Social Roles As An Effective Learning Mechanism

Using the `Buyer-Seller' game as an idealized form of social interaction across complementary roles, we examine two forms of `myopic learning', where individuals try to improve their response to their immediately past (social) environment. In role sampling , individuals examine a (random) sample of role equivalents, `updating' strategy play by evaluating the success of self and sampled others. In opponent sampling, individuals examine a (random) sample of potential future `game opponents' from the population employing the complementary role. Learning through role sampling can always increase or preserve best response play (to the immediate past), given an appropriate learning rule, while opponent sampling never does; it is thus better to ignore the world of opponents completely, choosing strategies based on observed outcomes of role equivalents. Under role learning, play either cycles about or spirals away from the Nash equilibrium of the game, with no one actually playing Nash in either case. With moderate rates of learning, the cycle is sufficiently distant from the equilibrium that Nash is of little value in predicting actual strategy play; here, the greater the uncertainty of the social world (e.g. variable game payoffs, preserving the buyer-seller structure), the less useful Nash play as a predictor of actual play. Under moderate, myopic (role) learning, game-theoretic emphasis on equilibrium as a predictor of individual behavior may be misplaced in even simple social situations.