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game theory

  A theory of interdependent decision-making where individuals (\'players\') must choose courses of action (\'strategies\') while remaining ignorant of other players\' choices, but with knowledge of the costs and benefits (\'payoffs\') of all the resulting potential outcomes. The goal of the theory is to determine through formal reasoning alone the rational course of action for any given player, and the consequences that ensue for the collective. One of game theory\'s most interesting results, and most familiar incarnations, the prisoner\'s dilemma, demonstrates that individual rational choice produces collective sub-optimality. What appears best for the individual because of interdependent decision-making turns out not to be best for anyone.

Game theory arose at the turn of the century, but was solidified as a sub-discipline in the mid-1940s with the publication of von Neumann\'s and Morgenstern\'s (1944) The theory of games and economic behavior. Because game theory represents a set of general theorems about behaviour, it is utilized in a swath of disciplines: biology, political science, sociology, philosophy, economics, and human geography (one of the earliest and now classic papers in the geographical literature is Gould\'s, 1963).

The simplest case is the strictly competitive two-person, zero-sum game. Here there is no potential for cooperation, because whatever one person gains, the other must lose. In geography the classic example is the derivation of the Hotelling model involving two ice-cream vendors on an elongated beach who must decide where to locate given a uniform distribution of sunbathers. Given the propensity of customers always to buy from the closest vendor, both ice-cream sellers will end up in the middle of the beach, back-to-back. It is a zero-sum game because if one vendor should move even slightly off centre towards one end, s/he will immediately lose some business while the other vendor will correspondingly gain. Under such conditions, the best strategy is one of maximin, that is, acting in such a way that guarantees at least a minimum payoff regardless of the actions of the other player. In the Hotelling case, the maximin solution is always to stand in the middle of the beach because a minimum market of at least half the total customers is always guaranteed irrespective of the actions of the other ice-cream seller. When both vendors adopt a maximin strategy, equilibrium obtains.

More complicated games have been devised that involve non-zero-sum pay-offs, i.e. through interaction all players can potentially gain. Here the bargaining model of John Nash (1950) has proved immensely useful, demonstrating that non-cooperative strategies can be the basis of non-zero-sum games. Other assumptions modified include increasing the number of players, allowing for incomplete information, running a sequence of games (\'supergames\') rather than assuming each one is a single play, and postulating satisficing behaviour instead of rational choice. This latter modification has proven particularly difficult to undertake, reinforcing the point that game theory sits squarely within the tradition of rational choice theory, and its concomitant approach of methodological individualism.

Some of the more interesting recent work in game theory revolves around the possibility of cooperation. The problem is that usually it is not rational for rational individuals to cooperate in a game, or, more generally, to engage in any form of collective action. At issue is the so-called free-rider problem. Associated with collective action are often individual costs if others do not cooperate (for example, being the only industrialist to install expensive anti-pollution equipment in a plant), but large collective gains if they do (for example, clean air and water for everyone). Given this structure of pay-offs, it is individually rational not to engage in collective action, but instead to free-ride on the actions of others (Olson, 1965). By so doing, any losses, such as losing business because of higher costs, are minimized, while any gains, such as an improved environment, can still be obtained, providing others act collectively. Of course, if everyone free-rides then there is no collective action, and as a consequence collective suboptimality eventuates from individual rational choice.

The free-rider argument has proven powerful. Many political theorists, beginning with Hobbes, have used it to justify the necessity of the state — if everyone free-rides, important public goods such as domestic security or even a healthy environment would never be provided (Taylor, 1987). This said, voluntary cooperation and collective action clearly do occur: workers go on strike, students defend democracy, and environmentalists block bulldozers and logging trucks. In each case, individuals act in a way to benefit collective interests, rather than their narrowly defined self-interest. But why does this happen? Four reasons have been proposed:

{img src=show_image.php?name=2022.gif } the pay-off structure may not reflect all the incentives impinging on collective action — for example, feelings of guilt or injustice with respect to others; {img src=show_image.php?name=2022.gif } the very interactions into which individuals enter can endogenously alter preferences in favour of collective action, for example, being swept up in revolutionary fervour; {img src=show_image.php?name=2022.gif } individuals may irrationally believe that if they engage in collective action then others will too; and finally, and most frequently discussed, {img src=show_image.php?name=2022.gif } there may be more than a single play to the game, in which case players are able to devise certain meta-strategies that favour cooperation (the most successful of which is \'tit-for-tat\', Axelrod, 1984).In each case because of some form of interdependence among individuals, the norm of free-riding is replaced by one of collective action.

Very little geographical work exists on cooperative game playing. Sheppard and Barnes (1990), however, attempt to ground geographically the four justifications for collective action given above. They argue that the interdependencies among individuals necessary for cooperative behaviour most readily occur in place. This is further justified by Olson\'s (1965) original work which suggested that free-rider effects are most likely to break down within small groups of people as might be found within specific locales. (TJB)

References Axelrod, R. 1984: The evolution of cooperation. New York: Basic Books. Gould, P.R. 1963: Man against his environment: a game-theoretical framework. Annals of the Association of American Geographers 53: 290-7. Nash, J.F. 1950: The bargaining problem. Econometrica 18: 155-62. Olson, M. 1965: The logic of collective action: public goods and the logic of groups. Cambridge, MA: Harvard University Press. Sheppard, E.S. and Barnes, T.J. 1990: The capitalist space economy: geographical analysis after Ricardo, Marx and Sraffa. London: Unwin Hyman. Taylor, M. 1987: The possibility of cooperation. Cambridge: Cambridge University Press. von Neumann, J. and Morgenstern, O. 1944: Theory of games and economic behavior. Princeton: Princeton University Press.

Suggested Reading Axelrod (1984). Sheppard and Barnes (1990), ch. 10. Taylor (1987).



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