In a partnership game, each player's utility depends on the other players' actions through a commonly observed consequence (e.g. output, profit, price), which is itself a function of the players' actions and an exogenous stochastic environment. If a partnership game is repeated infinitely, and each player's payoff in the infinite game (supergame) is the long-run average of his expected one-period utilities, then efficient combinations of one-period actions can be sustained as Nash equilibria of the supergame even if the players cannot observe other players' actions or information, but can only observe the resulting consequences.

Prices and the Turnpike: III. Paths of Economic Growth that are Optimal with Regard only to Final States: A Turnpike Theorem1 Roy Radner Roy Radner Berkeley, California Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 28, Issue 2, February 1961, Pages 98–104, https://doi.org/10.2307/2295707 Published: 01 February 1961

We examine the proposition that competitive firms must behave as if they were maximizing profits; otherwise they would go bankrupt, or even fail to be financed in a competitive capital market. We investigate a model in which an entrepreneur raises funds for a risky enterprise on a competitive capital market, by offering a “dividend policy” based on the realized (stochastic) flow of earnings. We show that an entrepreneur who maximizes the expected sum of discounted dividends is sure to fail in finite time. On the other hand, many other behaviours yield positive expected profits and are able to attract investment funds, and yet result in a positive probability of surviving forever. As a consequence, if new firms have sufficiently diverse behaviours, then even if there is a constant stream of new entrants, after a long time practically all of the surviving firms will not have been maximizing profits.

In this note we present an example of a repeated partnership game with imperfect monitoring in which all supergame equilibria with positive discount rates are bounded away from full efficiency uniformly in the discount rate, provided the latter is strictly positive. On the other hand, if the players do not discount the future, then every efficient one-period payoff vector that dominates the one-period equilibrium payoff vector can be attained by an equilibrium of the repeated game. Thus the correspondence that maps the players' discount rate into the corresponding set of repeated-game equilibrium payoff vectors is discontinuous at the point at which the discount rate is zero.