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Emergence of multiplicity of time scales in the modeling of climate, matter, life, and economyJul 01 2019We address dfferences between characteristic times in climate change and show the universal emergence of multiple time scales in material sciences, biomedicine and economics.

Clustering and Expected Seat-Share for District MapsJun 28 2019In the context of modern sampling methods for redistricting, we define the clustering of a political party (or of a geographic region), and we study how clustering affects the expected election outcome.

Clustering and Expected Seat-Share for District MapsJun 28 2019Aug 08 2019In the context of modern sampling methods for redistricting, we define the clustering of a political party (or of a geographic region), and we study how clustering affects the expected election outcome.

Conditions for discreteness of the spectrum to multi-dimensional Schrödinger operatorJun 05 2019This work is a continuation of our previos paper \cite{Zel1}, where for the the Schr\"odinger operator $H=-\Delta+ V(\e)\cdot$ $(V(\e)\ge 0)$, acting in the space $L_2(\R^d)\,(d\ge 3)$, some constructive sufficient conditions for discreteness of its spectrum ... More

Bayesian Game of Locks, Bombs and TestingJun 03 2019We consider the game with discrete units of resources for protection and destruction of some sites. In our model, Defender (DF) has locks and Attacker (AT) has bombs to allocate among sites, trying to destroy these sites. One or more bombs can be placed ... More

Non-Maxwellian kinetic equations modeling the evolution of wealth distributionMay 30 2019We introduce a class of new one-dimensional linear Fokker--Planck type equations describing the evolution in time of the wealth in a multi-agent society. The equations are obtained, via a standard limiting procedure, by introducing an economically relevant ... More

Heuristics in Multi-Winner Approval VotingMay 28 2019In many real world situations, collective decisions are made using voting. Moreover, scenarios such as committee or board elections require voting rules that return multiple winners. In multi-winner approval voting (AV), an agent may vote for as many ... More

Heuristics in Multi-Winner Approval VotingMay 28 2019May 30 2019In many real world situations, collective decisions are made using voting. Moreover, scenarios such as committee or board elections require voting rules that return multiple winners. In multi-winner approval voting (AV), an agent may vote for as many ... More

Capacity Games with Supply Function CompetitionMay 27 2019This paper studies a setting in which multiple suppliers compete for a buyer's procurement business. The buyer faces uncertain demand and there is a requirement to reserve capacity in advance of knowing the demand. Each supplier has costs that are two ... More

Pure Nash Equilibria and Best-Response Dynamics in Random GamesMay 26 2019Aug 05 2019In finite games mixed Nash equilibria always exist, but pure equilibria may fail to exist. To assess the relevance of this nonexistence, we consider games where the payoffs are drawn at random. In particular, we focus on games where a large number of ... More

Equivariant one-parameter formal deformations of Hom-Leibniz algebrasMay 19 2019We introduce an equivariant $1$-parameter formal deformation theory of Hom-Leibniz algebras equipped with finite group actions on Hom-Leibniz algebras. We define a suitable equivariant deformation cohomology which controls deformations.

Equivariant one-parameter formal deformations of Hom-Leibniz algebrasMay 19 2019Jun 02 2019We introduce an equivariant $1$-parameter formal deformation theory of Hom-Leibniz algebras equipped with finite group actions on Hom-Leibniz algebras. We define a suitable equivariant deformation cohomology which controls deformations.

A characterization of martingale-equivalent compound mixed Poisson processMay 18 2019If a given aggregate process $S$ is a compound mixed Poisson process under a probability measure $P$, a characterization of all probability measures $Q$ on the domain of $P$, such that $P$ and $Q$ are progressively equivalent and $S$ remains a compound ... More

Capacity and Price Competition in Markets with Congestion EffectsMay 14 2019We study oligopolistic competition in service markets where firms offer a service to customers. The service quality of a firm (from a customer's perspective) depends on the level of congestion and the charged price. A firm can set a price for the service ... More

Average Weights and Power in Weighted Voting GamesMay 10 2019We investigate a class of weighted voting games for which weights are randomly distributed over the unit simplex. We provide close-formed formulae for the expectation and density of the distribution of weight of the $k$-th largest player under the uniform ... More

