Essays on auctions, mechanism design, and repeated games

Chapter 1 revisits the classic mechanism design question of when buyers with private information in an auction setting can expect to receive economic rents. It is well known that under standard assumptions, the seller can fully extract rent for generic prior distributions over the valuations of the buyers. However, a crucial assumption underlying this result is that the buyers are not able to acquire any additional information about each other. This assumption can be seen as a special case of a general model where buyers have access to some information acquisition technology. We provide necessary and sufficient conditions on the information acquisition technology for the seller to be able to guarantee full rent extraction. Chapter 2 studies auctions when there is ambiguity over the joint information structures generating the valuations and signals of players. We analyse how two standard auction effects interact with ambiguity. First, a ‘competition effect’ arises when different beliefs about the correlation between bidders’ valuations imply different likelihoods of facing competitive bids. Second, a ‘winner’s value effect’ arises when different beliefs imply different inferences about the winner’s value. In private value auctions, only the first effect exists, and the distribution of bids first order stochastically dominates the distribution of bids in the absence of ambiguity. In common value auctions both effects exist, and the seller’s revenue decreases with ambiguity. Chapter 3 characterises the equilibrium payoff set of a repeated game with local interaction and local monitoring. A Nash threats folk theorem holds without any restrictions on the network structure when players are arbitrarily patient, i.e. any feasible payoff above the Nash equilibrium point can be approximated arbitrarily well in sequential equilibrium. When players discount the future, the folk theorem cannot hold unless further restrictions are made either on payoffs or the network structure

Electrokinetic phenomena in nanopore transport

Nanopores are apertures of nanometric dimensions in an insulating matrix. They are routinely used to sense and measure properties of single molecules such as DNA. This sensing technique relies on the process of translocation, whereby a molecule in aqueous solution moves through the pore under an applied electric field. The presence of the molecule modulates the ionic current through the pore, from which information can be obtained regarding the molecule's properties. Whereas the electrical properties of the nanopore are relatively well known, much less work has been done regarding their fluidic properties. In this thesis I investigate the effects of fluid flow within the nanopore system. In particular, the charged nature of the DNA and pore walls results in electrically-driven flows called electroosmosis. Using a setup which combines the nanopore with an optical trap to measure forces with piconewton sensitivity, we elucidate the electroosmotic coupling between multiple DNA molecules inside the confined environment of the pore. Outside the pore, these flows produce a nanofluidic jet, since the pore behaves like a small electroosmotic pump. We show that this jet is well-described by the low Reynolds number limit of the classical Landau-Squire solution of the Navier-Stokes equations. The properties of this jet vary in a complex way with changing conditions: the jet reverses direction as a function of salt concentration, and exhibits asymmetry with respect to voltage reversal. Using a combination of simulations and analytic modelling, we are able to account for all of these effects. The result of this work is a more complete understanding of the fluidic properties of the nanopore. These effects govern the translocation process, and thus have consequences for better control of single molecule sensing. Additionally, the phenomena we have uncovered could potentially be harnessed in novel microfluidic applications, whose technological implications range from lab-on-a-chip devices to personalised medicine

Private and common value auctions with ambiguity over correlation

We analyze auctions when individuals have ambiguity over the joint information structures generating the valuations and signals of players. We analyze how two standard auction effects interact with the ambiguity of bidders over correlation structures. First, a “competition effect” arises when different beliefs about the correlation between bidders' valuations imply different likelihoods of facing competitive bids. Second, a “winner's value effect” arises when different beliefs imply different inferences about the winner's value. In the private values case, only the first effect exists and this implies that the distribution of bids first order stochastically dominates the distribution of bids in the absence of ambiguity. In common value auctions both effects exist and we show that compared to the canonical model, both in the first-price and second-price auctions, these effects combine to imply that the seller's revenue decreases with ambiguity (in contrast with the private values case). We then characterise the optimal auction in both the private and common value cases. A novel feature that arises in the optimal mechanism in the common values case is that the seller only partially insures the high type against ambiguity

A partially self-regenerating synthetic cell

Self-regeneration is a fundamental function of all living systems. Here we demonstrate partial molecular self-regeneration in a synthetic cell. By implementing a minimal transcription-translation system within microfluidic reactors, the system is able to regenerate essential protein components from DNA templates and sustain synthesis activity for over a day. By quantitating genotype-phenotype relationships combined with computational modeling we find that minimizing resource competition and optimizing resource allocation are both critically important for achieving robust system function. With this understanding, we achieve simultaneous regeneration of multiple proteins by determining the required DNA ratios necessary for sustained self-regeneration. This work introduces a conceptual and experimental framework for the development of a self-replicating synthetic cell. A fundamental function of living systems is regenerating essential components. Here the authors design an artificial cell using a minimal transcription-translation system in microfluidic reactors for sustained regeneration of multiple essential proteins

