Morales Siles, Antonio Jose; (1999) Learning, imitation and economic rationality. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

This thesis studies a population of agents facing repeatedly the same decision problem. Each agent knows the set of strategies available, but not the payoff distribution associated with each strategy. Agents follow simple behaviour rules which have no memory beyond what is encoded in the current "state" of the decision maker. We consider two different frameworks: (i) Individual learning and (ii) imitation learning. We also distinguish rules where the "state space" of the decision maker is the set of pure strategies, and behavior rules where it is the set of mixed strategies. The results for these two cases differ dramatically. In the case of individual learning, we say that a behaviour rule is maximising (approximately maximising) if asymptotically, for all underlying payoff distributions, the decision maker will play with probability one (close to one) the expected payoff maximising strategy. We show that no behaviour rule with pure strategy state space is (approximately) maximising. For the class of mixed strategy behaviour rules, we identify a property called monotonicity which implies approximate maximisation, provided learning proceeds in small steps. We characterise monotone learning rules, showing that they are closely related to the "replicator dynamics" of evolutionary game theory. When considering imitation learning, we postulate that at each iteration agents have the opportunity of randomly sampling another agent, observing the strategy which this agent played and his payoff. We consider two different settings. In the first, the behaviour of the observed population is exogenously given and constant. We show that no pure strategy imitation rule is (approximately) maximising. For mixed strategy behaviour rules, we characterise the set of all monotone rules, showing that monotone rules involve imitation probabilities which are proportional to payoff differences. In the second setup all agents in the population are allowed to adjust their behaviour according to some imitation rule. We show that no pure strategy imitation rule is maximising i.e. there does not exist a rule such that, if every member of the population adopts it, asymptotically every agent plays the expected payoff maximising strategy with probability one, regardless of the true payoff distribution. We then define and analyse a weaker requirement, "equilibrium" imitation rules.

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