When Do We Learn to Cooperate? The Role of Social Learning in Social Dilemmas

In this paper, I look at the interaction between social learning and cooperative behavior. I model this using a social dilemma game with publicly observed sequential actions and asymmetric information about pay offs. I find that some informed agents in this model act, individually and without collusion, to conceal the privately optimal action. Because the privately optimal action is socially costly the behavior of informed agents can lead to a Pareto improvement in a social dilemma. In my model I show that it is possible to get cooperative behavior if information is restricted to a small but non-zero proportion of the population. Moreover, such cooperative behavior occurs in a finite setting where it is public knowledge which agent will act last. The proportion of cooperative agents within the population can be made arbitrarily close to 1 by increasing the finite number of agents playing the game. Finally, I show that under a broad set of conditions that it is a Pareto improvement on a corner value, in the ex-ante welfare sense, for an interior proportion of the population to be informed.

Nondictatorial Arrovian Social Welfare Functions: An Integer Programming Approach

In the line opened by Kalai and Muller (1997), we explore new conditions on prefernce domains which make it possible to avoid Arrow's impossibility result. In our main theorem, we provide a complete characterization of the domains admitting nondictorial Arrovian social welfare functions with ties (i.e. including indifference in the range) by introducing a notion of strict decomposability. In the proof, we use integer programming tools, following an approach first applied to social choice theory by Sethuraman, Teo and Vohra ((2003), (2006)). In order to obtain a representation of Arrovian social welfare functions whose range can include indifference, we generalize Sethuraman et al.'s work and specify integer programs in which variables are allowed to assume values in the set {0, 1/2, 1}: indeed, we show that, there exists a one-to-one correspondence between solutions of an integer program defined on this set and the set of all Arrovian social welfare functions - without restrictions on the range.