Graduate Studies

 

First Advisor

Hau Chan

Degree Name

Doctor of Philosophy (Ph.D.)

Department

Computer Science

Date of this Version

5-2024

Document Type

Dissertation

Citation

A dissertation presented to the faculty of the Graduate College of the University of Nebraska in partial fulfillment of requirements for the degree of Doctor of Philosophy

Major: Computer Science

Under the supervision of Professor Hau Chan

Lincoln, Nebraska, May 2024

Comments

Copyright 2024, Jared Soundy. Used by permission

Abstract

Existing computational game theory studies consider compact representations of games that capture agent interaction in real-world environments and examine computation aspects of computing equilibrium concepts to analyze or predict agent behavior.

One of the most well-studied representations that capture many commonly studied real-world environments is aggregate games. Aggregate games, first systematically studied by Nobel laureate Reinhard Selten, have various applications in modeling the decision-making interdependence of agents, where each agent’s utility function depends on their own actions and the aggregations or summarizations of the actions of all agents. These applications include Cournot oligopoly competition, public good contribution, and voting, where an agent’s action (e.g., goods to produce) depends only on the aggregation of all other agents’ actions (e.g., total goods produced).

For the first part of this thesis, we extend aggregate games to model two new complementary non-cooperative game-theoretic scenarios capturing certain aspects of real-world characteristics that are not known to be modeled by aggregate games previously. For the first scenario, we introduce (collaborative) public project contribution games with thresholds, where each agent determines which projects to contribute to and each project's success depends on the total contribution exceeding their threshold. The thresholds model project failure from insufficient contributions not modeled by prior work. The second scenario examines (competitive) multi-dimensional congestion games, where each agent determines which resources to use and the cost of using each resource depending on its total demands in multiple dimensions. These games are a recent extension of the popular congestion games. For these two games and their variants, we examine the open computational complexity of determining and computing Nash Equilibria (NE), a fundamental solution concept in game theory, and related problems.

For the second part of this thesis, we consider aggregate games and examine open computational questions on NE and strong NE, which extends NE for agent coalitions, utilizing insights from the first part of this thesis. We also demonstrate how aggregate game computational results (e.g., algorithms for NE and strong NE) are applicable to several popular games.

Advisor: Hau Chan

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