Nash Equilibria, collusion in games and the coevolutionary particle swarm algorithm

In recent work, we presented a deterministic algorithm to investigate collusion between players in a game where the players’ payoff functions are subject to a variational inequality describing the equilibrium of a transportation system. In investigating the potential for collusion between players, the diagonalization algorithm returned a local optimum. In this paper, we apply a coevolutionary particle swarm optimization (PSO) algorithm developed in earlier research in an attempt to return the global maximum. A numerical experiment is used to verify the performance of the algorithm in overcoming local optimum

Tolling, Capacity Selection and Equilibrium Problems with Equilibrium Constraints

An Equilibrium problem with an equilibrium constraint is a mathematical construct that can be applied to private competition in highway networks. In this paper we consider the problem of finding a Nash Equilibrium regarding competition in toll pricing on a network utilising 2 alternative algorithms. In the first algorithm, we utilise a Gauss Siedel fixed point approach based on the cutting constraint algorithm for toll pricing. In the second algorithm, we extend an existing sequential linear complementarity approach for finding Nash equilibrium subject to Wardrop Equilibrium constraints. Finally we consider how the equilibrium may change between the Nash competitive equilibrium and a collusive equilibrium where the two players co-operate to form the equivalent of a monopoly operation

A Coevolutionary Particle Swarm Algorithm for Bi-Level Variational Inequalities: Applications to Competition in Highway Transportation Networks

A climate of increasing deregulation in traditional highway transportation, where the private sector has an expanded role in the provision of traditional transportation services, provides a background for practical policy issues to be investigated. One of the key issues of interest, and the focus of this chapter, would be the equilibrium decision variables offered by participants in this market. By assuming that the private sector participants play a Nash game, the above problem can be described as a Bi-Level Variational Inequality (BLVI). Our problem differs from the classical Cournot-Nash game because each and every player’s actions is constrained by another variational inequality describing the equilibrium route choice of users on the network. In this chapter, we discuss this BLVI and suggest a heuristic coevolutionary particle swarm algorithm for its resolution. Our proposed algorithm is subsequently tested on example problems drawn from the literature. The numerical experiments suggest that the proposed algorithm is a viable solution method for this problem

Second best toll and capacity optimisation in network: solution algorithm and policy implications

This paper looks at the first and second-best jointly optimal toll and road capacity investment problems from both policy and technical oriented perspectives. On the technical side, the paper investigates the applicability of the constraint cutting algorithm for solving the second-best problem under elastic demand which is formulated as a bilevel programming problem. The approach is shown to perform well despite several problems encountered by our previous work in Shepherd and Sumalee (2004). The paper then applies the algorithm to a small sized network to investigate the policy implications of the first and second-best cases. This policy analysis demonstrates that the joint first best structure is to invest in the most direct routes while reducing capacities elsewhere. Whilst unrealistic this acts as a useful benchmark. The results also show that certain second best policies can achieve a high proportion of the first best benefits while in general generating a revenue surplus. We also show that unless costs of capacity are known to be low then second best tolls will be affected and so should be analysed in conjunction with investments in the network

The correlation of externalities in marginal cost pricing: lessons learned from a real-world case study

Negative externalities cause inefficiencies in the allocation of capacities and resources in a transport system. Marginal social cost pricing allows to correct for these inefficiencies in a simulation environment and to derive real-world policy recommendations. In this context, it has been shown for analytical models considering more than one externality, that the correlation between the externalities needs to be taken into account. Typically, in order to avoid overpricing, this is performed by introducing correction factors which capture the correlation effect. However, the correlation structure between, say, emission and congestion externalities changes for every congested facility over time of day. This makes it close to impossible to calculate the factors analytically for large-scale systems. Hence, this paper presents a simulation-based approach to calculate and internalize the correct dynamic price levels for both externalities simultaneously. For a real-world case study, it is shown that the iterative calculation of prices based on cost estimates from the literature allows to identify the amplitude of the correlation between the two externalities under consideration: for the urban travelers of the case study, emission toll levels—without pricing congestion—turn out to be 4.0% too high in peak hours and 2.8% too high in off-peak hours. In contrary, congestion toll levels—without pricing emissions—are overestimated by 3.0% in peak hours and by 7.2% in off-peak hours. With a joint pricing policy of both externalities, the paper shows that the approach is capable to determine the amplitude of the necessary correction factors for large-scale systems. It also provides the corrected average toll levels per vehicle kilometer for peak and off-peak hours for the case study under consideration: again, for urban travelers, the correct price level for emission and congestion externalities amounts approximately to 38 EURct/km in peak hours and to 30 EURct/km in off-peak hours. These toll levels can be used to derive real-world pricing schemes. Finally, the economic assessment indicators for the joint pricing policy provided in the paper allow to compare other policies to this benchmark state of the transport system

Measuring Marginal Congestion Costs of Urban Transportation: Do Networks Matter?

In determining the marginal cost of congestion, economists have traditionally relied upon directly measuring traffic congestion on network links, disregarding any “network effects,” since the latter are difficult to estimate. While for simple networks the comparison can be done within a theoretical framework, it is important to know whether such network effects in real large-scale networks are quantitatively significant. In this paper we use a strategic transportation planning model (START) to compare marginal congestion costs computed link-by-link with measures taking into account network effects. We find that while in aggregate network effects are not significant, congestion measured on a single link is a poor predictor of total congestion costs imposed by travel on that link. Also, we analyze the congestion proliferation effect on the network to see how congestion is distributed within an urban area.marginal congestion costs, congestion pricing, urban networks

Economics of Road Network Ownership

This paper seeks to understand the economic impact of centralized and decentralized ownership structures and their corresponding pricing and investment strategies on transportation network performance and social welfare for travelers. In a decentralized network economic system, roads are owned by many agencies or companies that are responsible for pricing and investment strategies. The motivation of this study is two-fold. First, the question of which ownership structure, or industrial organization, is optimal for transportation networks has yet to be resolved. Despite several books devoted to this research issue, quantitative methods that translate ownership-related policy variables into short- and long-run network performance are lacking. Second, the U.S. and many other countries have recently seen a slowly but steadily increasing popularity of road pricing as an alternative to traditional fuel taxes. Not only is the private sector encouraged to finance new roads, this transition in revenue mechanism also makes it possible for lower-level government agencies and smaller jurisdictions to participate in network pricing and investment practice. The issue of optimal ownership is no longer a purely theoretical debate, but bears practical importance. This research adopts an agent-based simulator of network dynamics to explore the implications of centralized and decentralized ownership on mobility and social welfare, as well as potential financial issues and regulatory needs. Components of the simulator: the travel demand model, cost functions, and key variables of pricing and investment strategies, are empirically estimated and validated. Results suggest that road network is a market with imperfect competition. While there is a significant performance lag between the optimal strategy and the current network financing practice in the U.S. (characterized by centralized control, fuel taxes, and budget-balancing investment), a completely decentralized network suffers from issues such as higher-than-optimal tolls and over-investment. For the decentralized ownership structure, appropriate regulation on pricing and investment practices is necessary. Further analysis based on simulation comparisons suggests that with appropriate price regulation, a decentralized road economy consisting of profit-seeking road owners could outperform the existing centralized control, achieve net social benefits close to the theoretical optimum, and distribute a high percentage of welfare gains to travelers. Decentralized control is especially valuable in rapidly changing environments because it promptly responds to travel demand. These results seem to favor the idea of privatizing or decentralizing road ownership on congested networks. Further tests on real-world transportation networks are necessary and should make an interesting future study.Network economics, Modeling network dynamics, Road pricing, Transportation financing, Privatization.