Simulation of a Random Variable and its Application to Game Theory

2021 ◽  
Author(s):  
Mehrdad Valizadeh ◽  
Amin Gohari
Keyword(s):  
Repeated Games ◽  
Side Information ◽  
Random Variable ◽  
Long Run ◽  
Variation Distance ◽  
N Stage ◽  
Target Source ◽  
Stage Game ◽  
The Difference ◽  
Zero Sum

We provide a new tool for simulation of a random variable (target source) from a randomness source with side information. Considering the total variation distance as the measure of precision, this tool offers an upper bound for the precision of simulation, which is vanishing exponentially in the difference of Rényi entropies of the randomness and target sources. This tool finds application in games in which the players wish to generate their actions (target source) as a function of a randomness source such that they are almost independent of the observations of the opponent (side information). In particular, we study zero-sum repeated games in which the players are restricted to strategies that require only a limited amount of randomness. Let be the max-min value of the n stage game. Previous works have characterized [Formula: see text], that is, the long-run max-min value, but they have not provided any result on the value of vn for a given finite n-stage game. Here, we utilize our new tool to study how vn converges to the long-run max-min value.

Repeated Bidding Games with Incomplete Information and Bounded Values: On the Exponential Speed of Convergence

2017 ◽  
Vol 19 (01) ◽  
pp. 1650017 ◽  
Author(s):  
Marina Sandomirskaia
Keyword(s):  
Asymmetric Information ◽  
Incomplete Information ◽  
Repeated Games ◽  
Finite Limit ◽  
Discussion Paper ◽  
Price Fluctuations ◽  
Games With Incomplete Information ◽  
Stage Game ◽  
Zero Sum ◽  
Multistage Bidding

We consider the repeated zero-sum bidding game with incomplete information on one side with non-normalized total payoff. De Meyer and Marino [(2005) Continuous versus discrete market game, Cowles Foundation Discussion Paper 1535] and Domansky and Kreps [(2005) Repeated games with asymmetric information and random price fluctuations at finance markets, Proc. Appl. Ind. Math. 12(4), 950–952 (in Russian)] investigated a game [Formula: see text] modeling multistage bidding with asymmetrically informed agents and proved that for this game [Formula: see text] converges to a finite limit [Formula: see text], i.e., the error term is [Formula: see text]. In this paper, we show that for this example [Formula: see text] converges to the limit exponentially fast. For this purpose we apply the optimal strategy [Formula: see text] of insider in the infinite-stage game obtained by Domansky [(2007) Repeated games with asymmetric information and random price fluctuations at finance markets, Int. J. Game Theor. 36(2), 241–257] to the [Formula: see text]-stage game and deduce that it is [Formula: see text]-optimal with [Formula: see text] exponentially small.

scholarly journals A New Mixed Functional-probabilistic Approach for Finite Element Accuracy

2020 ◽  
Vol 20 (4) ◽  
pp. 799-813
Author(s):  
Joël Chaskalovic ◽  
Franck Assous
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Asymptotic Relation ◽  
Probabilistic Approach ◽  
Random Variable ◽  
High Order ◽  
Relative Accuracy ◽  
The Difference ◽  
New Perspective

AbstractThe aim of this paper is to provide a new perspective on finite element accuracy. Starting from a geometrical reading of the Bramble–Hilbert lemma, we recall the two probabilistic laws we got in previous works that estimate the relative accuracy, considered as a random variable, between two finite elements {P_{k}} and {P_{m}} ({k<m}). Then we analyze the asymptotic relation between these two probabilistic laws when the difference {m-k} goes to infinity. New insights which qualify the relative accuracy in the case of high order finite elements are also obtained.

scholarly journals Stochastic Comparisons of Some Distances between Random Variables

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 981
Author(s):  
Patricia Ortega-Jiménez ◽  
Miguel A. Sordo ◽  
Alfonso Suárez-Llorens
Keyword(s):  
Financial Risk ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Stochastic Ordering ◽  
Random Variable ◽  
Distribution Functions ◽  
Stochastic Comparisons ◽  
Stochastic Orderings ◽  
Absolute Value ◽  
The Difference

The aim of this paper is twofold. First, we show that the expectation of the absolute value of the difference between two copies, not necessarily independent, of a random variable is a measure of its variability in the sense of Bickel and Lehmann (1979). Moreover, if the two copies are negatively dependent through stochastic ordering, this measure is subadditive. The second purpose of this paper is to provide sufficient conditions for comparing several distances between pairs of random variables (with possibly different distribution functions) in terms of various stochastic orderings. Applications in actuarial and financial risk management are given.

