# nLab game theory

Game theory is the study of strategic interaction between agents. It is often used for mathematical modelling of real-world situations in which agents interact, including in microeconomics, computer science and ecology.

Game theory should not be confused with game semantics, which has some terminology and history in common but has little overlap in practice.

## Via coalgebras

Several authors have approached game theory through coalgebraic systems theory, defining games as elements of the terminal coalgebra of an appropriate functor. This puts the concepts of state and state transition in a game to centre stage. It is closely related to extensive form games, whereby a game is defined by its tree of plays.

Perhaps the first paper to use this approach is Pavlovic 2009. Others are Abramsky and Winschel 2017 and Ghani, Kupke, Lambert and Forsberg 2018, the latter of which connects coalgebraic game theory with compositional game theory.

## Compositional game theory

Open games approach games as open systems, making them morphisms of a symmetric monoidal category which can be depicted as string diagrams, in the spirit of applied category theory. See Ghani, Hedges, Winschel and Zahn 2018.

Open games have a close connection to lenses. This can be used to situate open games inside a symmetric monoidal double category in a game-theoretically interesting way, see Hedges 2018.

## Homotopy and game theory

Homotopies between strategy profiles have been considered as a practical method to compute Nash equilibria (see Herings and Peeters 2010). This has never been studied categorically, but it suggests a possible route towards a higher-categorical approach to game theory.

## References

Last revised on July 15, 2019 at 13:09:41. See the history of this page for a list of all contributions to it.