Game Theory Introduction

The bare minimum you need to know about game theory for the purposes of this course.

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Notes

What Is a Game?

Different researchers offer different statements. Games are various characterised as interactions, decriptions of interactions and situations:

A game is ‘any interaction between agents that is governed by a set of rules specifying the possible moves for each participant and a set of outcomes for each possible combination of moves’ (Hargreaves-Heap & Varoufakis, 2004, p. 3)

‘A game is a description of strategic interaction that includes the constraints on the actions that the players can take and the players’ interests, but does not specify the actions that the players do take’ (Osborne & Rubinstein, 1994, p. 2).

‘All situations in which at least one agent can only act to maximize his utility through anticipating (either consciously, or just implicitly in his behavior) the responses to his actions by one or more other agents is called a game’ (Ross, 2018).

Although the different characterisations of games are probably not strictly equivalent, the differences are unlikley to matter for our purposes.

We will focus on noncooperative games which are one-off events (so not repeated).

Books

There are many different game theory text books you could use. Tadelis (2013) and Osborne & Rubinstein (1994) are relatively concise and formal. Hargreaves-Heap & Varoufakis (2004) is more chatty and probably easier to get started with, but my impression is that it is sometimes difficult to get a clear sense of what game theory is from this book. Dixit, Skeath, & Reiley (2014) is a beautifully written and very clear book that takes things quite slowly; any of the five editions in the library will be fine, but select a later edition if you have the choice.

Why Study Game Theory and Its Limits?

Our overall concern is with understanding joint action in particular and social interaction more generally (see Introduction: Why Investigate Philosophical Issues in Behavioural Science?). Many researchers imply that game theory is relevant to this concern:

‘we treat game theory not as a branch of mathematics but as a social science whose aim is to understand the behavior of interacting decision-makers’ (Osborne & Rubinstein, 1994, p. 2; compare Dixit et al., 2014, pp. 36--7).

and:

‘game theory is the most important and useful tool in the analyst's kit whenever she confronts situations in which what counts as one agent's best action (for her) depends on expectations about what one or more other agents will do, and what counts as their best actions (for them) similarly depend on expectations about her’ (Ross, 2018).

Notably, even critics of game theory suggest that it is useful for understanding social interaction:

‘understanding why game theory does not, in the end, constitute the science of society (even though it comes close) is terribly important in understanding the nature and complexity of social processes’ (Hargreaves-Heap & Varoufakis, 2004, p. 3)

For sources on applications of game theory to understanding law, conflict and foraging (among other things), see Consequences and Applications of Game Theory.

Ask a Question

Your question will normally be answered in the question session of the next lecture.

More information about asking questions.

Glossary

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).

noncooperative game : ‘Games in which joint-action agreements are enforceable are called _cooperative_ games; those in which such enforcement is not possible, and individual participants must be allowed to act in their own interests, are called _noncooperative_ games’ (Dixit et al., 2014, p. 26).

strict dominance : 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.)

weak dominance : 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.)

References

Dixit, 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~S1

Jeffrey, 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.

Rasmusen, E. (2007). Games and information: An introduction to game theory (4th ed). Malden, MA ; Oxford: Blackwell Pub.

Ross, D. (2018). Game Theory. In E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (Fall 2018). Metaphysics Research Lab, Stanford University.

Tadelis, S. (2013). Game theory: An introduction. Princeton: Princeton University Press.