The Difference Principle, Capitalism, and Property-Owning Democracy

2018 ◽  
Vol 5 (1) ◽  
pp. 151-172
Author(s):  
Andrew Lister
Keyword(s):  
Welfare State ◽  
Equal Opportunity ◽  
Main Idea ◽  
Political Influence ◽  
Income Growth ◽  
Difference Principle ◽  
State Capitalism ◽  
Long Run ◽  
The Future ◽  
The Difference

Abstract Jason Brennan and John Tomasi have argued that if we focus on income alone, the Difference Principle supports welfare-state capitalism over property-owning democracy, because capitalism maximizes long run income growth for the worst off. If so, the defense of property-owning democracy rests on the priority of equal opportunity for political influence and social advancement over raising the income of the worst off, or on integrating workplace control into the Difference Principle’s index of advantage. The thesis of this paper is that even based on income alone, the Difference Principle is not as hostile to property-owning democracy as it may seem, because the Difference Principle should not be interpreted to require maximizing long run income growth. The main idea is that it is unfair to make the present worst off accept inequality that doesn’t benefit them, for the sake of benefitting the future worst off, if the future worst off will be better off than they are anyway.

Poisson approximation for a sum of dependent indicators: an alternative approach

2002 ◽  
Vol 34 (03) ◽  
pp. 609-625 ◽  
Author(s):  
N. Papadatos ◽  
V. Papathanasiou
Keyword(s):  
Total Variation ◽  
Upper Bound ◽  
Random Variables ◽  
Random Variable ◽  
Poisson Approximation ◽  
Total Variation Distance ◽  
Poisson Random Variable ◽  
Birthday Problem ◽  
Alternative Approach ◽  
Variation Distance

The random variablesX1,X2, …,Xnare said to be totally negatively dependent (TND) if and only if the random variablesXiand ∑j≠iXjare negatively quadrant dependent for alli. Our main result provides, for TND 0-1 indicatorsX1,x2, …,Xnwith P[Xi= 1] =pi= 1 - P[Xi= 0], an upper bound for the total variation distance between ∑ni=1Xiand a Poisson random variable with mean λ ≥ ∑ni=1pi. An application to a generalized birthday problem is considered and, moreover, some related results concerning the existence of monotone couplings are discussed.

scholarly journals On the control of the difference between two Brownian motions: a dynamic copula approach

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
Thomas Deschatre
Keyword(s):  
Cumulative Distribution Function ◽  
Survival Function ◽  
Random Variable ◽  
Cumulative Distribution ◽  
Gaussian Copula ◽  
Brownian Motions ◽  
Dynamic Copula ◽  
Copula Approach ◽  
The Difference ◽  
The Right

AbstractWe propose new copulae to model the dependence between two Brownian motions and to control the distribution of their difference. Our approach is based on the copula between the Brownian motion and its reflection. We show that the class of admissible copulae for the Brownian motions are not limited to the class of Gaussian copulae and that it also contains asymmetric copulae. These copulae allow for the survival function of the difference between two Brownian motions to have higher value in the right tail than in the Gaussian copula case. Considering two Brownian motions B1t and B2t, the main result is that the range of possible values for is the same for Markovian pairs and all pairs of Brownian motions, that is with φ being the cumulative distribution function of a standard Gaussian random variable.

scholarly journals Some Remarks on a Recent Paper by Borch

1961 ◽  
Vol 1 (5) ◽  
pp. 265-272 ◽  
Author(s):  
Paul Markham Kahn
Keyword(s):  
Distribution Function ◽  
Random Variable ◽  
Fixed Number ◽  
Point Of View ◽  
Optimum Amount ◽  
Measurable Transformation ◽  
The Difference ◽  
Image Position ◽  
Stop Loss ◽  
Condition B

