Risk Sensitivity of Price of Anarchy under Uncertainty

In game theory, the price of anarchy framework studies efficiency loss in decentralized environments. Optimization and decision theory, on the other hand, explore tradeoffs between optimality and robustness in the case of single-agent decision making under uncertainty. What happens when we combine both approaches? We examine connections between the efficiency loss due to decentralization and the efficiency loss due to uncertainty and establish tight performance guarantees for distributed systems in uncertain environments. We present applications based on novel variants of atomic congestion games with uncertain costs, for which we provide tight performance bounds under a wide range of risk attitudes. Our results establish that the individual’s attitude toward uncertainty has a critical effect on system performance and therefore should be a subject of close and systematic investigation.