A Study of Truck Platooning Incentives Using a Congestion Game

We introduce an atomic congestion game with two types of agents, cars and trucks, to model the traffic flow on a road over various time intervals of the day. Cars maximize their utility by finding a trade-off between the time they choose to use the road, the average velocity of the flow at that time, and the dynamic congestion tax that they pay for using the road. In addition to these terms, the trucks have an incentive for using the road at the same time as their peers because they have platooning capabilities, which allow them to save fuel. The dynamics and equilibria of this game-theoretic model for the interaction between car traffic and truck platooning incentives are investigated. We use traffic data from Stockholm to validate parts of the modeling assumptions and extract reasonable parameters for the simulations. We use joint strategy fictitious play and average strategy fictitious play to learn a pure strategy Nash equilibrium of this game. We perform a comprehensive simulation study to understand the influence of various factors, such as the drivers' value of time and the percentage of the trucks that are equipped with platooning devices, on the properties of the Nash equilibrium.Comment: Updated Introduction; Improved Literature Revie

Tight Inefficiency Bounds for Perception-Parameterized Affine Congestion Games

Congestion games constitute an important class of non-cooperative games which was introduced by Rosenthal in 1973. In recent years, several extensions of these games were proposed to incorporate aspects that are not captured by the standard model. Examples of such extensions include the incorporation of risk sensitive players, the modeling of altruistic player behavior and the imposition of taxes on the resources. These extensions were studied intensively with the goal to obtain a precise understanding of the inefficiency of equilibria of these games. In this paper, we introduce a new model of congestion games that captures these extensions (and additional ones) in a unifying way. The key idea here is to parameterize both the perceived cost of each player and the social cost function of the system designer. Intuitively, each player perceives the load induced by the other players by an extent of {\rho}, while the system designer estimates that each player perceives the load of all others by an extent of {\sigma}. The above mentioned extensions reduce to special cases of our model by choosing the parameters {\rho} and {\sigma} accordingly. As in most related works, we concentrate on congestion games with affine latency functions here. Despite the fact that we deal with a more general class of congestion games, we manage to derive tight bounds on the price of anarchy and the price of stability for a large range of pa- rameters. Our bounds provide a complete picture of the inefficiency of equilibria for these perception-parameterized congestion games. As a result, we obtain tight bounds on the price of anarchy and the price of stability for the above mentioned extensions. Our results also reveal how one should "design" the cost functions of the players in order to reduce the price of anar- chy

Fair Interventions in Weighted Congestion Games

In this work we study the power and limitations of fair interventions in weighted congestion games. Specifically, we focus on interventions that aim at improving the equilibrium quality (price of anarchy) and are fair in the sense that identical players receive identical treatment. Within this setting, we provide three key contributions: First, we show that no fair intervention can reduce the price of anarchy below a given factor depending solely on the class of latencies considered. Interestingly, this lower bound is unconditional, i.e., it applies regardless of how much computation interventions are allowed to use. Second, we propose a taxation mechanism that is fair and show that the resulting price of anarchy matches this lower bound, while the mechanism can be efficiently computed in polynomial time. Third, we complement these results by showing that no intervention (fair or not) can achieve a better approximation if polynomial computability is required. We do so by proving that the minimum social cost is NP-hard to approximate below a factor identical to the one previously introduced. In doing so, we also show that the randomized algorithm proposed by Makarychev and Sviridenko (Journal of the ACM, 2018) for the class of optimization problems with a "diseconomy of scale" is optimal, and provide a novel way to derandomize its solution via equilibrium computation

Improving Approximate Pure Nash Equilibria in Congestion Games

Congestion games constitute an important class of games to model resource allocation by different users. As computing an exact or even an approximate pure Nash equilibrium is in general PLS-complete, Caragiannis et al. (2011) present a polynomial-time algorithm that computes a ($2 + \epsilon$)-approximate pure Nash equilibria for games with linear cost functions and further results for polynomial cost functions. We show that this factor can be improved to $(1.61+\epsilon)$ and further improved results for polynomial cost functions, by a seemingly simple modification to their algorithm by allowing for the cost functions used during the best response dynamics be different from the overall objective function. Interestingly, our modification to the algorithm also extends to efficiently computing improved approximate pure Nash equilibria in games with arbitrary non-decreasing resource cost functions. Additionally, our analysis exhibits an interesting method to optimally compute universal load dependent taxes and using linear programming duality prove tight bounds on PoA under universal taxation, e.g, 2.012 for linear congestion games and further results for polynomial cost functions. Although our approach yield weaker results than that in Bil\`{o} and Vinci (2016), we remark that our cost functions are locally computable and in contrast to Bil\`{o} and Vinci (2016) are independent of the actual instance of the game

Uncertainty in Multi-Commodity Routing Networks: When does it help?

We study the equilibrium behavior in a multi-commodity selfish routing game with many types of uncertain users where each user over- or under-estimates their congestion costs by a multiplicative factor. Surprisingly, we find that uncertainties in different directions have qualitatively distinct impacts on equilibria. Namely, contrary to the usual notion that uncertainty increases inefficiencies, network congestion actually decreases when users over-estimate their costs. On the other hand, under-estimation of costs leads to increased congestion. We apply these results to urban transportation networks, where drivers have different estimates about the cost of congestion. In light of the dynamic pricing policies aimed at tackling congestion, our results indicate that users' perception of these prices can significantly impact the policy's efficacy, and "caution in the face of uncertainty" leads to favorable network conditions.Comment: Currently under revie