Applications and Limits of Game Theory
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Notes
Problems for applications of game theory are easy to find. Hargreaves-Heap & Varoufakis, 2004 is particularly full of them, but any recent-ish textbook will cover some.
What’s puzzling about game theory is that, despite the problems, there are many cases where it is successfully used to explain things.
This section introduces one case where game theory has been successfully used to explain behaviour (Sinervo & Lively, 1996). There are many others, including:
- law: inequality, culture and power (McAdams, 2008)
- network security (Roy et al., 2010)
- evolution of social contract (Skyrms, 2000)
- distribution of water resources (Madani, 2010)
- the tragedy of the commons (Tadelis, 2013, p. §5.2.2)
- foraging behaviours (Hansen, 1986)
If studying game theory, it would be a good idea to consider how it has been applied in a domain of interest to you.[1]
Why is game theory so useful given that limits so easy to find?
Two Limits
For our purposes, two limits on the application of game theory to specifying which actions are rational are particularly important:
- in Hi-Lo[2], it is impossible using vanilla game theory to show that choosing Hi is more rational than choosing Lo; and
- in the Prisoners’ Dilemma[2:1], game theory implies that it is not rational to cooperate even though both agents’ doing so secures them the highest gain.
In general, a limit of a theory is either (i) a true proposition (or class of propositions) which cannot be derived from the theory and which falls within the domain the theory is supposed to illuminate; or (ii) a false proposition (or class of propositions) which can be derived from the theory.
Note that there are no limits on game theory as such, only on applications of game theory. (Applications include (i) explaining patterns in observed behaviours and (ii) specifying which actions are rational.) This is because game theory is a model, so not the kind of thing that can have limits or be right or wrong.
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Glossary
References
Endnotes
I am not particularly recommending the sources cited here. Please share with me any good sources you find. ↩︎
These games are specified in the Appendix: Index of Games ↩︎ ↩︎