We are working on questions of rationality and cooperation in games, as well as logical epistemic and deontic logic. For that, we use an array of tools from mathematical and computational philosophy, game theory, and social choice.
Rationality and Cooperation in Games
How can rational players coordinate their choices when this can be to their mutual advantage? How can they cooperate even when it requires some personal sacrifice? Is there a difference between “mere” coordination and “full” cooperative or collective agency? Despite its successes and wide range of applications, these questions have turned out vexing for classical, non-cooperative game theory. We are currently studying the so-called theory of team reasoning and are trying to assess its potential to complement classical game theory in order to explain coordination, cooperation, and collective agency. In team reasoning agents are assumed to switch from one mode of reasoning asking “What should I do?” to another in which the answer to the question “What should we do?” dictates the agents’ choices. We are particularly interested in understanding the conditions under which team reasoning emerges and is stable in a population. For that, we draw both from philosophical work on collective intentionality and computational, agent-based modeling. See, in particular, the SCoLA project for more details and results.
Issues about the stability and the evolution of different strategies in a population are studied by a branch of game theory called evolutionary game theory, while the players’ interactive reasoning in a game is explicitly modeled by another branch named epistemic game theory. In the latter, the basic idea is to view rational decision-making in games as not essentially different from rational decision-making under uncertainty: it is a matter of coherence of choices and coherence of beliefs. With this in hand, one can look at what traditional, decision-theoretic norms would prescribe to players in games. When we do that it quickly becomes clear that higher-order beliefs (beliefs about beliefs) are central to the theory of rational decision making in strategic interaction, and that rationality in games is also a matter of rational belief revision.
There is a natural interplay between the evolutionary approach and the epistemic approach to games. While agents in a population may perform some strategies, e.g. cooperating with others, that may or may not be stable from an evolutionary point of view, their strategy choice also depends on their strategic reasoning, i.e., on their beliefs about the co-players’ choices, about the beliefs of the co-players on their choices, and so on, that is, it depends on the epistemic aspects of the game. In a broader perspective, we are hence interested in the connections between the epistemic approach and the evolutionary approach, where strategies can also be interpreted as more general choice principles, such as being cooperative, being selfish, being altruistic, and similar.
Epistemic Logic and Collective Attitudes
For many years now we have been working on logical and, more recently also computational models of knowledge, beliefs, and preferences, both for individuals and for collectives. We have been particularly interested in the application of epistemic logic to epistemic game theory, because it provides compact and perspicuous representations of higher-order knowledge and belief, i.e. knowledge and beliefs about the knowledge and beliefs of others. See, for instance, the SEP Entry of Epistemic Foundations of Game Theory for details. In more recent years we have been involved, on the one hand, in the development of models of higher-order information that address some aspect of the so-called logical omniscience problem, arguably one of the most well-known idealizations of standard epistemic logic. This has been done, for instance, through the joint German-Czech project SEGA. More recently we have also started to study models of group knowledge and belief that lift another important, but often overlooked assumption, namely that the identity of the group members is common knowledge. See this paper for a recent contribution along those lines. We have also been studying, on the other hand, the formation of collective attitudes, this time through the French-German ColAForm project. Through that project, we have been developing computational models of group deliberation and the formation of coherent collective preferences. That work is still ongoing, but this paper reports on some of the findings.
Deontic Logic and Theories of Legal Rights
Deontic logic and its application to theories of legal rights are also long-standing research topics here at the chair. Between 2015 and 2018 the German-Polish PIOTR project allowed us to study the relationship between obligations and permissions, and as well as questions more specifically related to the modeling of permissions in law and in ethics. This has led to several publications, for instance this one, as well as to Huimin Dong’s PhD dissertation. Following the PIOTR project we have been focusing on formalization of legal rights in deontic logic, and in particular on the notions of “powers” and “immunity” in the taxonomy developed by W. Hohfeld. For that we extended the standard theory of so-called normative position with tools originally developed in Dynamic epistemic logic, see for instance this publication, or this one (pp.323-338) for an application to notions of epistemic rights.
Deontic Logic and Permissions
The question of rationality in games raises important issues regarding the very logical structure of norms and their justification. Permissions are particularly interesting in from that point of view. It seems that in many contexts it makes more sense to talk about what is rationally permitted to do in games. Solution concepts rarely give unique prescriptions. To capture that we have been developing a new understanding of deontic modals, the logic of “obligations as weakest permissions,” and have been looking at the famous “Free Choice Permission” principle. This raises interesting question for deontic logic, action theory and defeasible reasoning.
Most of the current research on deontic logic at the Chair is currently done under the Permissions, Information and Institutional Dynamics, Obligations and Rights (PIOTR) project. This project is supported by the DFG-NCN (Poland) program "Beethoven". It studies the generation of obligations and duties from permissions and rights in deontic logic and law. The Principal Investigator is Prof. Dr. Olivier Roy. See the project website for more information.