Consequences of demanding that agents employ computable strategies

Theme 3 - Novel Mathematical, Physical and Computer Science

It has often been conjectured that the imperfections of game theory's ability to accurately describe human strategic behaviour is due to its neglect of the limited information processing abilities of the agents. Correspondingly, there has been a call to study "bounded rationality", and to explore what rational behaviour under such information processing constraints means. In this project, I will study the consequences of demanding that agents employ computable strategies. A specific focus will be on multiplayer games. The project thus links logic and operational research to reveal a new perspective on the latter.

The aim of this project is a better understanding of the role of limited information processing ability of agents for notions of rational behaviour. In this, we are using computer science in order to develop a new and improved game theory. As a first step, we use Weihrauch reducibility as a methodology. This is a framework from logic/computability theory to capture how non-computable certain tasks are. In order to classify the Weihrauch degrees of problems from game theory, existing proof techniques will need to adapted and new ones developed. This will provide an initial indication of how big the impact of bounded information processing ability on the traditional notions of rational behaviour is. Subsequently, this impression can be enhanced by practical experiments letting machine learning algorithms interact in strategic situations. The very ambitious end goal is to propose a notion of rationality with built-in acknowledgment of limited computing power.