Friday, August 29, 2014

Is Game Theory Useless?

It is often said that, sometimes citing examples such as the travelers' dilemma, that game theory is useless precisely because its analysis is predicated on pure rationality and "real people" simply do not act this way. Another version of this critique runs that game theory assumes that people are selfish and therefore its analysis is likewise doomed to misprediction. While it is certainly true that the "first cut" at many problems makes both assumptions, it would be a very poor analysis indeed were this also the "last cut." As we saw above, the tools of game theory are easily adapted to situations where irrationality is part of the environment. Moreover, unlike other social sciences preoccupied with irrationality, game theory is capable of delineating between situations where irrationality will alter outcomes and situations where it will not. Roughly speaking, situations where long chains of foxing and outfoxing are required to arrive at a solution are easily altered by irrationality. Situations where only short chains--or no chains at all in some cases--are more robust.

As to the assumption of selfish behavior, it too might be a first cut, but game theory is, in fact, agnostic about the source of the preferences producing payoffs. The same tools used to analyze situations involving choices among selfish individuals may be used for choices involving sainted individuals who care deeply about others. The comparison between the two merely represent a change in the payoffs to each party from a given combination of choices.

For instance, consider a prisoners' dilemma type situation where individuals might cooperate (C) or defect (D). With purely selfish preferences, we might model payoffs as CC = {3,3}, DD = {1,1}, DC ={4,0} and CD = {0,4}. Dominance would tell us that, in a one-off setting, both sides would defect. By contrast, this same game played by individuals who care only about societal wealth and not its distribution, would produce payoffs of CC = {6,6}, DD = {2,2}, CD = DC = {4, 4}. This game too has a dominant strategy, to always cooperate and so, in a one-off setting, both sides would cooperate and the "dilemma" vanishes. Combinations of these preferences are similarly modeled.

To be fair, some versions of non-selfishness entail more than a simple payoff adjustment, depending on whether these preferences derive from outcomes or process. When social preferences derive from outcomes, i.e. I care about society's distribution of income but not about the path by which this distribution was reached, then it truly is merely a matter of adjusting payoffs. When preferences derive from process, i.e. I care about opportunities available to individuals but not necessarily the final outcomes produced by which opportunities are chosen, the situation is far more complex but still analyzable using game theoretic tools.

This difference is, of course, vitally important to the structure of just institutions. Indeed, a common expression of this difference concerns whether justice hinges on equality of opportunity or equality of outcome with appropriately different institutions and legal remedies depending on which preferences society holds.

Branches of game theory, notably implementation theory and mechanism design, take the view that institutions themselves---divided government, civil versus common law, federalism---can be understood as "games" devised by societies as a means of achieving preference goals, including, of course, social preferences.

It would be entirely fair to deride game theory for its absurd assumptions of pure rationality and pure selfishness were those, in fact, the only assumptions by which this mode of analysis might be employed. Fortunately, they are not. Unfortunately, this caricature of game theory still persists widely--game theorists may be brilliant at analyzing interactive decisions, but seem to be lousy at marketing their craft to the wider world. Sophisticated firms, such as Google, Amazon, eBay, Yahoo, and many others recognize the speciousness of these arguments and employ game theory (and game theorists) to good effect.

So when next you hear someone dismiss game theory with these facile arguments, do society (and yourself) a favor and rebut them.

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