Some Structure Properties of Finite Normal-Form GamesMay 02 2019Game theory provides a mathematical framework for analysing strategic situations involving at least two players. Normal-form games model situations where the players simultaneously pick their moves. In this thesis we explore the strategic structure of ... More

Fast Calculation of Credit Exposures for Barrier and Bermudan options using Chebyshev interpolationMay 01 2019We introduce a new method to calculate the credit exposure of Bermudan, discretely monitored barrier and European options. Core of the approach is the application of the dynamic Chebyshev method of Glau et al. (2019). The dynamic Chebyshev method delivers ... More

Some Energy Estimates for Stable Solutions to Fractional Allen-Cahn EquationsApr 16 2019In this paper we study stable solutions to the fractional equation \begin{align} (-\Delta)^s u =f(u), \quad |u| < 1 \quad \mbox{in $\mathbb{R}^d$}, \end{align}where $0<s<1$ and $f:[-1,1] \rightarrow \mathbb{R}$ is a $C^{1,\alpha}$ function for $\alpha>\max\{0, ... More

Asymptotic independence and support detection techniques for heavy-tailed multivariate dataApr 01 2019One of the central objectives of modern risk management is to find a set of risks where the probability of multiple simultaneous catastrophic events is negligible. That is, risks are taken only when their joint behavior seems sufficiently independent. ... More

Individual-level randomness in a nonatomic populationApr 01 2019This paper provides a construction of an uncountable family of i.i.d. random vectors, indexed by the points of a nonatomic measure space, such that (a) a sample is a measurable function from the index space, and (b) an idealization of the Glivenko-Cantelli ... More

Accumulation charts for instant-runoff electionsMar 14 2019We propose a new graphical format for instant-runoff voting election results. We call this proposal an "accumulation chart." This model, a modification of standard bar charts, is easy to understand, clearly indicates the winner, depicts the instant-runoff ... More

Shapley regressions: A framework for statistical inference on machine learning modelsMar 11 2019Machine learning models often excel in the accuracy of their predictions but are opaque due to their non-linear and non-parametric structure. This makes statistical inference challenging and disqualifies them from many applications where model interpretability ... More

Price competition with uncertain quality and costMar 10 2019Consumers in many markets are uncertain about firms' qualities and costs, so buy based on both the price and the quality inferred from it. Optimal pricing depends on consumer heterogeneity only when firms with higher quality have higher costs, regardless ... More

Price competition with uncertain quality and costMar 10 2019Apr 10 2019Consumers in many markets are uncertain about firms' qualities and costs, so buy based on both the price and the quality inferred from it. Optimal pricing depends on consumer heterogeneity only when firms with higher quality have higher costs, regardless ... More

On Fractional Approach to Analysis of Linked NetworksMar 02 2019In this paper, we present the outer product decomposition of a product of compatible linked networks. It provides a foundation for the fractional approach in network analysis. We discuss the standard and Newman's normalization of networks. We propose ... More

Temporal Bibliographic NetworksMar 02 2019We present two ways (instantaneous and cumulative) to transform bibliographic networks, using the works' publication year, into corresponding temporal networks based on temporal quantities. We also show how to use the addition of temporal quantities to ... More

Temporal Bibliographic NetworksMar 02 2019May 01 2019We present two ways (instantaneous and cumulative) to transform bibliographic networks, using the works' publication year, into corresponding temporal networks based on temporal quantities. We also show how to use the addition of temporal quantities to ... More

General form of Chebyshev type inequality for generalized Sugeno integralFeb 23 2019We prove a~general form of Chebyshev type inequality for generalized upper Sugeno integral in the form of necessary and sufficient condition. A key role in our considerations is played by the~class of $m$-positively dependent functions which includes ... More

Revising SA-CCRFeb 22 2019Apr 08 2019From SA-CCR to RSA-CCR: making SA-CCR self-consistent and appropriately risk-sensitive by cashflow decomposition in a 3-Factor Gaussian Market Model

