scholarly journals COMMENTS ON 'REVERSE AUCTION: THE LOWEST UNIQUE POSITIVE INTEGER GAME'

2008 â—½  
Vol 08 (01) â—½  
pp. C1-C4 â—½  
Author(s):  
A. P. FLITNEY
Keyword(s):  
Exact Solution â—½  
Approximate Solution â—½  
Nash Equilibrium â—½  
Positive Integer â—½  
Arbitrary Number â—½  
Reverse Auction â—½  
Expected Payoff â—½  
Utility Maximizer â—½  
Computational Capability â—½  
Rational Players

In Zeng et al. [Fluct. Noise Lett. 7 (2007) L439–L447] the analysis of the lowest unique positive integer game is simplified by some reasonable assumptions that make the problem tractable for arbitrary numbers of players. However, here we show that the solution obtained for rational players is not a Nash equilibrium and that a rational utility maximizer with full computational capability would arrive at a solution with a superior expected payoff. An exact solution is presented for the three- and four-player cases and an approximate solution for an arbitrary number of players.

LEARNING IN BAYESIAN GAMES BY BOUNDED RATIONAL PLAYERS II: NONMYOPIA

1998 â—½  
Vol 2 (2) â—½  
pp. 141-155 â—½  
Author(s):  
Konstantinos Serfes â—½  
Nicholas C. Yannelis
Keyword(s):  
Nash Equilibrium â—½  
Arbitrary Number â—½  
Bayesian Learning â—½  
Full Information â—½  
Bayesian Games â—½  
Response Strategies â—½  
Bayesian Nash Equilibrium â—½  
Current Period â—½  
Best Response â—½  
Rational Players

We generalize results of earlier work on learning in Bayesian games by allowing players to make decisions in a nonmyopic fashion. In particular, we address the issue of nonmyopic Bayesian learning with an arbitrary number of bounded rational players, i.e., players who choose approximate best-response strategies for the entire horizon (rather than the current period). We show that, by repetition, nonmyopic bounded rational players can reach a limit full-information nonmyopic Bayesian Nash equilibrium (NBNE) strategy. The converse is also proved: Given a limit full-information NBNE strategy, one can find a sequence of nonmyopic bounded rational plays that converges to that strategy.

Kinematic analysis and deformation of a planar lattice with an arbitrary number of panels

2020 â—½  
pp. 15-19
Author(s):  
M.N. Kirsanov
Keyword(s):  
Exact Solution â—½  
Kinematic Analysis â—½  
Arbitrary Number â—½  
Design Parameters â—½  
Lattice Deformation â—½  
Planar Lattice â—½  
Force Loading

Formulae are obtained for calculating the deformations of a statically determinate lattice under the action of two types of loads in its plane, depending on the number of panels located along one side of the lattice. Two options for fixing the lattice are analyzed. Cases of kinematic variability of the structure are found. The distribution of forces in the rods of the lattice is shown. The dependences of the force loading of some rods on the design parameters are obtained. Keywords: truss, lattice, deformation, exact solution, deflection, induction, Maple system. [email protected]

scholarly journals Approximate Method for Solving the Linear Fuzzy Delay Differential Equations

10.1155/2015/273830 â—½  
2015 â—½  
Vol 2015 â—½  
pp. 1-9 â—½  
Author(s):  
S. Narayanamoorthy â—½  
T. L. Yookesh
Keyword(s):  
Differential Equation â—½  
Exact Solution â—½  
Approximate Solution â—½  
Differential Equations â—½  
Approximate Method â—½  
Delay Differential Equations â—½  
Decomposition Method â—½  
Adomian Decomposition Method â—½  
Adomian Decomposition â—½  
Delay Differential

We propose an algorithm of the approximate method to solve linear fuzzy delay differential equations using Adomian decomposition method. The detailed algorithm of the approach is provided. The approximate solution is compared with the exact solution to confirm the validity and efficiency of the method to handle linear fuzzy delay differential equation. To show this proper features of this proposed method, numerical example is illustrated.

