A Compositional Coalgebraic Semantics of Strategic Games
Achim Blumensath, Viktor Winschel

TL;DR
This paper introduces a compositional coalgebraic framework for modeling complex strategic games, enabling modular analysis, representation of self-referential phenomena, and direct implementation in functional programming languages.
Contribution
It presents a novel coalgebraic semantics for strategic games that supports compositional modeling of complex, self-referential social systems with various types of decision-making processes.
Findings
Framework supports arbitrarily complex game networks
Enables representation of self-referential structures like belief formation
Games can be directly implemented and analyzed in functional programming languages
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…
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Taxonomy
TopicsLogic, Reasoning, and Knowledge · Computability, Logic, AI Algorithms · Semantic Web and Ontologies
