Multi-Source Multi-Sink Nash Flows over Time

Nash flows over time describe the behavior of selfish users eager to reach their destination as early as possible while traveling along the arcs of a network with capacities and transit times. Throughout the past decade, they have been thoroughly studied in single-source single-sink networks for the deterministic queuing model, which is of particular relevance and frequently used in the context of traffic and transport networks. In this setting there exist Nash flows over time that can be described by a sequence of static flows featuring special properties, so-called `thin flows with resetting\u27. This insight can also be used algorithmically to compute Nash flows over time. We present an extension of these results to networks with multiple sources and sinks which are much more relevant in practical applications. In particular, we come up with a subtle generalization of thin flows with resetting, which yields a compact description as well as an algorithmic approach for computing multi-terminal Nash flows over time

Selfish Routing on Dynamic Flows

Selfish routing on dynamic flows over time is used to model scenarios that vary with time in which individual agents act in their best interest. In this paper we provide a survey of a particular dynamic model, the deterministic queuing model, and discuss how the model can be adjusted and applied to different real-life scenarios. We then examine how these adjustments affect the computability, optimality, and existence of selfish routings.Comment: Oberlin College Computer Science Honors Thesis. Supervisor: Alexa Sharp, Oberlin Colleg

Strategic Payments in Financial Networks

In their seminal work on systemic risk in financial markets, Eisenberg and Noe [Larry Eisenberg and Thomas Noe, 2001] proposed and studied a model with n firms embedded into a network of debt relations. We analyze this model from a game-theoretic point of view. Every firm is a rational agent in a directed graph that has an incentive to allocate payments in order to clear as much of its debt as possible. Each edge is weighted and describes a liability between the firms. We consider several variants of the game that differ in the permissible payment strategies. We study the existence and computational complexity of pure Nash and strong equilibria, and we provide bounds on the (strong) prices of anarchy and stability for a natural notion of social welfare. Our results highlight the power of financial regulation - if payments of insolvent firms can be centrally assigned, a socially optimal strong equilibrium can be found in polynomial time. In contrast, worst-case strong equilibria can be a factor of ?(n) away from optimal, and, in general, computing a best response is an NP-hard problem. For less permissible sets of strategies, we show that pure equilibria might not exist, and deciding their existence as well as computing them if they exist constitute NP-hard problems

The Price of Anarchy in Transportation Networks: Efficiency and Optimality Control

Uncoordinated individuals in human society pursuing their personally optimal strategies do not always achieve the social optimum, the most beneficial state to the society as a whole. Instead, strategies form Nash equilibria which are often socially suboptimal. Society, therefore, has to pay a price of anarchy for the lack of coordination among its members. Here we assess this price of anarchy by analyzing the travel times in road networks of several major cities. Our simulation shows that uncoordinated drivers possibly waste a considerable amount of their travel time. Counterintuitively,simply blocking certain streets can partially improve the traffic conditions. We analyze various complex networks and discuss the possibility of similar paradoxes in physics.Comment: major revisions with multicommodity; Phys. Rev. Lett., accepte

Competitive Packet Routing with Priority Lists

In competitive packet routing games, packets are routed selfishly through a network and scheduling policies at edges determine which packages are forwarded first if there is not enough capacity on an edge to forward all packages at once. We analyze the impact of priority lists on the worst-case quality of pure Nash equilibria. A priority list is an ordered list of players that may or may not depend on the edge. Whenever the number of packets entering an edge exceeds the inflow capacity, packets are processed in list order. We derive several new bounds on the price of anarchy and stability for global and local priority policies. We also consider the question of the complexity of computing an optimal priority list. It turns out that even for very restricted cases, i.e., for routing on a tree, the computation of an optimal priority list is APX-hard

The river sharing problem: A review of the technical literature for policy economists

Water is essential for life. However, the basic problem of water resource allocation has been that water tends to be over-allocated. Demand for water exceeds the available supply. Essentially, the water economy is bankrupt. Bankruptcy problems have been almost exhaustively studied in the literature on economic theory-primarily from the perspective of cooperative game theory. The main concern of this literature has been how to fairly divide up the assets of a bankrupt entity. In water resource economics cooperative game theory has often been employed as a means of analyzing water resource allocation. It was only recently that the problem of directional flow was incorporated into such analyses. This has come to be known as the “river sharing problem” in the theoretical literature. Accounting for the direction of flow in water resource allocation problems has profound implications for policies that wish to facilitate both fair and efficient water allocations. This is the case whether proposed policies are interventionist or market based in nature. There is now a considerable literature on the allocation and distribution of water resources characterized by unidirectional flow. In this paper I critically review and appraise this literature with a view to making it more accessible to applied and policy economists. A key feature of the paper is that the connection between the bankruptcy literature, which has recently also realized the importance of flow, and the river sharing literature is discussed. The current state of the art in game theoretic models of water resource allocation with directional flow is discussed and implications and consequences for water resource policy highlightedRiver sharing problem, Bankruptcy, Cooperative game theory, Water resouyrce allocation, distributive justice