From SA-CCR to RSA-CCR: making SA-CCR self-consistent and appropriately risk-sensitive by cashflow decomposition in a 3-Factor Gaussian Market ModelFeb 22 2019SA-CCR has major issues including: lack of self-consistency for linear trades; lack of appropriate risk sensitivity (zero positions can have material add-ons; moneyness is ignored); dependence on economically-equivalent confirmations. We show that SA-CCR ... More

Kinetic modeling of alcohol consumptionFeb 21 2019In most countries, alcohol consumption distributions have been shown to possess universal features. Their unimodal right-skewed shape is usually modeled in terms of the Lognormal distribution, which is easy to fit, test, and modify. However, empirical ... More

Analysis of a Traffic Remapping Attack Game in a Multi-hop Ad Hoc NetworkFeb 11 2019Multi-hop ad hoc networks are susceptible to selfish misbehavior such as traffic remapping attacks (TRAs). Selfish nodes launching such attacks acquire unduly high quality of service (QoS) by assigning higher priority to source packets and lower priority ... More

REST: A Strategy for the Traffic Remapping Attack Game in Multi-hop Ad Hoc NetworksFeb 11 2019Jul 16 2019Multi-hop ad hoc networks are susceptible to selfish misbehavior such as traffic remapping attacks (TRAs). Selfish nodes launching such attacks receive unjustifiably high quality of service (QoS) by assigning higher priority to source packets and lower ... More

$N$-player games and mean-field games with smooth dependence on past absorptionsFeb 07 2019Mean-field games with absorption is a class of games, that have been introduced in Campi and Fischer [7] and that can be viewed as natural limits of symmetric stochastic differential games with a large number of players who, interacting through a mean-field, ... More

Discrete Operational Calculus in Delayed Stochastic GamesJan 22 2019This article deals with classes of antagonistic games with two players. A game is specified in terms of two `hostile' stochastic processes representing mutual attacks upon random times exerting casualties of random magnitudes. The game ends when one of ... More

Expected characteristic in Tunnels & Trolls character creation, with generalizationsJan 21 2019In the roleplaying game Tunnels & Trolls the characteristics of player characters are determined by rolling dice in the following manner: First, one rolls three dice and calculates their sum. If the three dice all give the same result, another three dice ... More

Decomposition of games: some strategic considerationsJan 18 2019Candogan et al. (2011) provide an orthogonal direct-sum decomposition of finite games into potential, harmonic and non-strategic components. In this paper we study the issue of decomposing games that are strategically equivalent from a game-theoretical ... More

Cramer-Lundberg model for some classes of extremal Markov sequencesJan 17 2019We consider here the Cramer-Lundberg model based on generalized convolutions. In our model the insurance company invests at least part of its money, have employees, shareholders. The financial situation of the company after paying claims can be even better ... More

An interval-valued GARCH model for range-measured return processesJan 09 2019Range-measured return contains more information than the traditional scalar-valued return. In this paper, we propose to model the [low, high] price range as a random interval and suggest an interval-valued GARCH (Int-GARCH) model for the corresponding ... More

A game theory approach to the existence and uniqueness of nonlinear Perron-Frobenius eigenvectorsDec 24 2018We establish a generalized Perron-Frobenius theorem, based on a combinatorial criterion which entails the existence of an eigenvector for any nonlinear order-preserving and positively homogeneous map $f$ acting on the open orthant $\mathbb{R}_{\scriptscriptstyle ... More

Impact of LTE's Periodic Interference on Heterogeneous Wi-Fi TransmissionsDec 20 2018The problem of Wi-Fi and LTE coexistence has been significantly debated in the last years, with the emergence of LTE extensions enabling the utilization of unlicensed spectrum for carrier aggregation. Rather than focusing on the problem of resource sharing ... More

Naive Dictionary On Musical Corpora: From Knowledge Representation To Pattern RecognitionNov 29 2018In this paper, we propose and develop the novel idea of treating musical sheets as literary documents in the traditional text analytics parlance, to fully benefit from the vast amount of research already existing in statistical text mining and topic modelling. ... More

Constant payoff in zero-sum stochastic gamesNov 12 2018In a zero-sum stochastic game, at each stage, two adversary players take decisions and receive a stage payoff determined by them and by a random variable representing the state of nature. The total payoff is the discounted sum of the stage payoffs. Assume ... More

