Risk-Averse Equilibrium for Games

Yekkehkhany, Ali; Murray, Timothy; Nagi, Rakesh

doi:10.48550/arxiv.2002.08414

Cited by 4 publications

(4 citation statements)

References 15 publications

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“…, 1) with social delay D W ( p * W ) = 1. However, although the expected latency along the top link is less than or equal to that of the bottom link, l 1 (m 1 ) ≤ l 2 (m 2 ), the variance of travel time along the top link at full capacity is larger than that along the bottom link, which increases the risk and uncertainty of traveling along the top link [70]- [72]. In fact, the bottom link with higher expected travel time is more likely to have a lower delay than the top link at full capacity, i.e., P L 2 (0) ≤ L 1 (n) = 0.6 > 0.5.…”

Section: A Illustrative Examplesmentioning

confidence: 99%

Risk-Averse Equilibria for Vehicle Navigation in Stochastic Congestion Games

Yekkehkhany

Nagi

2022

IEEE Trans. Intell. Transport. Syst.

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

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Section: A Illustrative Examplesmentioning

confidence: 99%

Risk-Averse Equilibria for Vehicle Navigation in Stochastic Congestion Games

Yekkehkhany

Nagi

2022

IEEE Trans. Intell. Transport. Syst.

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“…, 1) with social delay D W (p * W ) = 1. However, although the expected latency along the top link is less than or equal to that of the bottom link, l 1 (m 1 ) ≤ l 2 (m 2 ), the variance of travel time along the top link at full capacity is larger than that along the bottom link, which increases the risk and uncertainty of traveling along the top link (Yekkehkhany, Murray, and Nagi 2020, Yekkehkhany et al 2019. In fact, the bottom link with higher expected travel time is more likely to have a lower delay than the top link at full capacity, i.e., P L 2 (0) ≤ L 1 (n) = 0.6 > 0.5.…”

Section: Illustrative Examplesmentioning

confidence: 99%

Risk-Averse Equilibrium for Autonomous Vehicles in Stochastic Congestion Games

Yekkehkhany,

Nagi

2020

Preprint

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

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“…A further research direction is that of combining the model of multidimensional congestion games with other variants of congestion games (e.g., risk-averse congestion games [31][32][33][34] and congestion games with link failures [35][36][37]).…”

Section: Conclusion and Open Problemsmentioning

confidence: 99%

On Multidimensional Congestion Games

et al. 2020

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We introduce multidimensional congestion games, that is, congestion games whose set of players is partitioned into d+1 clusters C0,C1,…,Cd. Players in C0 have full information about all the other participants in the game, while players in Ci, for any 1≤i≤d, have full information only about the members of C0∪Ci and are unaware of all the others. This model has at least two interesting applications: (i) it is a special case of graphical congestion games induced by an undirected social knowledge graph with independence number equal to d, and (ii) it represents scenarios in which players have a type and the level of competition they experience on a resource depends on their type and on the types of the other players using it. We focus on the case in which the cost function associated with each resource is affine and bound the price of anarchy and stability as a function of d with respect to two meaningful social cost functions and for both weighted and unweighted players. We also provide refined bounds for the special case of d=2 in presence of unweighted players.

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Risk-Averse Equilibrium for Games

Cited by 4 publications

References 15 publications

Risk-Averse Equilibria for Vehicle Navigation in Stochastic Congestion Games

Risk-Averse Equilibria for Vehicle Navigation in Stochastic Congestion Games

Risk-Averse Equilibrium for Autonomous Vehicles in Stochastic Congestion Games

On Multidimensional Congestion Games

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