Unfolding Social Hierarchies

Consider a large population of ...nitely-lived agents organized into n di¤erent hierarchical levels. Every period, all those placed at each level are randomly matched to play a given symmetric game. Based on the resulting outcome, a 1⁄2-fraction of agents who (within their own level) attain the highest payo¤s are promoted upwards. On the other hand, newcomers replacing those who die every period enter at the lowest level and choose irreversibly the strategy to be played for the rest of their life. This choice is made, with some noise, by imitating one of the strategies adopted at the highest level. In this setup, the unique long-run behavior of the system is fully characterized for the whole class of 2 £ 2 coordination games and two alternative variations of the model. The results crucially depend on the key “institutional” parameters 1⁄2 and n. In particular, it is shown that ine¢cient behavior prevails in the long run (even when risk-dominated) if promotion is only mildly selective – high 1⁄2 – and the social system is quite hierarchical – large n: In a stylized manner, these parameter conditions may be viewed as re‡ecting a sort of institutional de...ciency that impairs economic performance.