Final Report Summary - PSYCHOLOGICAL GAMES (Psychological game theory and Bayesian rationality)
The aim of this project has been to study how people reason in psychological games. These are games where the payoffs are motivation dependent, i.e. players care not only about their own payoffs but also about the expectations that the others have about their own behaviour, the beliefs that others have about everybody else's expectations, and so on. Clearly, in this class of games, which have been proven to be a very useful tool for studying emotions such as guilt or reciprocity, a very important factor is the players' belief hierarchies about each player's behaviour, implying that there is a strong link with epistemic game theory which studies the reasoning process of players.
During this project, I worked on different epistemic models that can be applied to psychological games as a special case. In my single-authored paper, titled 'Epistemic equivalence of lexicographic belief representations', I provide a unification between the different models used to study belief hierarchies. This paper has already been submitted to a leading game theory journal, and a revision has already been requested by the journal. Two more papers have been submitted for publication, titled 'Hierarchies of conditional beliefs derived from a commonly known prior', 'On consensus through communication without a commonly known consensus' (with Mark Voorneveld) and 'Reasoning-based introspection' (with Olivier Gossner), whereas I have also completed a number of working papers which are about to also be submitted for publication: 'Decision making with imperfect knowledge of the state space' (with Friederike Mengel and Alexander Vostroknutov), 'Awareness in repeated games', (with Friederike Mengel and Alexander Vostroknutov). Finally, I have a number of relevant on-going papers, begun during this project: 'Rational belief hierarchies', 'Dynamic games with bounded memory' (with Andres Perea), 'Nash equilibrium without commonly known conjectures' (with Christian Bach), and which will be completed and submitted in the near future.
The previous results help us clarify several issues that have recently attracted quite a lot of discussion among game theorists, especially epistemic game theorists. Moreover, they provide new insights for psychological game theory, thus making the project very relevant for our scientific community. It is also worthwhile mentioning that during the project I co-founded EpiCenter, a research group for the study of epistemic game theory in Maastricht University, which already counts five members: two faculty members, two postdoctoral fellows and one PhD student, and has been very active organising several events among which an international conference.
During this project, I worked on different epistemic models that can be applied to psychological games as a special case. In my single-authored paper, titled 'Epistemic equivalence of lexicographic belief representations', I provide a unification between the different models used to study belief hierarchies. This paper has already been submitted to a leading game theory journal, and a revision has already been requested by the journal. Two more papers have been submitted for publication, titled 'Hierarchies of conditional beliefs derived from a commonly known prior', 'On consensus through communication without a commonly known consensus' (with Mark Voorneveld) and 'Reasoning-based introspection' (with Olivier Gossner), whereas I have also completed a number of working papers which are about to also be submitted for publication: 'Decision making with imperfect knowledge of the state space' (with Friederike Mengel and Alexander Vostroknutov), 'Awareness in repeated games', (with Friederike Mengel and Alexander Vostroknutov). Finally, I have a number of relevant on-going papers, begun during this project: 'Rational belief hierarchies', 'Dynamic games with bounded memory' (with Andres Perea), 'Nash equilibrium without commonly known conjectures' (with Christian Bach), and which will be completed and submitted in the near future.
The previous results help us clarify several issues that have recently attracted quite a lot of discussion among game theorists, especially epistemic game theorists. Moreover, they provide new insights for psychological game theory, thus making the project very relevant for our scientific community. It is also worthwhile mentioning that during the project I co-founded EpiCenter, a research group for the study of epistemic game theory in Maastricht University, which already counts five members: two faculty members, two postdoctoral fellows and one PhD student, and has been very active organising several events among which an international conference.