Game-Theoretically Allocating Resources to Catch Evaders and Payments to Stabilize Teams

Abstract

Allocating resources optimally is a nontrivial task, especially when multipleself-interested agents with conflicting goals are involved. This dissertationuses techniques from game theory to study two classes of such problems:allocating resources to catch agents that attempt to evade them, and allocatingpayments to agents in a team in order to stabilize it. Besides discussing whatallocations are optimal from various game-theoretic perspectives, we also studyhow to efficiently compute them, and if no such algorithms are found, whatcomputational hardness results can be proved.The first class of problems is inspired by real-world applications such as theTOEFL iBT test, course final exams, driver's license tests, and airport securitypatrols. We call them test games and security games. This dissertation firststudies test games separately, and then proposes a framework of Catcher-Evadergames (CE games) that generalizes both test games and security games. We showthat the optimal test strategy can be efficiently computed for scored testgames, but it is hard to compute for many binary test games. Optimal Stackelbergstrategies are hard to compute for CE games, but we give an empiricallyefficient algorithm for computing their Nash equilibria. We also prove that theNash equilibria of a CE game are interchangeable.The second class of problems involves how to split a reward that is collectivelyobtained by a team. For example, how should a startup distribute its shares, andwhat salary should an enterprise pay to its employees. Several stability-basedsolution concepts in cooperative game theory, such as the core, the least core,and the nucleolus, are well suited to this purpose when the goal is to avoidcoalitions of agents breaking off. We show that some of these solution conceptscan be justified as the most stable payments under noise. Moreover, by adjustingthe noise models (to be arguably more realistic), we obtain new solutionconcepts including the partial nucleolus, the multiplicative least core, and themultiplicative nucleolus. We then study the computational complexity of thosesolution concepts under the constraint of superadditivity. Our result is basedon what we call Small-Issues-Large-Team games and it applies to popularrepresentation schemes such as MC-nets.</p