scholarly journals On self-correcting logic circuits of unreliable gates

2021 â—½  
pp. 1-18
Author(s):  
Kirill Andreevich Popkov
Keyword(s):  
Positive Integer â—½  
Boolean Function â—½  
Boolean Functions â—½  
Arbitrary Number â—½  
Logic Circuits â—½  
Logic Circuit â—½  
Complete Basis

The following statements are proved: 1) for any integer m ≥ 3 there is a basis consisting of Boolean functions of no more than m variables, in which any Boolean function can be implemented by a logic circuit of unreliable gates that self-corrects relative to certain faults in an arbitrary number of gates; 2) for any positive integer k there are bases consisting of Boolean functions of no more than two variables, in each of which any Boolean function can be implemented by a logic circuit of unreliable gates that self-correct relative to certain faults in no more than k gates; 3) there is a functionally complete basis consisting of Boolean functions of no more than two variables, in which almost no Boolean function can be implemented by a logic circuit of unreliable gates that self-correct relative to at least some faults in no more than one gate.

Analysis of Deep Beams

10.1115/1.4010271 â—½  
1951 â—½  
Vol 18 (2) â—½  
pp. 163-172
Author(s):  
H. D. Conway â—½  
L. Chow â—½  
G. W. Morgan
Keyword(s):  
Exact Solution â—½  
Approximate Solution â—½  
Stress Distribution â—½  
Finite Difference â—½  
Boundary Conditions â—½  
Normal Stress â—½  
Stress Function â—½  
Beam Theory â—½  
Deep Beam â—½  
Stress Functions

Abstract This paper presents a method of analyzing the stress distribution in a deep beam of finite length by superimposing two stress functions. The first stress function is chosen in the form of a trigonometric series which satisfies all but one of the boundary conditions—that of zero normal stress on the ends of the beam. The principle of least work is then used to obtain a second stress function giving the distribution of normal stress on the ends which is left by the first stress function. By superimposing the two solutions, all the boundary conditions are satisfied. Two particular cases of a given type of loading are solved in this way to investigate the stresses in a deep beam and their deviation from the ordinary beam theory. In addition, an approximate solution by the numerical method of finite difference is worked out for one of the two cases. Results from the two methods are compared and discussed. A method of obtaining an exact solution to the problem is given in an Appendix.

On a new modified fractional analysis of Nagumo equation

2019 â—½  
Vol 12 (03) â—½  
pp. 1950034 â—½  
Author(s):  
Khaled M. Saad â—½  
Si̇nan Deni̇z â—½  
Dumi̇tru Baleanu
Keyword(s):  
Exact Solution â—½  
Approximate Solution â—½  
Convergence Analysis â—½  
Fractional Derivatives â—½  
Transform Method â—½  
Average Residual â—½  
Homotopy Analysis â—½  
Fractional Analysis â—½  
Nagumo Equation â—½  
Modified Equation

In this work, a new modified fractional form of the Nagumo equation has been presented and deeply analyzed. Using the Caputo–Fabrizio and Atangana–Baleanu time-fractional derivatives, classical Nagumo model is transformed to a new fractional version. The modified equation has been solved by using the homotopy analysis transform method. The convergence analysis has been also examined with the help of the so-called [Formula: see text]-curves and average residual error. Comparing the obtained approximate solution with the exact solution leaves no doubt believing that the proposed technique is very efficient and converges toward the exact solution very rapidly.

scholarly journals Reproducing Kernel Method for Solving Nonlinear Fractional Fredholm Integrodifferential Equation

Complexity â—½  
2018 â—½  
Vol 2018 â—½  
pp. 1-7 â—½  
Author(s):  
Bothayna S. H. Kashkari â—½  
Muhammed I. Syam
Keyword(s):  
Exact Solution â—½  
Approximate Solution â—½  
Integrodifferential Equation â—½  
Reproducing Kernel â—½  
Kernel Method â—½  
Integrodifferential Equations â—½  
Reproducing Kernel Method â—½  
Numerical Studies â—½  
Uniformly Convergence â—½  
Present Algorithm