A Multidimensional Fatou Lemma for Conditional ExpectationsNov 01 2018The classical multidimensional version of Fatou's lemma (Schmeidler 1970) originally obtained for unconditional expectations and the standard non-negative cone in a finite-dimensional linear space is extended to conditional expectations and general closed ... More

New algorithms for solving stochastic gamesOct 30 2018May 15 2019Stochastic games are a classical model in game theory in which two opponents interact over a finite set of states that change stochastically over time. The central solution concepts for these games are the discounted values and the limit value, which ... More

New complexity bounds in stochastic gamesOct 30 2018Stochastic games are a classical model in game theory in which two opponents interact over a finite set of states that change stochastically over time. The two central solution concepts for these games are the discounted values and the limit values. Efficiently ... More

Shapley-Snow kernels in zero-sum stochastic gamesOct 20 2018We establish, for the first time, a connection between stochastic games and multi-parameter eigenvalue problems, using the theory developed by Shapley and Snow (1950) in the context of matrix games. This connection provides new results, new proofs, and ... More

Shapley-Snow kernels, multiparameter eigenvalue problems and stochastic gamesOct 20 2018May 22 2019We establish, for the first time, a connection between stochastic games and multiparameter eigenvalue problems, using the theory developed by Shapley and Snow (1950). This connection provides new results, new proofs, and new tools for studying stochastic ... More

Bandit learning in concave $N$-person gamesOct 03 2018This paper examines the long-run behavior of learning with bandit feedback in non-cooperative concave games. The bandit framework accounts for extremely low-information environments where the agents may not even know they are playing a game; as such, ... More

The logic of uncertainty as a logic of experience and chance and the co~event-based Bayes' theoremSep 28 2018The logic of uncertainty is not the logic of experience and as well as it is not the logic of chance. It is the logic of experience and chance. Experience and chance are two inseparable poles. These are two dual reflections of one essence, which is called ... More

Eventological H-theoremSep 19 2018We prove the eventological $H$-theorem that complements the Boltzmann H-theorem from statistical mechanics and serves as a mathematical excuse (mathematically no less convincing than the Boltzmann H-theorem for the second law of thermodynamics) for what ... More

A solution for stochastic gamesSep 17 2018Sep 27 2018Stochastic games are two-player repeated games in which a state variable follows a Markov chain controlled by both players. The model was initially proposed by Shapley (1953) who proved the existence of the discounted values. In spite of the great interest ... More

Learning in time-varying gamesSep 10 2018In this paper, we examine the long-term behavior of regret-minimizing agents in time-varying games with continuous action spaces. In its most basic form, (external) regret minimization guarantees that an agent's cumulative payoff is no worse in the long ... More

On zero-sum game formulation of non zero-sum gameSep 09 2018We consider a formulation of a non zero-sum n players game by an n+1 players zero-sum game. We suppose the existence of the n+1-th player in addition to n players in the main game, and virtual subsidies to the n players which is provided by the n+1-th ... More

The Multilinear Minimax Relaxation of Bimatrix Games and Comparison with Nash Equilibria via Lemke-HowsonSep 05 2018Jul 05 2019Extensive study on the complexity of computing Nash Equilibrium has resulted in the definition of the complexity class PPAD by Papadimitriou \cite{Papa2}, Subsequently shown to be PPAD-complete, first by Daskalakis, Goldberg, and Papadimitriou \cite{Papa} ... More

The Multilinear Minimax Relaxation of Bimatrix Games and Comparison with Nash Equilibria via Lemke-HowsonSep 05 2018Extensive study on the complexity of computing Nash Equilibrium has resulted in the definition of the complexity class PPAD by Papadimitriou \cite{Papa2}, Subsequently shown to be PPAD-complete, first by Daskalakis, Goldberg, and Papadimitriou \cite{Papa} ... More

Human Behavior And Lognormal Distribution. A Kinetic DescriptionSep 05 2018In recent years it has been increasing evidence that lognormal distributions are widespread in physical and biological sciences, as well as in various phenomena of economics and social sciences. In social sciences, the appearance of lognormal distribution ... More

Quantifier-free description of the solutions set of the generalized interval-quantifier system of linear equationsSep 04 2018A quantifier-free description of the set of solutions of the generalized interval-quantifier system of linear equations is obtain.

