Conclusion
This lecture introduced game theory and mentioned some of its applications and limits.
The limits motivated considering team reasoning.
According to its proponents, some social interactions are better modelled by team reasoning
than by game theory. But is this true?
Notes
At this point you should know what a game is and how games are represented by game theorists.
You should also be comfortable with some basic game-theoretic notions, dominance and
the nash equilibrium, and how these can be used in an attempt to specify general principles about
what rational agents should do in a game.
Because game theory is an extension of decision theory, deriving general principles
in game theory relies on the axioms needed for decision theory (see What Are Preferences?).
In addition, game theorists rely on some further assumptions. A key assumption is this: not only
are all the agents rational, but it is common knowledge to the agents that they are all rational.
The successful applications of game theory indicate that it is a useful model;
but its limits suggest that it cannot be the whole story about interaction among
rational agents.
The limits motivated considering team reasoning, which is supposed to provide a better
model of social interactions than game theory alone can.
Ask a Question
Your question will normally be answered in the question
session of the next lecture.
More information about asking questions.
Glossary
decision theory :
I use ‘decision theory’ for the theory elaborated by Jeffrey (1983). Variants are variously called ‘expected utility theory’ (Hargreaves-Heap & Varoufakis, 2004), ‘revealed preference theory’ (Sen, 1973) and ‘the theory of rational choice’ (Sugden, 1991). As the differences between variants are not important for our purposes, the term can be used for any of core formal parts of the standard approaches based on Ramsey (1931) and Savage (1972).
dominance :
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.)
game theory :
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).
model :
A model is a way some part or aspect of the world could be.
nash equilibrium :
‘a list of strategies, one for each player, such that no player can get a better payoff by switching to some other strategy that is available to her while all the other players adhere to the strategies specified for them in the list’ (Dixit, Skeath, & Reiley, 2014, p. 95).
team reasoning :
‘somebody team reasons if she works out the best possible feasible combination of actions for all the members of her team, then does her part in it’ (Bacharach, 2006, p. 121).
References
Bacharach, M. (2006).
Beyond individual choice. Princeton: Princeton University Press. Retrieved from
http://webcat.warwick.ac.uk/record=b3272720~S1Dixit, A., Skeath, S., & Reiley, D. (2014).
Games of strategy. New York: W. W. Norton; Company.
Hargreaves-Heap, S., & Varoufakis, Y. (2004).
Game theory: A critical introduction. London: Routledge. Retrieved from
http://webcat.warwick.ac.uk/record=b2587142~S1Jeffrey, R. C. (1983).
The logic of decision, second edition. Chicago: University of Chicago Press.
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.
Ramsey, F. (1931). Truth and probability. In R. Braithwaite (Ed.),
The foundations of mathematics and other logical essays. London: Routledge.
Rasmusen, E. (2007).
Games and information: An introduction to game theory (4th ed). Malden, MA ; Oxford: Blackwell Pub.
Savage, L. J. (1972).
The foundations of statistics (2nd rev. ed). New York: Dover Publications.
Sen, A. (1973). Behaviour and the Concept of Preference.
Economica,
40(159), 241–259.
https://doi.org/10.2307/2552796Sugden, R. (1991). Rational Choice: A Survey of Contributions from Economics and Philosophy.
The Economic Journal,
101(407), 751–785.
https://doi.org/10.2307/2233854Tadelis, S. (2013).
Game theory: An introduction. Princeton: Princeton University Press.