Abstract
Compositional Game Theory is a new, recently introduced model of economic games based upon the computer science idea of compositionality. In it, complex and irregular games can be built up from smaller and simpler games, and the equilibria of these complex games can be defined recursively from the equilibria of their simpler subgames. This paper extends the model by providing a final coalgebra semantics for infinite games. In the course of this, we introduce a new operator on games to model the economic concept of subgame perfection.
Highlights
Compositionality, where one sees complex systems as being built from smaller subsystems, is widely regarded within computer science as a key enabling technique for scalability
Can compositionality be applied to economic games? In general, not all reasoning is compositional, especially if significant emergent behaviour is present in a large system but not in its subsystems
If σ is an optimal strategy for a game G, is σ part of an optimal strategy for G ∗ H, where G ∗ H is a super-game built from G and H? Clearly not, e.g. the Iterated Prisoner’s Dilemma has equilibria — such as cooperative equilibria — that do not arise from repeatedly playing the Nash equilibrium from the Prisoner’s Dilemma [2]
Summary
Compositionality, where one sees complex systems as being built from smaller subsystems, is widely regarded within computer science as a key enabling technique for scalability. Not all reasoning is compositional, especially if significant emergent behaviour is present in a large system but not in its subsystems. This is the case for economic games. Generally contain an operator to compositionally build infinite iterations of games. The general approach of Compositional Game Theory deals with a new concept of coutility.
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