Investment Tournaments: Should a Rational Agent Put All His Eggs in One Basket?

Investment tournament is a type of decision problem introduced and studied in this paper. These problems involve allocation of investments among several alternatives whose values are subject to exogenous shocks. The payoff to the decision maker is a weighted sum of final values of each alternatives with weights convex in final values. (1) For the case of constant returns to scale it is optimal to allocate all resources to the most promising alternative. (2) In tournaments for a promotion the agents would rationally choose to put forth more effort in the early stage of the tournament in a bid to capture a larger share of mentoring resources.

Adoption of Standards under Uncertainty

The presence of noise in compliance times may have a critical impact on the selection of new technological standards. A technically superior standard is not necessarily viable because an arbitrarily small amount of noise may render coordination on that standard impossible. The criterion for the viability of a standard is that the sum of \support ratios" of all players must be smaller than one, where \support ratio" is dened as the ratio of the rm's per-period cost of supporting the standard to the per-period gross benet that the rm receives after all players comply with the standard.

Coordination under Uncertainty

A decision maker needs to schedule several activities that take uncertain time to complete and are only valuable together. Some activities are bound to be finished earlier than others, thus incurring waiting costs. We show how to schedule activities optimally, how to give independent agents performing them incentives that implement the efficient schedule, how to form teams, and how to optimally reduce uncertainty when it is possible to do so at a cost. The paper offers insights into important economic decisions such as planning large projects and coordinating product development activities.

Quantum deformation of planar amplitudes

In maximally supersymmetric four-dimensional gauge theories planar on-shell diagrams are closely related to the positive Grassmannian and the cell decomposition of it into the union of so called positroid cells \cite{A}. We establish that volume forms on positroids used to express scattering amplitudes can be $q$-deformed to Hochschild homology classes of corresponding quantum algebras. The planar amplitudes are represented in \cite {A} as sums of contributions of some set of positroid cells; we quantize these contributions. In classical limit our considerations allow us to obtain explicit formulas for contributions of positroid cells to scattering amplitudes

Internet Advertising and the Generalized Second Price Auction: Selling Billions of Dollars Worth of Keywords

We investigate the "generalized second price" auction (GSP), a new mechanism which is used by search engines to sell online advertising that most Internet users encounter daily. GSP is tailored to its unique environment, and neither the mechanism nor the environment have previously been studied in the mechanism design literature. Although GSP looks similar to the Vickrey-Clarke-Groves (VCG) mechanism, its properties are very different. In particular, unlike the VCG mechanism, GSP generally does not have an equilibrium in dominant strategies, and truth-telling is not an equilibrium of GSP. To analyze the properties of GSP in a dynamic environment, we describe the generalized English auction that corresponds to the GSP and show that it has a unique equilibrium. This is an ex post equilibrium that results in the same payoffs to all players as the dominant strategy equilibrium of VCG.