An analysis of stochastic shortest path problems
Mathematics of Operations Research
Algorithms, games, and the internet
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
Selfish Routing in Capacitated Networks
Mathematics of Operations Research
Resource selection games with unknown number of players
AAMAS '06 Proceedings of the fifth international joint conference on Autonomous agents and multiagent systems
Stochastic shortest paths via Quasi-convex maximization
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Algorithmic Game Theory
Shortest paths in stochastic networks with correlated link costs
Computers & Mathematics with Applications
A survey on networking games in telecommunications
Computers and Operations Research
Wardrop Equilibria with Risk-Averse Users
Transportation Science
Approximation algorithms for reliable stochastic combinatorial optimization
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
ACM SIGecom Exchanges
Risk sensitivity of price of anarchy under uncertainty
Proceedings of the fourteenth ACM conference on Electronic commerce
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We embark on an agenda to investigate how stochastic delays and risk aversion transform traditional models of routing games and the corresponding equilibrium concepts. Moving from deterministic to stochastic delays with risk-averse players introduces nonconvexities that make the network game more difficult to analyze even if one assumes that the variability of delays is exogenous. (For example, even computing players' best responses has an unknown complexity [24].) This paper focuses on equilibrium existence and characterization in the different settings of atomic vs. nonatomic players and exogenous vs. endogenous factors causing the variability of edge delays. We also show that succinct representations of equilibria always exist even though the game is non-additive, i.e., the cost along a path is not a sum of costs over edges of the path as is typically assumed in selfish routing problems. Finally, we investigate the inefficiencies resulting from the stochastic nature of delays. We prove that under exogenous stochastic delays, the price of anarchy is exactly the same as in the corresponding game with deterministic delays. This implies that the stochastic delays and players' risk aversion do not further degrade a system in the worst-case more than the selfishness of players.