Game-theoretic approaches to resource allocation problems

Abstract

Resource allocation problems have been studied in order to allocate limited resources in an optimal way. This dissertation addresses two different resource allocation problems with game-theoretic approaches. The first study is to allocate the overall benefits from bilateral netting of the financial system to individual financial institutions in the system. To this end, we develop a bilateral netting model of the system based on the cooperative game model and seek a solution that allocates the total benefits of bilateral netting by applying the Shapley value, an appropriate solution concept for this, to the game to find out how each financial institution plays a role in bilateral netting. In particular, to represent a different type of systemic importance of each financial institution, we propose three different characteristic functions. Numerical experiments show that the benefit attribution of a bank is strongly related to the bank’s interbank reliance and its vulnerability to shock scenarios. The second work is that a single decision-maker allocates a sampling budget to alternatives in a repeated sequential decision-making problem. The decision maker repeats the action of choosing one of the alternatives per time point for a finite amount of time, ultimately aiming to achieve several objectives related to the payoff. Since the payoffs for each alternative follow a probabilistic distribution that is not known in advance, the decision maker seeks to find the optimal sampling budget allocation to ultimately achieve the multiple goals while obtaining the information about the characteristics of payoffs of each alternative. To address this issue, we develop adaptive decision-making policies in which all objectives are achieved with high probability based on rigorous asymptotic analysis.