In his recent paper, “An Attempt to Determine the Optimum Amount of Stop Loss Reinsurance”, presented to the XVIth International Congress of Actuaries, Dr. Karl Borch considers the problem of minimizing the variance of the total claims borne by the ceding insurer. Adopting this variance as a measure of risk, he considers as the most efficient reinsurance scheme that one which serves to minimize this variance. If x represents the amount of total claims with distribution function F (x), he considers a reinsurance scheme as a transformation of F (x). Attacking his problem from a different point of view, we restate and prove it for a set of transformations apparently wider than that which he allows.The process of reinsurance substitutes for the amount of total claims x a transformed value Tx as the liability of the ceding insurer, and hence a reinsurance scheme may be described by the associated transformation T of the random variable x representing the amount of total claims, rather than by a transformation of its distribution as discussed by Borch. Let us define an admissible transformation as a Lebesgue-measurable transformation T such thatwhere c is a fixed number between o and m = E (x). Condition (a) implies that the insurer will never bear an amount greater than the actual total claims. In condition (b), c represents the reinsurance premium, assumed fixed, and is equal to the expected value of the difference between the total amount of claims x and the total retained amount of claims Tx borne by the insurer.

Perturbed Zero-Sum Games with Applications to Stochastic and Repeated Games

2001 ◽  
pp. 165-181
Author(s):  
Eitan Altman ◽  
Eugene A. Feinberg ◽  
Jerzy Filar ◽  
Vladimir A. Gaitsgory
Keyword(s):  
Repeated Games ◽  
Zero Sum Games ◽  
Zero Sum

scholarly journals Naming customs as an indication of assimilation: a study of first names in the two Jewish congregations of Stockholm and Malmö 1895–1921

2000 ◽  
Vol 21 (1-2) ◽  
pp. 111-122
Author(s):  
Rita Bredefeldt
Keyword(s):  
Gender Difference ◽  
Jewish Identity ◽  
Mothers And Daughters ◽  
Long Run ◽  
Decisive Importance ◽  
Swedish Society ◽  
The Difference ◽  
Fathers And Sons

Jews in both congregations wanted to mark their will to integrate into Swedish society. In this case, the congregation milieu was not of decisive importance. We can see a drop in Jewish names shortly after the most intensive immigration period of Orthodox Eastern Jews in both Malmö and Stockholm. Non-Jewish names dominate strongly in the congregation of Stockholm because of its long history and liberal traditions. The difference between generations is a similar phenomenon in both congregations. The parents had more often Jewish names than their children and this was more so in Malmö than in Stockholm. Another similarity between the congregations is the gender difference. Fathers and sons had more often Jewish names than mothers and daughters. In this case, it seems that in the long run, the Jewish minority wanted to be much like the Swedish majority. While some still marked their Jewish identity with a Jewish name, a growing group marked its will of integration and assimilation.

scholarly journals INTERVENSI KEBIJAKAN MONETER TERHADAP INVESTASI PORTOFOLIO: KASUS INDONESIA DAN AMERIKA SERIKAT

2020 ◽  
Vol 2 (1) ◽  
pp. 1
Author(s):  
Nanda Alfarina ◽  
Hasdi Aimon
Keyword(s):  
United States ◽  
Interest Rate ◽  
Secondary Data ◽  
The United States ◽  
Portfolio Investment ◽  
Mechanism Analysis ◽  
Long Run ◽  
Negative Effect ◽  
The Difference ◽  
Effect Of Monetary Policy

This study aims to determine the effect of monetary policy measured by the central bank’s policy rate (X1) on portfolio investment (Y) in Indonesia and United States in the long run. The data used are secondary data seouced from SEKI BI, FRED The FEd, coinmarketcap.com, and investing.com, with the VECM (Vector Error Correction Mechanism) analysis methode. The study show The study shows the differences between the results that occur in Indonesia and the United States. The policy interest rate has a significant positive effect on portfolio investment in the long run in Indonesia, while in the United States the interest rate in the long run has a significant negative effect on portfolio investment. The difference in research results between the two countries shows the need for different treatment for monetary authorities in encouraging portfolio investment 

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