Exploring the effects of computational costs in extensive games via modeling and simulation

Game theory has become a standard tool for depicting and demonstrating various game-like phenomena by providing appropriate mathematical models and for analyzing and predicting agents' behaviors and their decisions by formalizing solution concepts. The conventional game model mainly concerns ideal systems that would always guarantee optimal responses, which appears unrealistic for practical game scenarios since decision-making usually entails resource costs. Therefore, this study considers players' decision-making in extensive games when the computational cost of searching the strategy space is limited. We start with a new mathematical model of extensive games that features a bound on computational resources during players' decision-making process such that they can only foresee a part of the available alternatives in the future. This model is more appropriate in predicting players' strategies than the conventional model, under which we investigate the effects of computational costs on players' strategies as well as the computational complexity. Furthermore, a simulation experiment is performed to seek the connection between the amount of resources and the goodness of the outcomes. This study is expected to provide a foundation for players' rational decision-making with computational costs.

Automated summary

This study introduces a new mathematical model of extensive games with limitations on computational resources for players' decision-making. It investigates the effects of computational costs on players' strategies and computational complexity, also conducting simulation experiments to explore the relationship between the amount of resources and the goodness of outcomes.