Price of Anarchy for Non-atomic Congestion Games with Stochastic Demands

We generalize the notions of user equilibrium and system optimum to non-atomic congestion games with stochastic demands. We establish upper bounds on the price of anarchy for three different settings of link cost functions and demand distributions, namely, (a) affine cost functions and general distributions, (b) polynomial cost functions and general positive-valued distributions, and (c) polynomial cost functions and the normal distributions. All the upper bounds are tight in some special cases, including the case of deterministic demands.Comment: 31 page

Atomic congestion games with random players : network equilibrium and the price of anarchy

In this paper, we present a new model of congestion games with finite and random number of players, and an analytical method to compute the random path and link flows. We study the equilibrium condition, reformulate it as an equivalent variational inequality problem, and establish the existence and non-uniqueness of the equilibria. We also upper bound the price of anarchy with affine cost functions to characterize the quality of the equilibria. The upper bound is tight in some special cases, including the case of deterministic players. Finally a general lower bound is also provided

Price of anarchy for congestion games with stochastic demands

The price of anarchy is a game-theoretical concept and it measures system degradation caused by players' selfish behaviours. This thesis extends models of congestion games to take stochastic demands into account and studies the price of anarchy on the basis of generalised models developed in this research. In the presence of stochastic demands, the models developed in this study better re flect the reality of a transportation network. The study would help provide a theoretical foundation and insights into mechanism design of transportation games and traffic control in practice. This thesis is concerned with both non-atomic and atomic congestion games, which involve an infinite and finite number of travellers respectively. We introduce the notions of user equilibrium and system optimum under stochastic demands and investigate the behaviours of travellers and central coordinators in a stochastic environment. At a user equilibrium, travellers choose routes independently and aim to minimise their own expected travel costs, while at a system optimum, traffic is fully coordinated to minimise the expected total cost over the whole network. We extend two existing methods of bounding the price of anarchy and compute the quality upper bounds for polynomial cost functions and very general settings of demand distributions. More specifically, we consider positive-valued distributions and normal distributions for non-atomic congestion games, and positive-valued discrete distributions for atomic congestion games. Our results show that the price of anarchy depends on the class of cost functions, demand distributions and, to some extent, network topologies. All the upper bounds are tight in some special cases, including the case of deterministic demands. The two bounding methods are also compared

Spatially Heterogeneity Response of Critical Ecosystem Service Capacity to Address Regional Development Risks to Rapid Urbanization: The Case of Beijing-Tianjin-Hebei Urban Agglomeration in China

Urban agglomerations have become the new spatial unit of global economic competition. The intense socioeconomic activities attributed to the development of urban agglomerations are bound to cause damage to the ecosystem services of these urban agglomerations. This study adopts the Beijing-Tianjin-Hebei urban agglomeration in China as the research object, analyzes the spatiotemporal evolution of its critical ecosystem service capacity to address regional ++-development risks from 2000–2018, and employs the Moran’s I and geographically weighted regression model to explore the spatial correlation and spatial heterogeneity in the responses of urbanization and ecosystem services. The study indicates that (1) from 2000–2018, the ecosystem services of the Beijing-Tianjin-Hebei urban agglomeration exhibit an increase and then a decline, reaching the highest index in 2015; (2) the ecosystem services reveal obvious spatial heterogeneity with the Yan and Taihang Mountains region as the boundary; (3) built-up area ratio, GDP density, and population density exhibit highly obvious negative correlation driving characteristics on ecosystem services; and (4) the construction land ratio exerts a notable impact on areas with a high ecosystem services, while the spatial response of the effect magnitude of the population and GDP densities is largely influenced by intensive, high-pollution and energy-consuming industries. This article also proposes strategies for the optimization of ecological resources and spatial control, which are dedicated to mitigating the negative impacts of rapid urbanization processes on ecosystem services