Risk-Averse Equilibria for Vehicle Navigation in Stochastic Congestion Games

The fast-growing market of autonomous vehicles, unmanned aerial and fleets in general necessitates the design smart automatic navigation systems considering stochastic latency along different paths traffic network. longstanding shortest path problem a deterministic network, whose counterpart congestion game setting is Wardrop equilibrium, has been studied extensively, but it well known that finding notion an optimal challenging network with arc delays. In this work, we propose three classes risk-averse equilibria for atomic its form where delay distributions are load dependent not necessarily independent each other. equilibrium (RAE), mean-variance (MVE), conditional value at risk level $\alpha $ ( notation="LaTeX">$\text{CVaR}_{\alpha}\text{E}$ ) notions best responses based on maximizing probability taking path, minimizing linear combination mean variance delay, expected specified risky quantile distributions, respectively. We prove any finite game, risk-averse, mean-variance, notation="LaTeX">$\text{CVaR}_{\alpha}$ exist. show travelers, Braess paradox may occur to extent presented originally since players do travel expectation, they take uncertainty time into consideration as well. through some examples price anarchy can be improved when according one rather than equilibrium.