Monotone imitation
The authors derive the precise characteristics that a social learning process has to satisfy in order to lead the population to choose the actions which fully informed rational agents would choose. Consistency of decisions with the order defined by first-order stochastic dominance may be regarded as one of the most elemental characteristics of rational choice. The results reveal that very simple and rather natural behavioral rules may display this property. In this sense the results implied by the characterization of first-order monotone (FOM) rules suggest that rules could be characterized in terms of the dynamics of the fraction of the population who play first-order stochastic dominant actions. The characterization provided by the authors reveals that the set of FOM rules can be obtained in either way. Therefore, the behavioral rules that lead to decision making are consistent with first-order stochastic dominance. It is easy to see that every (non-trivial) improving rule is FOM, because it is based on the notion of first-order stochastic dominance and not on the notion of expected values. The authors provide two characterizations for FOM rules. The first characterization reveals that a necessary condition for first-order monotonicity is that the behavioral rule must be imitative. A behavioral rule is called imitative if each individual plays either the action that she played in the previous period or the action played by the individual she observed. Furthermore, this characterization shows that when the payoff distribution of one action strictly first-order stochastically dominates the payoff distribution of the other, then the expected net-switch to the first-order dominant action is strictly positive. The analysis also reveals that this condition requires the behavioral rule to be impartial. A behavioral rule is called impartial if, when all the distributions of payoffs associated to the different actions are the same, the proportion of individuals who choose each action is expected to remain the same. The second characterization describes FOM rules in terms of their functional form. For each pair of actions \(a\) and \(a'\), the authors define the net-switching function from \(a\) to \(a'\). This is the difference between the probability of playing \(a'\) in the next period by an individual who played \(a\) in this period and observed another individual who played \(a'\), and the probability of playing action \(a\) in the next period by an individual who played \(a'\) in this period and observed another individual who played \(a\), when the payoff obtained from each action in both cases is the same. The arguments of this function are the payoffs obtained from playing each action. This characterization reveals that the net-switching functions are symmetric in the obtained payoffs in the sense that if the payoff obtained with action \(a\) is substituted for the payoff obtained with action \(a'\) and vice versa, then only the sign of the net-switching function changes. The magnitude remains the same. From the proof of this result it is easy to see that this feature is derived from the impartial property. Furthermore the net-switching function from \(a\) to \(a'\) is increasing in the payoff obtained with action \(a'\). Likewise, and as a consequence of the symmetry described above, the net-switching function is decreasing in the payoff obtained with action \(a\). Therefore, the net-switching functions are strictly positive if the payoff of the action to which the probability is being switched is strictly greater than the payoff of the action from which the probability is being switched. However, the net-switching functions do not need to be strictly increasing in the payoff of the action that receives the probability. A technical lemma that is a corner stone for the proof of this result is presented in the article. The characterizations of FOM rules assume that all the individuals in the population use the same behavioral rule. It is straightforward to generalize these characterizations to the case of heterogeneous behavioral rules. At the end of the paper the authors discuss and motivate alternative directions for further research. Some of these extensions are analyzed formally in appendices. Particularly, appendix C provides the analysis of individually monotone behavioral rules. These rules are imitative rules such that when the payoff distribution of one of the actions an individual observes first-order stochastically dominates the payoff distribution of the other, then the expected probability of playing the dominant action is higher than the expected probability of playing the other. Appendix D analyzes second-order monotone (SOM) rules. These rules are the analogous of FOM rules with regards to second-order stochastic dominance. The FOM rules serve to provide a foundation for a number of behavioral rules in the literature. Future research shall test if experimental subjects use behavioral rules that are FOM.
scientific article; zbMATH DE number 5620104