This article is devoted to both theoretical and numerical studies of nonlinear fractional Fredholm integrodifferential equations. In this paper, we implement the reproducing kernel method (RKM) to approximate the solution of nonlinear fractional Fredholm integrodifferential equations. Numerical results demonstrate the accuracy of the present algorithm. In addition, we prove the existence of the solution of the nonlinear fractional Fredholm integrodifferential equation. Uniformly convergence of the approximate solution produced by the RKM to the exact solution is proven.

scholarly journals Analytic Solution for Systems of Two-Dimensional Time Conformable Fractional PDEs by Using CFRDTM

2019 â—½  
Vol 2019 â—½  
pp. 1-7
Author(s):  
Abir Chaouk â—½  
Maher Jneid
Keyword(s):  
Exact Solution â—½  
Approximate Solution â—½  
Analytic Solution â—½  
Closed Form Solution â—½  
Form Solution â—½  
Two Dimensional â—½  
Fractional Pdes â—½  
Differential Transform â—½  
Computational Work â—½  
Similar Solutions

In this study we use the conformable fractional reduced differential transform (CFRDTM) method to compute solutions for systems of nonlinear conformable fractional PDEs. The proposed method yields a numerical approximate solution in the form of an infinite series that converges to a closed form solution, which is in many cases the exact solution. We inspect its efficiency in solving systems of CFPDEs by working on four different nonlinear systems. The results show that CFRDTM gave similar solutions to exact solutions, confirming its proficiency as a competent technique for solving CFPDEs systems. It required very little computational work and hence consumed much less time compared to other numerical methods.

scholarly journals Nash versus coarse correlation

2020 â—½  
Vol 23 (4) â—½  
pp. 1178-1204 â—½  
Author(s):  
Konstantinos Georgalos â—½  
Indrajit Ray â—½  
Sonali SenGupta
Keyword(s):  
Nash Equilibrium â—½  
Correlated Equilibrium â—½  
Individual Choice â—½  
Pure Nash Equilibrium â—½  
Expected Payoff â—½  
Equilibrium Payoff â—½  
Payoff Dominance â—½  
Dominated Strategies â—½  
Person Game â—½  
Nash Point

Abstract We run a laboratory experiment to test the concept of coarse correlated equilibrium (Moulin and Vial in Int J Game Theory 7:201–221, 1978), with a two-person game with unique pure Nash equilibrium which is also the solution of iterative elimination of strictly dominated strategies. The subjects are asked to commit to a device that randomly picks one of three symmetric outcomes (including the Nash point) with higher ex-ante expected payoff than the Nash equilibrium payoff. We find that the subjects do not accept this lottery (which is a coarse correlated equilibrium); instead, they choose to play the game and coordinate on the Nash equilibrium. However, given an individual choice between a lottery with equal probabilities of the same outcomes and the sure payoff as in the Nash point, the lottery is chosen by the subjects. This result is robust against a few variations. We explain our result as selecting risk-dominance over payoff dominance in equilibrium.

scholarly journals Numerical solution of nonlinear system of integro-differential equations using Chebyshev wavelets

2015 â—½  
Vol 11 (2) â—½  
pp. 15-34
Author(s):  
H. Aminikhah â—½  
S. Hosseini
Keyword(s):  
Exact Solution â—½  
Approximate Solution â—½  
Nonlinear System â—½  
Differential Equations â—½  
Numerical Solution â—½  
Chebyshev Wavelets â—½  
Linear And Nonlinear

Abstract This paper introduces an approach for obtaining the numerical solution of the linear and nonlinear integro-differential equations using Chebyshev wavelets approximations. Illustrative examples have been discussed to demonstrate the validity and applicability of the technique and the results have been compared with the exact solution. Comparison of the approximate solution with exact solution shows that the used method is effectiveness and practical for classes of linear and nonlinear system of integro-differential equations.

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