This paper presents a matching mechanism for assigning drivers to routes where the drivers pay a toll for the marginal delay they impose on other drivers. The simple matching mechanism is derived from the RANKING algorithm for online bipartite matching proposed by Karp et al. [8]. The toll, which is anticipatory in design, is an adaption of one proposed by Dong et al. [5]. Our research proves that the matching mechanism proposed here is pareto user-optimal and can be adapted to give network optimal results for the minimizing total social cost of travel.
Are rewards or penalties more effective in influencing user behavior? This work compares the effectiveness of subsidies and tolls in incentivizing users in congestion games. The predominantly studied method of influencing user behavior in network routing problems is to institute taxes which alter users' observed costs in a manner that causes their self-interested choices to more closely align with a system-level objective. Another feasible method to accomplish the same goal is to subsidize the users' actions that are preferable from a system-level perspective. We show that, when users behave s…
Markov decision process (MDP) congestion game is an extension of classic congestion games, where a continuous population of selfish agents solves Markov decision processes with congestion: the payoff of a strategy decreases as more population uses it. We draw parallels between key concepts from capacitated congestion games and MDP. In particular, we show that population mass constraints in MDP congestion games are equivalent to imposing tolls/incentives on the reward function, which can be utilized by social planners to achieve auxiliary objectives. We demonstrate such methods in a simulated S…
Under the Markov decision process (MDP) congestion game framework, we study the problem of enforcing population distribution constraints on a population of players with stochastic dynamics and coupled congestion costs. Existing research demonstrates that the constraints on the players' population distribution can be satisfied by enforcing tolls. However, computing the minimum toll value for constraint satisfaction requires accurate modeling of the player's congestion costs. Motivated by settings where an accurate congestion cost model is unavailable (e.g. transportation networks), we consider …
We consider a network pricing game on a parallel network with congestion effects in which link owners set tolls for travel so as to maximize profit. A central authority is able to regulate this competition by means of a (uniform) price cap. The first question we want to answer is how such a cap should be designed in order to minimize the total congestion. We provide an algorithm that finds an optimal price cap for networks with affine latency functions and a full support Wardrop equilibrium. Second, we consider the induced network performance at an optimal price cap. We show that for two link …
The introduction of autonomous (self-driving) and shared autonomous vehicles (AVs and SAVs) will affect travel destinations and distances, mode choice, and congestion. From a traffic perspective, although some congestion reduction may be achieved (thanks to fewer crashes and tighter headways), car-trip frequencies and vehicle miles traveled (VMT) are likely to rise significantly, reducing the benefits of driverless vehicles. Congestion pricing (CP) and road tolls are key tools for moderating demand and incentivizing more socially and environmentally optimal travel choices. This work develops m…
Are rewards or penalties more effective in influencing user behavior? This work compares the effectiveness of subsidies and tolls in incentivizing user behavior in congestion games. The predominantly studied method of influencing user behavior in network routing problems is to institute taxes which alter users' observed costs in a manner that causes their self-interested choices to more closely align with a system-level objective. Another conceivable method to accomplish the same goal is to subsidize the users' actions that are preferable from a system-level perspective. We show that, when use…
We describe a new coordination mechanism for non-atomic congestion games that leads to a (selfish) social cost which is arbitrarily close to the non-selfish optimal. This mechanism does not incur any additional extra cost, like tolls, which are usually differentiated from the social cost as expressed in terms of delays only.
