V-equilibrium, may fail to exist, even though pure equilibria (if any) transfer over. What is the impact of such valuations on the existence, structure and complexity of mixed equilibria? We address this fundamental question for a particular concave valuation: expectation plus variance, denoted as RA, which stands for risk-averse; so, variance enters as a measure of risk and it is used as an additive adjustment to expectation. We obtain the following results about RA-equilibria: · A collection of general structural properties of RA-equilibria connecting to (i)E-equilibria and Var-equilibria, which correspond to the expectation and variance valuations E and Var, respectively, and to (ii) other weaker or incomparable equilibrium properties. · A second collection of (i) existence, (ii) equivalence and separation (with respect to E-equilibria), and (iii) characterization results for RA-equilibria in the new class of player-specific scheduling games. Using examples, we provide the first demonstration that going from E to RA may as well create new mixed (RA-)equilibria. · A purification technique to transform a player-specific scheduling game on identical links into a player-specific scheduling game so that all non-pureRA-equilibria are eliminated while new pure equilibria cannot be created; so, a particular game on two identical links yields one with noRA-equilibrium. As a by-product, the first ${\cal PLS}$-completeness result for the computation of RA-equilibria follows.