Speaker: Aldo Ramirez-Abarca
Date and Time: Thursday, April 5th 2018, 16:00-17:30
Venue: ILLC Seminar Room F1.15, Science Park 107.
Title: Playing with stit-fire
Abstract: Stit logic has a strong connection to game theory. It is well known that some of the by-now established stit semantics were heavily inspired by game theoretical notions at their conception, under a clear correlation between ‘strategies’, on one hand, and ‘actions’, on the other. Furthermore, standards of game theory (such as utilities and dominance of strategies) have been explicitly imported into stit semantics to model different aspects of agentive behavior. A typical example is Horty’s (2001) stit formalization of obligation using weak dominance of strategies. It comes as no surprise, then, that the basic components for games (outcomes and individual/group/joint strategies) can be formalized with stit logic. This leads to what we may call game models for a stit language of individual/collective action (van Benthem & Pacuit, 2014; van de Putte, Tamminga, & Duijf, 2017). As it turns out, game models are in logical correspondence with a particular subclass of basic stit models (van de Putte, Tamminga, & Duijf, 2017). If we extend the basic stit language with both obligation and knowledge/belief operators, then, we can formalize traditional concepts found in richer representations of games (rationality, common knowledge, ex-interim/ex-ante/ ex-post knowledge, perfect/imperfect information, extensive-form-information games, uniformity of strategies, expected utility, solution concepts, etc.). The advantage of such a formalization is two-fold: in the game-theory-to-stit direction, it opens the door to producing highly applicable deontic epistemic/doxastic stit logics with intuitions grounded on the preexisting game-theoretical literature; in the stit-to-game-theory direction, it allows us to look for expressive axiomatizations of games, with syntactic formulas corresponding to complex semantic formulations of game constraints. In this talk, I will present an overview of the main results that evidence the connection between stit logic and game theory, and I will address a few proposals to further the use of this connection.