We provide a model of a decentralized, dynamic auction market platform (e.g.,
eBay) in which a large number of buyers and sellers participate in simultaneous, singleunit
auctions each period. Our model accounts for the endogenous entry of agents and
the impact of intertemporal optimization on bids. Solving our model with a finite number
of bidders is computationally intractable due to the curse of dimensionality, so we prove
that a continuum version of our model provides a good approximation of an equilibrium
in the finite model. We use the approximation to estimate the structural primitives of our
model using Kindle sales on eBay. We find that just over one third of Kindle auctions on
eBay result in an inefficient allocation with deadweight loss amounting to 13.5% of total
possible market surplus. We also find that partial centralization - for example, runnng
half as many 2-unit, uniform price auctions each day - would eliminate a large fraction
of the inefficiency, but yield lower seller revenues. Our results highlight the importance
of understanding platform composition effects—selection of agents into the market—in
assessing the implications of market design.
We present a simple model for the evolution of social behavior in family-structured, finite sized
populations. Interactions are represented as evolutionary games describing frequency-dependent
selection. Individuals interact more frequently with siblings than with members of the general
population, as quantified by an assortment parameter r, which can be interpreted as “relatedness”.
Other models, mostly of spatially structured populations, have shown that assortment can promote the
evolution of cooperation by facilitating interaction between cooperators, but this effect depends on the
details of the evolutionary process. For our model, we find that sibling assortment promotes cooperation
in stringent social dilemmas such as the Prisoner's Dilemma, but not necessarily in other situations.
These results are obtained through straightforward calculations of changes in gene frequency. We also
analyze our model using inclusive fitness. We find that the quantity of inclusive fitness does not exist for
general games. For special games, where inclusive fitness exists, it provides less information than the
Benjamin AllenHarvard University, Emmanuel CollegeChristine SampleEmmanuel CollegeYulia DementievaEmmanuel CollegeRuben C. MedeirosEmmanuel CollegeChristopher PaolettiEmmanuel CollegeMartin A. NowakHarvard University
Publications of CMSA of Harvardmathscidoc:1702.38002
Over time, a population acquires neutral genetic substitutions as a consequence of random
drift. A famous result in population genetics asserts that the rate, K, at which these substitutions
accumulate in the population coincides with the mutation rate, u, at which they arise in
individuals: K = u. This identity enables genetic sequence data to be used as a “molecular
clock” to estimate the timing of evolutionary events. While the molecular clock is known to
be perturbed by selection, it is thought that K = u holds very generally for neutral evolution.
Here we show that asymmetric spatial population structure can alter the molecular clock
rate for neutral mutations, leading to either K<u or K>u. Our results apply to a general class
of haploid, asexually reproducing, spatially structured populations. Deviations from K = u
occur because mutations arise unequally at different sites and have different probabilities of
fixation depending on where they arise. If birth rates are uniform across sites, then K u. In
general, K can take any value between 0 and Nu. Our model can be applied to a variety of
population structures. In one example, we investigate the accumulation of genetic mutations
in the small intestine. In another application, we analyze over 900 Twitter networks to
study the effect of network topology on the fixation of neutral innovations in social evolution.
For a self-similar measure in d-dimensional Euclidean space with overlaps but satisfies the so-called bounded measure type condition introduced by Tang and the authors, we set up a framework for deriving a closed formula for the Lq-spectrum of the measure for nonnegative q. The framework allows us to include iterated function systems that have different contraction ratios and those in higher dimension. For self-similar measures with overlaps, closed formulas for the Lq-spectrum have only been obtained earlier for measures satisfying Strichartz second-order identities. We illustrate how to use our results to prove the differentiability of the Lq-spectrum, obtain the multifractal dimension spectrum, and compute the Hausdorff dimension of the measure.