The identification of 93 day periodic photometric variability for YSO YLW 16A

Aims. Periodic variability in young stellar objects (YSOs) offers indirect evidence for an active dynamical mechanism. Starspots, accretion, stellar companions, and disk veiling can contribute to the photometric variability of YSOs. Methods. As part of an ongoing study of the ρ Oph star forming region, we report the discovery of 92.6 day periodic variations for the Class I YSO YLW 16A, observed over a period of three years. A SED model was fit to available photometric data for the object. Results. We propose a triple-system with an inner binary with a period of 93 days eclipsed by a warped circum-binary disk. The nature of the secondary is unconstrained and could be stellar or sub-stellar. We confirm the discovery of a tertiary companion at a projected separation of ~40 AU that could account for the circum-binary disk warp. This light curve and model is similar to the model we proposed for WL 4 in previous work. Understanding these systems may lead to insights about the nature of stellar evolution and planetary formation, and provide valuable benchmarks for future theoretical modeling and near- and mid-infrared synoptic surveys of YSOs

Rewireable Building Blocks for Enzyme-Powered DNA Computing Networks

Neural networks enable the processing of large, complex data sets with applications in disease diagnosis, cell profiling, and drug discovery. Beyond electronic computers, neural networks have been implemented using programmable biomolecules such as DNA; this confers unique advantages, such as greater portability, electricity-free operation, and direct analysis of patterns of biomolecules in solution. Analogous to bottlenecks in electronic computers, the computing power of DNA-based neural networks is limited by the ability to add more computing units, i.e., neurons. This limitation exists because current architectures require many nucleic acids to model a single neuron. Each additional neuron compounds existing problems such as long assembly times, high background signal, and cross-talk between components. Here, we test three strategies to solve this limitation and improve the scalability of DNA-based neural networks: (i) enzymatic synthesis for high-purity neurons, (ii) spatial patterning of neuron clusters based on their network position, and (iii) encoding neuron connectivity on a universal single-stranded DNA backbone. We show that neurons implemented via these strategies activate quickly, with a high signal-to-background ratio and process-weighted inputs. We rewired our modular neurons to demonstrate basic neural network motifs such as cascading, fan-in, and fan-out circuits. Finally, we designed a prototype two-layer microfluidic device to automate the operation of our circuits. We envision that our proposed design will help scale DNA-based neural networks due to its modularity, simplicity of synthesis, and compatibility with various neural network architectures. This will enable portable computing power for applications in portable diagnostics, compact data storage, and autonomous decision making for lab-on-a-chips

Cell-free gene-regulatory network engineering with synthetic transcription factors

Gene-regulatory networks are ubiquitous in nature and critical for bottom-up engineering of synthetic networks. Transcriptional repression is a fundamental function that can be tuned at the level of DNA, protein, and cooperative protein-protein interactions, necessitating high-throughput experimental approaches for in-depth characterization. Here, we used a cell-free system in combination with a high-throughput microfluidic device to comprehensively study the different tuning mechanisms of a synthetic zinc-finger repressor library, whose affinity and co-operativity can be rationally engineered. The device is integrated into a comprehensive workflow that includes determination of transcription-factor binding-energy landscapes and mechanistic modeling, enabling us to generate a library of well-characterized synthetic transcription factors and corresponding promoters, which we then used to build gene-regulatory networks de novo. The well-characterized synthetic parts and insights gained should be useful for rationally engineering gene-regulatory networks and for studying the biophysics of transcriptional regulation

Self-Assembling Protein Surfaces for In Situ Capture of Cell-Free-Synthesized Proteins

We present a new method for the surface capture of proteins in cell-free protein synthesis (CFPS). We demonstrate the spontaneous self-assembly of the protein BslA into functionalizable surfaces on the surface of a CFPS reaction chamber. We show that proteins can be covalently captured by such surfaces, using “Catcher/Tag” technology. Importantly, proteins of interest can be captured either when synthesised in situ by CFPS above the BslA surfaces, or when added as pure protein. The simplicity and cost efficiency of this method suggest that it will find many applications in cell-free-based methods

Electroosmotic flow rectification in conical nanopores

Recent experimental work has suggested that electroosmotic flows (EOF) through conical nanopores exhibit rectification in the opposite sense to the well-studied effect of ionic current rectification. A positive bias voltage generates large EOF and small current, while negative voltages generate small EOF and large current. Here we systematically investigate this effect using finite-element simulations. We find that inside the pore, the electric field and salt concentration are inversely correlated, which leads to the inverse relationship between the magnitudes of EOF and current. Rectification occurs when the pore is driven into states characterized by different salt concentrations depending on the sign of the voltage. The mechanism responsible for this behaviour is concentration polarization, which requires the pore to exhibit the properties of permselectivity and asymmetry.Comment: 21 pages, 6 figure