A semantical approach to equilibria and rationality

Game theoretic equilibria are mathematical expressions of rationality. Rational agents are used to model not only humans and their software representatives, but also organisms, populations, species and genes, interacting with each other and with the environment. Rational behaviors are achieved not only through conscious reasoning, but also through spontaneous stabilization at equilibrium points. Formal theories of rationality are usually guided by informal intuitions, which are acquired by observing some concrete economic, biological, or network processes. Treating such processes as instances of computation, we reconstruct and refine some basic notions of equilibrium and rationality from the some basic structures of computation. It is, of course, well known that equilibria arise as fixed points; the point is that semantics of computation of fixed points seems to be providing novel methods, algebraic and coalgebraic, for reasoning about them.Comment: 18 pages; Proceedings of CALCO 200

A Cryptographic Moving-Knife Cake-Cutting Protocol

This paper proposes a cake-cutting protocol using cryptography when the cake is a heterogeneous good that is represented by an interval on a real line. Although the Dubins-Spanier moving-knife protocol with one knife achieves simple fairness, all players must execute the protocol synchronously. Thus, the protocol cannot be executed on asynchronous networks such as the Internet. We show that the moving-knife protocol can be executed asynchronously by a discrete protocol using a secure auction protocol. The number of cuts is n-1 where n is the number of players, which is the minimum.Comment: In Proceedings IWIGP 2012, arXiv:1202.422

New procedures for testing whether stock price processes are martingales

We propose procedures for testing whether stock price processes are martingales based on limit order type betting strategies. We first show that the null hypothesis of martingale property of a stock price process can be tested based on the capital process of a betting strategy. In particular with high frequency Markov type strategies we find that martingale null hypotheses are rejected for many stock price processes

Finding maxmin allocations in cooperative and competitive fair division

We consider upper and lower bounds for maxmin allocations of a completely divisible good in both competitive and cooperative strategic contexts. We then derive a subgradient algorithm to compute the exact value up to any fixed degree of precision.Comment: 20 pages, 3 figures. This third version improves the overll presentation; Optimization and Control (math.OC), Computer Science and Game Theory (cs.GT), Probability (math.PR

Towards Machine Wald

The past century has seen a steady increase in the need of estimating and predicting complex systems and making (possibly critical) decisions with limited information. Although computers have made possible the numerical evaluation of sophisticated statistical models, these models are still designed \emph{by humans} because there is currently no known recipe or algorithm for dividing the design of a statistical model into a sequence of arithmetic operations. Indeed enabling computers to \emph{think} as \emph{humans} have the ability to do when faced with uncertainty is challenging in several major ways: (1) Finding optimal statistical models remains to be formulated as a well posed problem when information on the system of interest is incomplete and comes in the form of a complex combination of sample data, partial knowledge of constitutive relations and a limited description of the distribution of input random variables. (2) The space of admissible scenarios along with the space of relevant information, assumptions, and/or beliefs, tend to be infinite dimensional, whereas calculus on a computer is necessarily discrete and finite. With this purpose, this paper explores the foundations of a rigorous framework for the scientific computation of optimal statistical estimators/models and reviews their connections with Decision Theory, Machine Learning, Bayesian Inference, Stochastic Optimization, Robust Optimization, Optimal Uncertainty Quantification and Information Based Complexity.Comment: 37 page

Temperature Dependence of Backbone Dynamics in Human Ileal Bile Acid-Binding Protein: Implications for the Mechanism of Ligand Binding

Human ileal bile acid-binding protein (I-BABP), a member of the family of intracellular lipid binding proteins plays a key role in the cellular trafficking and metabolic regulation of bile salts. The protein has two internal and, according to a recent study, an additional superficial binding site and binds di- and trihydroxy bile salts with positive cooperativity and a high degree of site-selectivity. Previously, in the apo form, we have identified an extensive network of conformational fluctuations on the millisecond time scale, which cease upon ligation. Additionally, ligand binding at room temperature was found to be accompanied by a slight rigidification of picosecond-nanosecond (ps-ns) backbone flexibility. In the current study, temperature-dependent N-15 NMR spin relaxation measurements were used to gain more insight into the role of dynamics in human I-BABP-bile salt recognition. According to our analysis, residues sensing a conformational exchange in the apo state can be grouped into two clusters with slightly different exchange rates. The entropy-enthalpy compensation observed for both clusters suggests a disorder-order transition between a ground and a sparsely populated higher energy state in the absence of ligands. Analysis of the faster, ps-ns motion of N-15-H-1 bond vectors indicates an unusual nonlinear temperature-dependence for both ligation states. Intriguingly, while bile salt binding results in a more uniform response to temperature change throughout the protein, the temperature derivative of the generalized order parameter shows different responses to temperature increase for the two forms of the protein in the investigated temperature range. Analysis of both slow and fast motions in human I-BABP indicates largely different energy landscapes for the apo and halo states suggesting that optimization of binding interactions might be achieved by altering the dynamic behavior of specific segments in the protein

