An Ultra-Refined Grammar for Interactions: Thoughts on Robert Aumann's Philosophy of Game Theory

This note identifies and comments on selected crucial traits of Robert Aumann’s philosophy of game theory. In doing so, it aims at carving out and expressing some notions tacitly held by many working game theorists and ideally even at triggering subsequent reflection on the philosophy of game theory in general. According to my reconstruction of Aumann’s position, sophisticated, relatively precise rules of language—an ultra-refined grammar for interactions—constitute the heart of game theory. Consequently, the heart of game theory is devoid, or almost devoid, of empirical content. The final section proposes a nomenclature for lucidly discussing the relationships between theories, different types of models, and “the real world” and employs it to explicate and slightly amend Aumann’s remarks on the role of truth and fruitfulness in game theory.