Nash equilibrium in asymmetric multi-players zero-sum game with two strategic variables and only one alienSep 04 2018We consider a partially asymmetric multi-players zero-sum game with two strategic variables. All but one players have the same payoff functions, and one player (Player $n$) does not. Two strategic variables are $t_i$'s and $s_i$'s for each player $i$. ... More

Sion's mini-max theorem and Nash equilibrium in a multi-players game with two groups which is zero-sum and symmetric in each groupSep 04 2018We consider the relation between Sion's minimax theorem for a continuous function and a Nash equilibrium in a multi-players game with two groups which is zero-sum and symmetric in each group. We will show the following results. 1. The existence of Nash ... More

Sion's mini-max theorem and Nash equilibrium in a five-players game with two groups which is zero-sum and symmetric in each groupSep 04 2018We consider the relation between Sion's minimax theorem for a continuous function and a Nash equilibrium in a five-players game with two groups which is zero-sum and symmetric in each group. We will show the following results. 1. The existence of Nash ... More

Nash equilibrium of partially asymmetric three-players zero-sum game with two strategic variablesSep 04 2018We consider a partially asymmetric three-players zero-sum game with two strategic variables. Two players (A and B) have the same payoff functions, and Player C does not. Two strategic variables are $t_i$'s and $s_i$'s for $i=A, B, C$. Mainly we will show ... More

Generalized exponential basis for efficient solving of homogeneous diffusion free boundary problems: Russian option pricingAug 24 2018This paper develops a method for solving free boundary problems for time-homogeneous diffusions. We combine the complete exponential system of solutions for the heat equation, transmutation operators and recently discovered Neumann series of Bessel functions ... More

Solving Quadratic Multi-Leader-Follower Games by Smoothing the Follower's Best ResponseAug 23 2018We derive Nash-s-stationary equilibria for a class of quadratic multi-leader-follower games using the nonsmooth best response function. To overcome the challenge of nonsmoothness, we pursue a smoothing approach resulting in a reformulation as smooth Nash ... More

Solving Quadratic Multi-Leader-Follower Games by Smoothing the Follower's Best ResponseAug 23 2018Mar 01 2019We derive Nash-s-stationary equilibria for a class of quadratic multi-leader-follower games using the nonsmooth best response function. To overcome the challenge of nonsmoothness, we pursue a smoothing approach resulting in a reformulation as smooth Nash ... More

Selective versions of $θ$-densityAug 22 2018In [8] the authors initiate the study of selective versions of the notion of $\theta$-separability in non-regular spaces. In this paper we continue this investigation by establishing connections between the familiar cardinal numbers arising in the set ... More

The story of conflict and cooperationAug 21 2018The story of conflict and cooperation has started millions of years ago, and now it is everywhere: In biology, computer science, economics, humanities, law, philosophy, political science, and psychology. Wars, airline alliances, trade, oligopolistic cartels, ... More

$k$th price auctions and Catalan numbersAug 17 2018This paper establishes an interesting link between $k$th price auctions and Catalan numbers by showing that for distributions that have linear density, the bid function at any symmetric, increasing equilibrium of a $k$th price auction with $k\geq 3$ can ... More

Kripke Semantics of the Perfectly Transparent EquilibriumJul 20 2018The Perfectly Transparent Equilibrium is algorithmically defined, for any game in normal form with perfect information and no ties, as the iterated deletion of non-individually-rational strategy profiles until at most one remains. In this paper, we characterize ... More

Augmented Lagrangian Methods for the Solution of Generalized Nash Equilibrium ProblemsJul 12 2018We propose an augmented Lagrangian-type algorithm for the solution of generalized Nash equilibrium problems (GNEPs). Specifically, we discuss the convergence properties with regard to both feasibility and optimality of limit points. This is done by introducing ... More

A new approach for American option pricing: The Dynamic Chebyshev methodJun 14 2018We introduce a new method to price American options based on Chebyshev interpolation. In each step of a dynamic programming time-stepping we approximate the value function with Chebyshev polynomials. The key advantage of this approach is that it allows ... More

