Donaldson invariants of CP^1 x CP^1 and Mock Theta Functions

We compute the Moore-Witten regularized u-plane integral on CP^1 x CP^1 directly in a chamber where the elliptic unfolding technique fails to work. This allows us to determine explicit formulas for its SU(2) and SO(3)-Donaldson invariants in terms of Mock modular forms.Comment: 20 pages, LaTe

Jacobian elliptic Kummer surfaces and special function identities

We derive formulas for the construction of all inequivalent Jacobian elliptic fibrations on the Kummer surface of two non-isogeneous elliptic curves from extremal rational elliptic surfaces by rational base transformations and quadratic twists. We then show that each such decomposition yields a description of the Picard-Fuchs system satisfied by the periods of the holomorphic two-form as either a tensor product of two Gauss' hypergeometric differential equations, an Appell hypergeometric system, or a GKZ differential system. As the answer must be independent of the fibration used, identities relating differential systems are obtained. They include a new identity relating Appell's hypergeometric system to a product of two Gauss' hypergeometric differential equations by a cubic transformation.Comment: 20 page

Normal forms for Kummer surfaces

We determine normal forms for the Kummer surfaces associated with abelian surfaces of polarization of type $(1,1)$, $(1,2)$, $(2,2)$, $(2,4)$, and $(1,4)$. Explicit formulas for coordinates and moduli parameters in terms of Theta functions of genus two are also given. The normal forms in question are closely connected to the generalized Riemann identities for Theta functions of Mumford's.Comment: 49 page

You Owe Me

In many cultures and industries gifts are given in order to influence the recipient, often at the expense of a third party. Examples include business gifts of firms and lobbyists. In a series of experiments, we show that, even without incentive or informational effects, small gifts strongly influence the recipient’s behavior in favor of the gift giver, in particular when a third party bears the cost. Subjects are well aware that the gift is given to influence their behavior but reciprocate nevertheless. Withholding the gift triggers a strong negative response. These findings are inconsistent with the most prominent models of social preferences. We propose an extension of existing theories to capture the observed behavior by endogenizing the “reference group” to whom social preferences are applied. We also show that disclosure and size limits are not effective in reducing the effect of gifts, consistent with our model. Financial incentives ameliorate the effect of the gift but backfire when available but not provided

Contractibility and the Design of Research Agreements

We analyze how variations in contractibility affect the design of contracts in the context of biotechnology research agreements. A major concern of firms financing biotechnology research is that the R&D firms might use the funding to subsidize other projects or substitute one project for another. We develop a model based on the property-rights theory of the firm that allows for researchers in the R&D firms to pursue multiple projects. When research activities are non-verifiable, we show that it is optimal for the financing company to obtain the option right to terminate the research agreement while maintaining broad property rights to the terminated project. The option right induces the biotechnology firm researchers not to deviate from the proposed research activities. The contract prevents opportunistic exercise of the termination right by conditioning payments on the termination of the agreement. We test the model empirically using a new data set on 584 biotechnology research agreements. We find that the assignment of termination and broad intellectual property rights to the financing firm occurs in contractually difficult environments in which there is no specifiable lead product candidate. We also analyze how the contractual design varies with the R&D firm's financial constraints and research capacities and with the type of financing firm. The additional empirical results allow us to distinguish the property-rights explanation from alternative stories, based on uncertainty and asymmetric information about the project quality or research abilities.

Overestimating Self_Control: Evidence from the Health Club Industry

Experimental evidence suggests that people make time-inconsistent choices and display overconfidence about positive personal attributes. Do these features affect consumer behavior in the market? To address this question we use a new panel data set from three US health clubs with information on the contract choices and the day-to-day attendance decisions of 7,978 health club members over three years. Members who choose a contract with a flat monthly fee of over $70 attend on average 4.8 times per month. They pay a price per expected visit of more than$17, even though a $10-per-visit fee is also available. On average, these users forgo savings of$700 during their membership. We review many aspects of the consumer behavior, including the interval between last attendance and contract termination, the survival probability, and the correlation between different consumption choices. The empirical results are difficult to reconcile with the standard assumption of time-consistent preferences and rational expectations. A model of time-inconsistent agents with overconfidence about future patience explains the findings. The agents overestimate the future attendance and delay contract cancellation whenever renewal is automatic. Salesman pressure and overstimation of future efficiency are the leading alternative explanations.

Are Investors Naive About Incentives?

Traditional economic analysis of markets with asymmetric information assumes that uninformed agents account for the incentives of informed agents to distort information. We analyze whether investors in the stock market internalize such incentives. Stock recommendations of security analysts are likely to be biased upwards, particularly if the issuing analyst is affiliated with the underwriter of the recommended stock. Using the NYSE Trades and Quotations database, we find that large (institutional) traders account for the upward bias and exert no abnormal trade reaction to buy recommendations, and significant selling pressure in response to hold recommendations. Small (individual) traders do not account for the upward shift and exert significantly positive pressure for buys and zero pressure for hold recommendations. Moreover, large traders discount positive recommendations from affiliated analysts more than from unaffiliated analysts, while small traders do not distinguish between them. The naive trading behavior of small investors induces negative abnormal portfolio returns.

Kummer sandwiches and Greene-Plesser construction

In the context of K3 mirror symmetry, the Greene-Plesser orbifolding method constructs a family of K3 surfaces, the mirror of quartic hypersurfaces in $\mathbb{P}^3$, starting from a special one-parameter family of K3 varieties known as the quartic Dwork pencil. We show that certain K3 double covers obtained from the three-parameter family of quartic Kummer surfaces associated with a principally polarized abelian surface generalize the relation of the Dwork pencil and the quartic mirror family. Moreover, for the three-parameter family we compute a formula for the rational point-count of its generic member and derive its transformation behavior with respect to $(2,2)$-isogenies of the underlying abelian surface.Comment: 27 pages; minor typos corrected in version