  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.
