Risk Sensitivity of Price of Anarchy under Uncertainty

Abstract

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 towards uncertainty has a critical effect on system performance and therefore should be a subject of close and systematic investigation.

Tight Inefficiency Bounds for Perception-Parameterized Affine Congestion Games

“…For example, these extensions include risk sensitivity of players in uncertain settings [18], altruistic player behavior [5,6] and congestion games with taxes [4]. We elaborate in more detail on these extensions in Section 2.…”

“…While the price of anarchy bounds are (mostly) known from previous results, the price of stability results are new. As in [4][5][6]18], we focus on congestion games with affine cost functions.…”

“…Risk sensitivity under uncertainty [18]. Nikolova, Piliouras and Shamma [18] consider congestion games in which there is a (non-deterministic) order of the players on every resource.…”

“…Nikolova, Piliouras and Shamma [18] consider congestion games in which there is a (non-deterministic) order of the players on every resource. A player is only affected by players in front of her.…”

“…That is, the load on resource e for player i in a strict ordering r, where r e (i) denotes the position of player i, is given by which is independent of the ordering r. 5 Note that the social cost corresponds to the case σ = 1 2 in our framework. Nikolova et al [18] study various risk attitudes towards the ordering r that is assumed to have a uniform distribution over all possible orderings. In particular, they consider players who are risk-neutral and players who apply Wald's minimax principle.…”