Free Entry in a Cournot Market with Imperfectly Substituting Goods

Two results are shown about the free-entry equilibrium in a Cournot market with asymmetric firms and imperfectly substituting goods. First, only one technology will survive in the production of each good. Second, some good(s) may not be produced. Specifically, we show that in a two-good model only one good is produced if the substitution parameter is higher than a critical value and both goods are produced for smaller substitution parameter values.Free-entry equilibrium; Cournot competition; substituting goods

Bounded Rationality and Irreversible Network Change

A network change is said to be irreversible if the initial network equilibrium cannot be restored by revoking the change. The phenomenon of irreversible network change has been observed in reality. To model this phenomenon, we develop a day-to-day dynamic model whose fixed point is a boundedly rational user equilibrium (BRUE) flow. Our BRUE based approach to modeling irreversible network change has two advantages over other methods based on Wardrop user equilibrium (UE) or stochastic user equilibrium (SUE). First, the existence of multiple network equilibria is necessary for modeling irreversible network change. Unlike UE or SUE, the BRUE multiple equilibria do not rely on non-separable link cost functions, which makes our model applicable to real-world large-scale networks, where well-calibrated non-separable link cost functions are generally not available. Second, travelers\u27 boundedly rational behavior in route choice is explicitly considered in our model. The proposed model is applied to the Twin Cities network to model the flow evolution during the collapse and reopening of the I-35W Bridge. The results show that our model can to a reasonable level reproduce the observed phenomenon of irreversible network change

A Link-Based Day-to-Day Traffic Assignment Model

Existing day-to-day traffic assignment models are all built upon path flow variables. This paper demonstrates two essential shortcomings of these path-based models. One is that their application requires a given initial path flow pattern, which is typically unidentifiable, i.e., mathematically nonunique and practically unobservable. In particular, we show that, for the path-based models, different initial path flow patterns constituting the same link flow pattern generally gives different day-to-day link flow evolutions. The other shortcoming of the path-based models is the path-overlapping problem. That is, the path-based models ignore the interdependence among paths and thus can give very unreasonable results for networks with paths overlapping with each other. These two path-based problems exist for most (if not all) deterministic day-to-day dynamics whose fixed points are the classic Wardrop user equilibrium. To avoid the two path-based problems, we propose a day-to-day traffic assignment model that directly deals with link flow variables. Our link-based model captures travelers\u27 cost-minimization behavior in their path finding as well as their inertia. The fixed point of our link-based dynamical system is the classic Wardrop user equilibrium

A Generalized Flow Splitting Model for Day-to-day Traffic Assignment

AbstractThe splitting rate model proposed by Smith and Mounce (2011) establishes a traffic evolution process on a link-node network representation, which overcomes the difficulties in applying traditional path-based models and provides the ease of implementing controls at nodes. While their model offers a new method for modeling traffic evolution, it contains an ad-hoc step of flow adjustment to preserve the flow conservation. This flow adjustment step leads to difficulties in analyzing the system properties. This paper proposes a generalized flow splitting model for day-to-day traffic assignment based on the concept of splitting flow at nodes. The proposed model preserves the flow conservation endogenously by introducing the inflow variable into the formulation. The generalized formulation provides the ease to construct a variety of day-to-day traffic assignment models, and serves as a framework for analyzing the models’ properties, such as the invariance property and the preservation of the Lipschitz continuity and strong monotonicity. Specifically, a proportional-adjustment model and a projection-type model are developed based on the proposed generalized formulation. A numerical example demonstrates the ease of implementing the proposed generalized model, as well as its convergence to user equilibrium

Strategic Choice of Channel Structure in an Oligopoly

The traditional wisdom holds that the benefits of a decentralized channel structure arise from downstream competitive relationships. In contrast, Arya and Mittendorf (2007) showed that the value of decentralization can also arise from upstream interaction when the downstream firm conveys internal strife (decentralization) to an upstream external supplier. This paper extends the single firm centralization-decentralization choice model of Arya and Mittendorf (2007) to a strategic choice model in which all downstream competitors play a strategic centralization-decentralization game. We demonstrate that whether the main conclusions in the context of non-strategic choice of channel structure continue to hold when all firms play a centralization-decentralization game depends critically on the market structure of the upstream input market. Specifically, the conclusions are valid if all firms have exclusive upstream input suppliers but not so if the upstream input market is monopolized. Thus, whether the value of decentralization can arise from upstream interaction depends critically on the market structure of the upstream market

Distributionally Consistent Simulation of Naturalistic Driving Environment for Autonomous Vehicle Testing

Microscopic traffic simulation provides a controllable, repeatable, and efficient testing environment for autonomous vehicles (AVs). To evaluate AVs' safety performance unbiasedly, ideally, the probability distributions of the joint state space of all vehicles in the simulated naturalistic driving environment (NDE) needs to be consistent with those from the real-world driving environment. However, although human driving behaviors have been extensively investigated in the transportation engineering field, most existing models were developed for traffic flow analysis without consideration of distributional consistency of driving behaviors, which may cause significant evaluation biasedness for AV testing. To fill this research gap, a distributionally consistent NDE modeling framework is proposed. Using large-scale naturalistic driving data, empirical distributions are obtained to construct the stochastic human driving behavior models under different conditions, which serve as the basic behavior models. To reduce the model errors caused by the limited data quantity and mitigate the error accumulation problem during the simulation, an optimization framework is designed to further enhance the basic models. Specifically, the vehicle state evolution is modeled as a Markov chain and its stationary distribution is twisted to match the distribution from the real-world driving environment. In the case study of highway driving environment using real-world naturalistic driving data, the distributional accuracy of the generated NDE is validated. The generated NDE is further utilized to test the safety performance of an AV model to validate its effectiveness.Comment: 32 pages, 9 figure