The Theorem of Gittins and Jones (1974) is, perhaps, the single most powerful result in the literature on Bandit problems. This result establishes that in independent-armed Bandit problems with geometric discounting over an infinite horizon, all optimal strategies may be obtained by solving a family of simple optimal stopping problems that associate with each arm an index known as the dynamic allocation index or, more popularly, as the Gittins index. Importantly, the Gittins index of an arm depends solely on the characteristics of that arm and the rate of discounting, and is otherwise completely independent of the problem under consideration. These features simplify significantly the task of characterizing optimal strategies in this class of problems.

The Bertrand-Edgeworth model describes competition among price setting sellers with production capacity constraints. The authors report on laboratory experiments that permit evaluation of different theories of Bertrand-Edgeworth competition: competitive pricing, Edgeworth cycles in prices, mixed strategy Nash equilibrium pricing, and tacit collusion. Each of the theories helps to explain some aspects of the data. However, none of these theories are completely consistent with the data. In relative terms, the Edgeworth cycle theory provides better predictions of key aspects of the data than the other theories. Coauthors are Stephen Rassenti, Stanley S. Reynolds, and Vernon L. Smith. Copyright 1994 by The Econometric Society.