Affine term structure models : a time-changed approach with perfect fit to market curves

We address the so-called calibration problem which consists of fitting in a tractable way a given model to a specified term structure like, e.g., yield or default probability curves. Time-homogeneous jump-diffusions like Vasicek or Cox-Ingersoll-Ross (possibly coupled with compounded Poisson jumps, JCIR), are tractable processes but have limited flexibility; they fail to replicate actual market curves. The deterministic shift extension of the latter (Hull-White or JCIR++) is a simple but yet efficient solution that is widely used by both academics and practitioners. However, the shift approach is often not appropriate when positivity is required, which is a common constraint when dealing with credit spreads or default intensities. In this paper, we tackle this problem by adopting a time change approach. On the top of providing an elegant solution to the calibration problem under positivity constraint, our model features additional interesting properties in terms of implied volatilities. It is compared to the shift extension on various credit risk applications such as credit default swap, credit default swaption and credit valuation adjustment under wrong-way risk. The time change approach is able to generate much larger volatility and covariance effects under the positivity constraint. Our model offers an appealing alternative to the shift in such cases.Comment: 44 pages, figures and table

Patterns in random walks and Brownian motion

We ask if it is possible to find some particular continuous paths of unit length in linear Brownian motion. Beginning with a discrete version of the problem, we derive the asymptotics of the expected waiting time for several interesting patterns. These suggest corresponding results on the existence/non-existence of continuous paths embedded in Brownian motion. With further effort we are able to prove some of these existence and non-existence results by various stochastic analysis arguments. A list of open problems is presented.Comment: 31 pages, 4 figures. This paper is published at http://link.springer.com/chapter/10.1007/978-3-319-18585-9_

Hysteresis in Pressure-Driven DNA Denaturation

In the past, a great deal of attention has been drawn to thermal driven denaturation processes. In recent years, however, the discovery of stress-induced denaturation, observed at the one-molecule level, has revealed new insights into the complex phenomena involved in the thermo-mechanics of DNA function. Understanding the effect of local pressure variations in DNA stability is thus an appealing topic. Such processes as cellular stress, dehydration, and changes in the ionic strength of the medium could explain local pressure changes that will affect the molecular mechanics of DNA and hence its stability. In this work, a theory that accounts for hysteresis in pressure-driven DNA denaturation is proposed. We here combine an irreversible thermodynamic approach with an equation of state based on the Poisson-Boltzmann cell model. The latter one provides a good description of the osmotic pressure over a wide range of DNA concentrations. The resulting theoretical framework predicts, in general, the process of denaturation and, in particular, hysteresis curves for a DNA sequence in terms of system parameters such as salt concentration, density of DNA molecules and temperature in addition to structural and configurational states of DNA. Furthermore, this formalism can be naturally extended to more complex situations, for example, in cases where the host medium is made up of asymmetric salts or in the description of the (helical-like) charge distribution along the DNA molecule. Moreover, since this study incorporates the effect of pressure through a thermodynamic analysis, much of what is known from temperature-driven experiments will shed light on the pressure-induced melting issue

Markovian Equilibrium in Infinite Horizon Economies with Incomplete Markets and Public Policy

We develop an isotone recursive approach to the problem of existence, computation, and characterization of nonsymmetric locally Lipschitz continuous (and, therefore, Clarke-differentiable) Markovian equilibrium for a class of infinite horizon multiagent competitive equilibrium models with capital, aggregate risk, public policy, externalities, one sector production, and incomplete markets. The class of models we consider is large, and examples have been studied extensively in the applied literature in public economics, macroeconomics, and financial economics. We provide sufficient conditions that distinguish between economies with isotone Lipschitizian Markov equilibrium decision processes (MEDPs) and those that have only locally Lipschitzian (but not necessarily isotone) MEDPs. As our fixed point operators are based upon order continuous and compact non-linear operators, we are able to provide sufficient conditions under which isotone iterative fixed point constructions converge to extremal MEDPs via successive approximation. We develop a first application of a new method for computing MEDPs in a system of Euler inequalities using isotone fixed point theory even when MEDPs are not necessarily isotone. The method is a special case of a more general mixed monotone recursive approach. We show MEDPs are unique only under very restrictive conditions. Finally, we prove monotone comparison theorems in Veinott's strong set order on the space of public policy parameters and distorted production functions