Discounted quotas

This paper extends the concept of a quota contract to account for discounting and for the possibility of infinitely many periods: a discounted quota fixes the number of expected discounted plays on each action. I first present a repeated principal-agent contracting environment in which menus of discounted quota contracts are optimal. I then recursively characterize the dynamics of discounted quotas for an infinitely repeated iid problem. Dynamics are described more explicitly for the limit as interactions become frequent, and for the case where only two actions are available.