Atomic Routing Games Research Articles

A traveler-centric mobility game: Efficiency and stability under rationality and prospect theory.

In this paper, we study a routing and travel-mode choice problem for mobility systems with a multimodal transportation network as a "mobility game" with coupled action sets. We formulate an atomic routing game to focus on the travelers' preferences and study the impact on the efficiency of the travelers' behavioral decision-making under rationality and prospect theory. To control the innate inefficiencies, we introduce a mobility "pricing mechanism," in which we model traffic congestion using linear cost functions while also considering the waiting times at different transport hubs. We show that the travelers' selfish actions lead to a pure-strategy Nash equilibrium. We then perform a Price of Anarchy and Price of Stability analysis to establish that the mobility system's inefficiencies remain relatively low and the social welfare at a NE remains close to the social optimum as the number of travelers increases. We deviate from the standard game-theoretic analysis of decision-making by extending our mobility game to capture the subjective behavior of travelers using prospect theory. Finally, we provide a detailed discussion of implementing our proposed mobility game.

Routing into parallel collision channels

We study a Medium Access game modeled as a splittable atomic routing game in a parallel link topology. Each player has to decide how to split her traffic among the links. We take the expected loss probability of a player as her cost and consider various loss scenarios: 1) the M/M/1/1 queue in which an arrival that finds another packet in service is lost, 2) Losses occur as in 1, except that if arrival occurs when another packet is served, then both are lost. We furthermore assume that the packet in service is aborted if there was a collision. 3) Like 2, but the packet in service is not aborted. We study the existence and uniqueness of equilibrium under these three types of losses.

Atomic Routing Game with Capacity Constraints

A model of an atomic routing game is considered. A network in this model has capacity constraints. Players in this game choose routes from some sources to one sink. The cost of passing each arc is determined by an increasing and convex function that depends on the number of players. Algorithms for finding the Nash equilibrium and social optimum are developed. These algorithms have a polynomial time complexity. The model can be used for transport networks with limited traffic flows.

A Library for Algorithmic Game Theory in Ssreflect/Coq

We report on the formalization in Ssreflect/Coq of a number of concepts and results from algorithmic game theory, including potential games, smooth games, solution concepts such as Pure and Mixed Nash Equilibria, Coarse Correlated Equilibria, epsilon-approximate equilibria, and behavioral models of games such as best-response dynamics. We apply the formalization to prove Price of Stability bounds for, and convergence under best-response dynamics of, the Atomic Routing game, which has applications in computer networking. Our second application proves that Affine Congestion games are (5/3, 1/3)-smooth, and therefore have Price of Anarchy 5/2. Our formalization is available online.

Coordinated online in-vehicle routing balancing user optimality and system optimality through information perturbation

The inconsistence between system optimality and user optimality represents one of the key difficulties on network traffic congestion control. The advanced connected vehicle systems, enabling smart vehicles to possess/exchange real-time information and conduct portable computation, provide new opportunities to address this challenge. Motivated by this view, this study proposes a coordinated online in-vehicle routing mechanism with intentional information provision perturbation (CRM-IP), which seeks to shape individual vehicles online routing decisions so that user optimality and system optimality are balanced, by exploiting bounded rationality of the users. The proposed CRM-IP is modeled as a pure strategy atomic routing game, and implemented by a sequentially updating distributed algorithm. The mathematical analysis is conducted to quantify the absolute gain of system optimality corresponding to the loss of user optimality resulting from a given level of the information perturbation in the worst case so that the efficiency of the information perturbation can be evaluated. Furthermore, numerical experiments conducted based on City of Sioux Falls network investigate the average effects of the CRM-IP on system optimality and user optimality under various network traffic conditions, comparing to the CRM developed by Du et al. (in press). The results indicate that the improvement of system optimality and the reduction of individual vehicles’ travel time from the CRM is more significant when the network traffic is under an mild congestion state, such as under the levels of service (LOS’s) C, D, and E, rather than under extremely sparse or congested states, such as under LOS’s A and B, or F. Moreover, higher level of information perturbation benefits system optimality more, but the marginal effect decreases after the perturbation reaching certain level, such as λ=0.1 in this case study. In addition, a portion of vehicles may sacrifice user optimality due to the information perturbation, but the extent of the sacrifice is not significant, even though it increases with the information perturbation level. Hence, a small information perturbation is recommended to achieve an efficient network traffic control through the CRM-IP. Overall, this study proposes the CRM-IP as an efficient routing mechanism, which has a great potential to guide the routing decisions of individual vehicles so that their collective behavior improve network performance in both system optimality and user optimality.

