A Compositional Coalgebraic Semantics of Strategic Games

Abstract: We provide a compositional coalgebraic semantics for strategic games. In our framework, like in the semantics of functional programming languages, coalgebras represent the observable behaviour of systems derived from the behaviour of the parts over an unobservable state space. We use coalgebras to describe and program stage games, finitely and potentially infinitely repeated hierarchical or parallel games with imperfect and incomplete information based on deterministic, non-deterministic or probabilistic decisions of learning agents in possibly endogenous networks. Our framework is compositional in that arbitrarily complex network of games can be composed. The coalgebraic approach allows to represent self-referential or reflexive structures like institutional dynamics, strategic network formation from within the network, belief formation, learning agents or other self-referential phenomena that characterise complex social systems of cognitive agents. And finally our games represent directly runnable code in functional programming languages that can also be analysed by sophisticated verification and logical tools of software engineering.