The stochastic evolution of competition depends on the respective effort rates of the firms. We show that several effects are at work. The state tends to evolve in the direction where joint payoffs are greater. Since joint payoffs are related to joint product-market profits less joint effort...

The paper presents two models of races in which there is both technological uncertainty and strategic interaction between competitors. The authors' aim is to see how the efforts of competitors in a race vary with the intensity of rivalry between them. In the principal model, which is of a...

Laboratory and field studies of time preference find that discount rates are much greater in the short-run than in the long-run. Hyperbolic discount functions capture this property. This paper solves the decision problem of a hyperbolic consumer who faces stochastic income and a borrowing...

This paper introduces two complementary models of firm-specific training: an informational model and a productivity-enhancement model. In both models, market provision of firm-specific training is inefficient. However, the nature of the inefficiency depends on the balance between the two key...

We study the dynamics of a two player continuous time bi-matrix fictitious play. In particular, we investigate the dynamics of a one-parameter family of 3 x 3 games that includes a well-known example of Shapley's as a special case. We adopt a geometric (dynamical systems) approach and study the...

We describe two auction forms for search engine advertising and present two simple theoretical results concerning i) the estimation of click-through rates and ii) how to adjust the auctions for broad match search. We also describe some of the practical issues involved in implementing a VCG auction.

We study a dynamic-contracting problem involving risk sharing between two parties -- the Proposer and the Responder -- who invest in a risky asset until an exogenous but random termination time. In any time period they must invest all their wealth in the risky asset, but they can share the...