Balancing Load via Small Coalitions in Selfish Ring Routing Games

This paper concerns the asymmetric atomic selfish routing game for load balancing in ring networks. In the selfish routing, each player selects a path in the ring network to route one unit traffic between its source and destination nodes, aiming at a minimum maximum link load along its own path. The selfish path selections by individuals ignore the system objective of minimizing the maximum load over all network links. This selfish ring load (SRL) game arises in a wide variety of applications in decentralized network routing, where network performance is often measured by the price of anarchy (PoA), the worst-case ratio between the maximum link loads in an equilibrium routing and an optimal routing. It has been known that the PoA of SRL with respect to classical Nash Equilibrium (NE) cannot be upper bounded by any constant, showing large loss of efficiency at some NE outcome. In an effort to improve the network performance in the SRL game, we generalize the model to so-called SRL with collusion (SRLC) which allows coordination within any coalition of up to k selfish players on the condition that every player of the coalition benefits from the coordination. We prove that, for m-player game on n-node ring, the PoA of SRLC is n - 1 when k ≤ 2, drops to 2 when k = 3 and is at least 1 + 2/m for k ≥ 4. Our study shows that on one hand, the performance of ring networks, in terms of maximum load, benefits significantly from coordination of self-interested players within small-sized coalitions; on the other hand, the equilibrium routing in SRL might not reach global optimum even if any number of players can coordinate.

Coordinated Online In-Vehicle Navigation Guidance Based on Routing Game Theory

This study proposed a coordinated online in-vehicle routing mechanism for smart vehicles with real-time information exchange and portable computation capabilities. The proposed coordinated routing mechanism was modeled as a pure-strategy atomic routing game and was implemented by a sequentially updating distributed algorithm. This study showed the existence of an equilibrium joint routing decision for the routing game and the convergence of the distributed algorithm to an equilibrium; this equilibrium was based on the assumption that individual smart vehicles were selfish players who tried to minimize their own travel time and shared their route choices with other smart vehicles directly or indirectly. Numerical experiments based on the Sioux Falls, South Dakota, network indicated that the proposed distributed algorithm converged very quickly; thus the algorithm has great potential for online applications. Moreover, the proposed coordinate routing mechanism outperformed traditional independent routing mechanisms under various traffic regimes. The mechanism reduced travel time for both the overall system and the majority of individual vehicles; this achievement was the core idea of intelligent transportation systems. These positive effects were more significant in congested traffic condition than in free traffic. The experiments also indicated that even with imperfect information provision, the proposed approach could work well for convergence as well as travel time reduction in systems and individual vehicles.

The Price of Routing Unsplittable Flow

In this paper we study the “price of for the general class of (weighted and unweighted) atomic “congestion with the sum of players' costs as the objective function. We show that for linear resource cost functions the price of anarchy is exactly $\frac{3 + \sqrt{5}}{2} \approx 2.618$ for weighted congestion games and exactly $2.5$ for unweighted congestion games. We show that for resource cost functions that are polynomials of degree $d$ the price of anarchy is $d^{\Theta(d)}$. Our results also hold for mixed strategies. In particular, these results apply to atomic routing games where the traffic demand from a source to a destination must be satisfied by choosing a single path between source and destination.

Collusion in Atomic Splittable Routing Games

We study how collusion affects the social cost in atomic splittable routing games. Suppose that players form coalitions and each coalition behaves as if it were a single player controlling all the flows of its participants. We investigate the following question: under what conditions would the social cost of the post-collusion equilibrium be bounded by the social cost of the pre-collusion equilibrium? We show that if (i) the network is "well-designed" (satisfying a natural condition), and (ii) the delay functions are affine, then collusion is always beneficial for the social cost in the equilibrium flows. On the other hand, if either of the above conditions is unsatisfied, collusion can worsen the social cost. Our main technique is a novel flow-augmenting algorithm to build equilibrium flows. Our positive result for collusion is obtained by applying this algorithm simultaneously to two different flow value profiles of players and observing the difference in the derivatives of their social costs. Moreover, for a non-trivial subclass of selfish routing games, this algorithm finds the exact equilibrium flows in polynomial time.

Atomic routing games on maximum congestion

We study atomic routing games on networks in which players choose a path with the objective of minimizing the maximum congestion along the edges of their path. The social cost is the global maximum congestion over all edges in the network. We show that the price of stability is 1. The price of anarchy, PoA, is determined by topological properties of the network. In particular, PoA=O(ℓ+logn), where ℓ is the length of the longest path in the player strategy sets, and n is the size of the network. Further, κ−1≤PoA≤c(κ2+log2n), where κ is the length of the longest cycle in the network, and c is a constant.