SPATIAL RESOURCE COMPETITION GAMES
This dissertation studies spatial resource competition settings where nomadic agents migrate across different locations, competing for time-varying and location-specific resources. Such setting arises in crowd-sourced transportation services, online communities, and traditional location-based economic activities. In these settings, many factors influence the agents’ behavior: the resource dynamics, the way resource is shared among agents at different locations, the information available to the agents, etc. Understanding agents’ behavior in equilibrium and how their decisions depend on these factors can help system operators design better mechanisms to improve social welfare of systems. Analyzing these settings systematically is challenging, since agents’ decisions influence each other spatially and temporally in a complicated nested way. This dissertation aims at building models that capture the essentials of spatial resource competitions, and are analytically tractable, to help understand the nature of agents’ interactions in these settings, from a game theoretical point of view. We first provide a general model for spatial resource competition settings. Using the methodology of mean field approximation, we analyze the dynamics and the game between the agents at a single location, in the limit where there are infinitely many locations. We characterize an equilibrium for agents in the mean field model where agents’ equilibrium strategies have a simple Markovian structure. We then provide a method to approximately compute the equilibrium for a common case of resource competition where the amount of resource each agent gets decreases as the number of agents competing with her increases. We study numerically how different factors affect agents’ equilibrium behavior. We also extend our model and analysis to more general settings where locations are non-homogeneous and there is a two-sided market at each location. Finally, we study information design problem in spatial resource competition scenarios. That is, how should a system operator communicate her extra information about the system to the agents in order to better position them and increase their welfare? We study both private and public signaling mechanisms. For private signaling, we provide a method to obtain the optimal mechanism in polynomial time. For public signaling, we show the sender preferred equilibrium has a simple threshold structure and characterize the structure of the optimal public mechanism under the sender preferred equilibrium. We show via numerical computations that the optimal private and public signaling mechanisms achieve substantially higher social welfare compared with no information sharing or full information sharing in many settings.
Game theory; Applied mathematics; Information design; Mechanism Design; mean field games; Computer science; Operations research; spatial games
Kleinberg, Robert David; Iyer, Krishnamurthy; Banerjee, Siddhartha
Operations Research and Information Engineering
Ph.D., Operations Research and Information Engineering
Doctor of Philosophy
dissertation or thesis