text: In this study, we formulate positive and negative externalities caused by changes in the supply of shared vehicles as ride sharing games. The study aims to understand the price of anarchy (PoA) and its improvement via a coordination technique in ride sharing games. A critical question is whether ride sharing games exhibit a pure Nash equilibrium (pNE) since the PoA bound assumes it. Our result shows a sufficient condition for a ride sharing game to have a finite improvement property and a pNE similar to potential games. This is the first step to analyze PoA bound and its improvement by coordination in ride sharing games. We also show an example of coordinating players in ride sharing games using signaling and evaluate the improvement in the PoA.
  @cite_0: A class of noncooperative games (of interest in certain applications) is described. Each game in the class is shown to possess at least one Nash equilibrium in pure strategies.
  @cite_12: Network equilibrium models that have traditionally been used for transportation planning have penetrated in recent years to other scientific fields. These models have recently been introduced in the telecommunication networks literature, as well as in the field of game theory. Researchers in the latter fields are not always aware of the very rich literature on equilibrium models outside of their application area. On the other hand, researchers that have used network equilibrium models in transportation may not be aware of new application areas of their tools. The aim of this paper is to present some central research issues and tools in network equilibria and pricing that could bring closer the three mentioned research communities.
  @cite_2: This text offers a systematic, rigorous, and unified presentation of evolutionary game theory, covering the core developments of the theory from its inception in biology in the 1970s through recent advances. Evolutionary game theory, which studies the behavior of large populations of strategically interacting agents, is used by economists to make predictions in settings where traditional assumptions about agents' rationality and knowledge may not be justified. Recently, computer scientists, transportation scientists, engineers, and control theorists have also turned to evolutionary game theory, seeking tools for modeling dynamics in multiagent systems. Population Games and Evolutionary Dynamics provides a point of entry into the field for researchers and students in all of these disciplines. The text first considers population games, which provide a simple, powerful model for studying strategic interactions among large numbers of anonymous agents. It then studies the dynamics of behavior in these games. By introducing a general model of myopic strategy revision by individual agents, the text provides foundations for two distinct approaches to aggregate behavior dynamics: the deterministic approach, based on differential equations, and the stochastic approach, based on Markov processes. Key results on local stability, global convergence, stochastic stability, and nonconvergence are developed in detail. Ten substantial appendixes present the mathematical tools needed to work in evolutionary game theory, offering a practical introduction to the methods of dynamic modeling. Accompanying the text are more than 200 color illustrations of the mathematics and theoretical results; many were created using the Dynamo software suite, which is freely available on the author's Web site. Readers are encouraged to use Dynamo to run quick numerical experiments and to create publishable figures for their own research.
summary: Since Rosenthal introduced the congestion game @cite_0 , it has been applied to problems of congestion externalities in several areas such as transportation and communication networks @cite_12 . In this game, players choose a combination of resources and the players' payoffs depend on the congestion level, i.e., the number of players using the same resources. The congestion game is a subclass of potential games, which feature the finite improvement property (FIP). This property guarantees that if each player updates his strategy in response to other players by turns, it will reduce his private cost and improve the common potential function, which eventually reaches a local minimum, the pure Nash equilibrium (pNE), where each player has a deterministic strategy. Because of this property, potential and congestion games have been well studied and have wide applications @cite_2 .