The Capacity Constrained Facility Location problemJun 04 2018Feb 15 2019We initiate the study of the capacity constrained facility location problem from a mechanism design perspective. The capacity constrained setting leads to a new strategic environment where a facility serves a subset of the population, which is endogenously ... More

Mechanism Design without Money for Common GoodsJun 04 2018We initiate the study of mechanism design without money for common goods. Our model captures a variation of the well-known one-dimensional facility location problem if the facility is assumed to have a capacity constraint $k<n$ where $n$ is the population ... More

Competitive pricing despite search costs if lower price signals qualityJun 03 2018I show that firms price almost competitively and consumers can infer product quality from prices in markets where firms differ in quality and production cost, and learning prices is costly. Bankruptcy risk or regulation links higher quality to lower cost. ... More

Spatially Inhomogeneous Evolutionary GamesMay 10 2018We introduce and study a mean-field model for a system of spatially distributed players interacting through an evolutionary game driven by a replicator dynamics. Strategies evolve by a replicator dynamics influenced by the position and the interaction ... More

A convergent hierarchy of non-linear eigenproblems to compute the joint spectral radius of nonnegative matricesMay 08 2018We show that the joint spectral radius of a finite collection of nonnegative matrices can be bounded by the eigenvalue of a non-linear operator. This eigenvalue coincides with the ergodic constant of a risk-sensitive control problem, or of an entropy ... More

Algorithm for Hamilton-Jacobi equations in density space via a generalized Hopf formulaMay 04 2018We design fast numerical methods for Hamilton-Jacobi equations in density space (HJD), which arises in optimal transport and mean field games. We overcome the curse-of-infinite-dimensionality nature of HJD by proposing a generalized Hopf formula in density ... More

Viability analysis of the first-order mean field gamesApr 30 2018The paper is concerned with the dependence of the solution of the deterministic mean field game on the initial distribution of players. The main object of study is the mapping which assigns to the initial time and the initial distribution of players the ... More

Viability analysis of the first-order mean field gamesApr 30 2018Feb 26 2019The paper is concerned with the dependence of the solution of the deterministic mean field game on the initial distribution of players. The main object of study is the mapping which assigns to the initial time and the initial distribution of players the ... More

A Reputation Scheme to Discourage Selfish QoS Manipulation in Two-Hop Wireless Relay NetworksApr 27 2018Jul 31 2018In wireless networks, stations can improve their received quality of service (QoS) by handling packets of source flows with higher priority. Additionally, in cooperative relay networks, the relays can handle transit flows with lower priority. We use game ... More

Stochastic Linear Quadratic Stackelberg Differential Game with Overlapping InformationApr 20 2018Apr 28 2018This paper is concerned with the stochastic linear quadratic Stackelberg differential game with overlapping information, where the diffusion terms contain the control and state variables. Here the term "overlapping" means that there are common part between ... More

On time-inconsistent stopping problems and mixed strategy stopping timesApr 19 2018May 07 2018A game-theoretic framework for time-inconsistent stopping problems where the time-inconsistency is due to the consideration of a non-linear function of an expected reward is developed. A class of mixed strategy stopping times that allows the agents in ... More

Formulas for translative functionsApr 09 2018Oct 31 2018In this report, we consider extended real-valued functions on some real vector space. Gerstewitz functionals are used to construct all translative functions. We derive formulas for translative functions which are lower semicontinuous, continuous or have ... More

Space of isospectral periodic tridiagonal matricesMar 30 2018Dec 14 2018A periodic tridiagonal matrix is a tridiagonal matrix with additional two entries at the corners. We study the space $X_{n,\lambda}$ of Hermitian periodic tridiagonal $n\times n$-matrices with a fixed simple spectrum $\lambda$. Using the discretized Shr\"{o}dinger ... More

A mean-field game model for homogeneous flockingMar 14 2018May 29 2018Empirically derived continuum models of collective behavior among large populations of dynamic agents are a subject of intense study in several fields, including biology, engineering and finance. We formulate and study a mean-field game model whose behavior ... More

