Applications and Limits of Game Theory
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
This section introduces one case where game theory has been
successfully used to explain behaviour (Sinervo & Lively, 1996).
There are many others, including:
If studying game theory, it would be a good idea to consider how it
has been applied in a domain of interest to you.
Why is game theory so useful given that problems are so easy to find?
For our purposes, two limits of game theory are particularly important:
- in Hi-Lo, it is impossible using vanilla game theory to show that choosing Hi is more rational than choosing Lo; and
- in the Prisoners’ Dilemma, game theory implies that it is not rational to cooperate even though both agents’ doing so secures them the highest gain.
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: An action (or strategy) strictly dominates another if it ensures better outcomes for its player no matter what other players choose. (See also weak dominance.)
: This term is used for any version of the theory based on the ideas of Neumann et al. (1953) and presented in any of the standard textbooks including. Hargreaves-Heap & Varoufakis (2004); Osborne & Rubinstein (1994); Tadelis (2013); Rasmusen (2007).
: In game theory, one action strictly dominates another action if the first action guarantees its player higher payoffs than the second action regardless of what other players choose to do. (See Definition 59.2 in Osborne & Rubinstein, 1994, p. 59 for a more general definition.)
: In game theory, one action weakly dominates another action if the first action guarantees its player payoffs at least as good as the other action and potentially better than it regardless of what other players choose to do. (Contrast strict dominance.)
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Hansen, A. J. (1986). Fighting Behavior in Bald Eagles: A Test of Game Theory. Ecology
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Hargreaves-Heap, S., & Varoufakis, Y. (2004). Game theory: A critical introduction
. London: Routledge. Retrieved from http://webcat.warwick.ac.uk/record=b2587142~S1
Madani, K. (2010). Game theory and water resources. Journal of Hydrology
(3), 225–238. https://doi.org/10.1016/j.jhydrol.2009.11.045
McAdams, R. H. (2008). Beyond the Prisoners’ Dilemma: Coordination, Game Theory, and Law. Southern California Law Review
Neumann, J. von, Morgenstern, O., Rubinstein, A., & Kuhn, H. W. (1953). Theory of Games and Economic Behavior
. Princeton, N.J. ; Woodstock: Princeton University Press.
Osborne, M. J., & Rubinstein, A. (1994). A course in game theory
. MIT press.
Rasmusen, E. (2007). Games and information: An introduction to game theory
(4th ed). Malden, MA ; Oxford: Blackwell Pub.
Roy, S., Ellis, C., Shiva, S., Dasgupta, D., Shandilya, V., & Wu, Q. (2010). A Survey of Game Theory as Applied to Network Security. In 2010 43rd Hawaii International Conference on System Sciences
(pp. 1–10). https://doi.org/10.1109/HICSS.2010.35
Sinervo, B., & Lively, C. M. (1996). The rockpaperscissors game and the evolution of alternative male strategies. Nature
(6571), 240–243. https://doi.org/10.1038/380240a0
Skyrms, B. (2000). Game theory, rationality and evolution of the social contract. Journal of Consciousness Studies
Tadelis, S. (2013). Game theory: An introduction
. Princeton: Princeton University Press.