How can we design mechanisms to promote efficient use of shared resources? Here, we answer this question in relation to the well-studied class of atomic congestion games, used to model a variety of problems, including traffic routing. Within this context, a methodology for designing tolling mechanisms that minimize the system inefficiency (price of anarchy) exploiting solely local information is so far missing in spite of the scientific interest. In this manuscript we resolve this problem through a tractable linear programming formulation that applies to and beyond polynomial congestion games.…
When selfish users share a road network and minimize their individual travel costs, the equilibrium they reach can be worse than the socially optimal routing. Tolls are often used to mitigate this effect in traditional congestion games, where all vehicle contribute identically to congestion. However, with the proliferation of autonomous vehicles and driver-assistance technology, vehicles become heterogeneous in how they contribute to road latency. This magnifies the potential inefficiencies due to selfish routing and invalidates traditional tolling methods. To address this, we consider a netwo…
Wardrop equilibria in nonatomic congestion games are in general inefficient as they do not induce an optimal flow that minimizes the total travel time. Network tolls are a prominent and popular way to induce an optimum flow in equilibrium. The classical approach to find such tolls is marginal cost pricing which requires the exact knowledge of the demand on the network. In this paper, we investigate under which conditions demand-independent optimum tolls exist that induce the system optimum flow for any travel demand in the network. We give several characterizations for the existence of such to…
We ask if it is possible to positively influence social behavior with no risk of unintentionally incentivizing pathological behavior. In network routing problems, if network traffic is composed of many individual agents, it is known that self-interested behavior among the agents can lead to suboptimal network congestion. We study situations in which a system planner charges monetary tolls for the use of network links in an effort to incentivize efficient routing choices by the users, but in which the users' sensitivity to tolls is heterogeneous and unknown. We seek locally-computed tolls that …
Congestion externalities are a well-known phenomenon in transportation and communication networks, healthcare etc. Optimization by self-interested agents in such settings typically results in equilibria which are sub-optimal for social welfare. Pigouvian taxes or tolls, which impose a user charge equal to the negative externality caused by the marginal user to other users, are a mechanism for combating this problem. In this paper, we study a non-atomic congestion game in which heterogeneous agents choose amongst a finite set of heterogeneous servers. The delay at a server is an increasing func…
How can a system designer exploit system-level knowledge to derive incentives to optimally influence social behavior? The literature on network routing contains many results studying the application of monetary tolls to influence behavior and improve the efficiency of self-interested network traffic routing. These results typically fall into two categories: (1) optimal tolls which incentivize socially-optimal behavior for a known realization of the network and population, or (2) robust tolls which provably reduce congestion given uncertainty regarding networks and user types, but may fail to o…
We revisit a classic coordination problem from the perspective of mechanism design: how can we coordinate a social welfare maximizing flow in a network congestion game with selfish players? The classical approach, which computes tolls as a function of known demands, fails when the demands are unknown to the mechanism designer, and naively eliciting them does not necessarily yield a truthful mechanism. Instead, we introduce a weak mediator that can provide suggested routes to players and set tolls as a function of reported demands. However, players can choose to ignore or misreport their type t…
Price of anarchy quantifies the degradation of social welfare in games due to the lack of a centralized authority that can enforce the optimal outcome. At its antipodes, mechanism design studies how to ameliorate these effects by incentivizing socially desirable behavior and implementing the optimal state as equilibrium. In practice, the responsiveness to such measures depends on the wealth of each individual. This leads to a natural, but largely unexplored, question. Does optimal mechanism design entrench, or maybe even exacerbate, social inequality? We study this question in nonatomic conges…
Credit-based congestion pricing (CBCP) has emerged as a mechanism to alleviate the social inequity concerns of road congestion pricing - a promising strategy for traffic congestion mitigation - by providing low-income users with travel credits to offset some of their toll payments. While CBCP offers immense potential for addressing inequity issues that hamper the practical viability of congestion pricing, the deployment of CBCP in practice is nascent, and the potential efficacy and optimal design of CBCP schemes have yet to be formalized. In this work, we study the design of CBCP schemes to ac…
Congestion pricing has long been hailed as a means to mitigate traffic congestion; however, its practical adoption has been limited due to the resulting social inequity issue, e.g., low-income users are priced out off certain roads. This issue has spurred interest in the design of equitable mechanisms that aim to refund the collected toll revenues as lump-sum transfers to users. Although revenue refunding has been extensively studied for over three decades, there has been no thorough characterization of how such schemes can be designed to simultaneously achieve system efficiency and equity obj…