Quantifier-free descriptions for quantifier solutions to interval linear systems of relationsFeb 26 2018We study systems of relations of the form $Ax\,\sigma\,b$, where $\sigma$ is a vector of binary relations with the components "$=$", "$\geq$" and "$\leq$", and the parameters (elements of the matrix $A$ and right-hand side vector $b$) can take values ... More

Call center service times are lognormal. A Fokker--Planck descriptionFeb 23 2018Call centers are service networks in which agents provide telephone-based services. An important part of call center operations is represented by service durations. In recent statistical analysis of real data, it has been noticed that the distribution ... More

Elements of the Kopula (eventological copula) theoryFeb 17 2018New in the probability theory and eventology theory, the concept of Kopula (eventological copula) is introduced. The theorem on the characterization of the sets of events by Kopula is proved, which serves as the eventological pre-image of the well-known ... More

Optimization of Fire Sales and Borrowing in Systemic RiskFeb 12 2018Oct 01 2018This paper provides a framework for modeling financial contagion in a network subject to fire sales and price impacts, but allowing for firms to borrow to cover their shortfall as well. We consider both uncollateralized and collateralized loans. The main ... More

Smale Strategies For The N-Person Iterated Prisoner's DilemmaFeb 11 2018Adapting methods introduced by Steven Smale, we describe good strategies for a symmetric version of the Iterated Prisoner's Dilemma with n players.

Frechet bounds of the 1-st kind for sets of half-rare eventsFeb 10 2018Frechet bounds of the 1-st kind for sets of events and its main properties are considered. The lemma on not more than two nonzero values of lower Frechet-bounds of the 1-st kind for a set of half-rare events is proved with the corollary on the analogous ... More

Modeling tagged pedestrian motion: a mean-field type game approachJan 26 2018Feb 22 2019This paper suggests a model for the motion of tagged pedestrians: pedestrians moving towards a specified targeted destination, which they are forced to reach. It aims to be a decision-making tool for the positioning of fire fighters, security personnel, ... More

Modeling tagged pedestrian motion: a mean-field type game approachJan 26 2018Jan 29 2019This paper suggests a model for the motion of tagged pedestrians: pedestrians moving towards a specified targeted destination, which they are forced to reach. It aims to be a decision-making tool for the positioning of fire fighters, security personnel, ... More

Postulating the theory of experience and chance as a theory of co~events (co~beings)Jan 17 2018The paper aim is the axiomatic justification of the theory of experience and chance, one of the dual halves of which is the Kolmogorov probability theory. The author's main idea was the natural inclusion of Kolmogorov's axiomatics of probability theory ... More

The Choquet integral with respect to fuzzy measures and applicationsJan 10 2018Fuzzy measures and Choquet asymmetric integral are considered here. As an application to economics some Core-Walras results are given.

Simulations to Analyze Cellular Voting Systems for Side Effects of Democratic RedistrictingJan 08 2018Motivated by the problem of partisan gerrymandering, we introduce an electoral system for a representative democracy called democratic cellular voting, designed to make modern packing and cracking strategies irrelevant by allowing districts to be influenced ... More

Metastability in Stochastic Replicator DynamicsJan 07 2018May 07 2018We consider a novel model of stochastic replicator dynamics for potential games that converts to a Langevin equation on a sphere after a change of variables. This is distinct from the models studied earlier. In particular, it is ill-posed due to non-uniqueness ... More

Quantum Interval-Valued Probability: Contextuality and the Born RuleDec 25 2017Apr 06 2018We present a mathematical framework based on quantum interval-valued probability measures to study the effect of experimental imperfections and finite precision measurements on defining aspects of quantum mechanics such as contextuality and the Born rule. ... More

Infinitely Split Nash Equilibrium Problems in Repeated GamesDec 21 2017In this paper, we introduce the concept of infinitely split Nash equilibrium in repeated games in which the profile sets are chain-complete posets. Then by using a fixed point theorem on posets in [8], we prove an existence theorem. As an application, ... More

Routeing properties in a Gibbsian model for highly dense multihop networksDec 20 2017Feb 15 2019We investigate a probabilistic model for routeing in a multihop ad-hoc communication network, where each user sends a message to the base station. Messages travel in hops via other users, used as relays. Their trajectories are chosen at random according ... More