scholarly journals Exact Solution of Modified Veselov–Novikov Equation and Some Applications in the Game Theory

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Damir Kurmanbayev
Keyword(s):  
Game Theory ◽  
Exact Solution ◽  
Exact Solutions ◽  
Geometric Interpretation ◽  
Higher Order ◽  
The Game Theory ◽  
Novikov Equation

A method of finding exact solutions of the modified Veselov–Novikov (mVN) equation is constructed by Moutard transformations, and a geometric interpretation of these transformations is obtained. An exact solution of the mVN equation is found on the example of a higher order Enneper surface, and given transformations are applied in the game theory via Kazakh proverbs in terms of trees.

scholarly journals Refinements and higher-order beliefs: a unified survey

2019 ◽  
Vol 71 (1) ◽  
pp. 7-34 ◽  
Author(s):  
Atsushi Kajii ◽  
Stephen Morris
Keyword(s):  
Game Theory ◽  
Normal Form ◽  
Econ Theory ◽  
Complete Information ◽  
Higher Order ◽  
Economic Modelling ◽  
The Game Theory ◽  
Standard Normal ◽  
Payoff Uncertainty ◽  
Theory Interpretation

AbstractThis paper presents a simple framework that allows us to survey and relate some different strands of the game theory literature. We describe a “canonical” way of adding incomplete information to a complete information game. This framework allows us to give a simple “complete theory” interpretation (Kreps in Game theory and economic modelling. Clarendon Press, Oxford, 1990) of standard normal form refinements such as perfection, and to relate refinements both to the “higher-order beliefs literature” (Rubinstein in Am Econ Rev 79:385–391, 1989; Monderer and Samet in Games Econ Behav 1:170–190, 1989; Morris et al. in Econ J Econ Soc 63:145–157, 1995; Kajii and Morris in Econ J Econ Soc 65:1283–1309, 1997a) and the “payoff uncertainty approach” (Fudenberg et al. in J Econ Theory 44:354–380, 1988; Dekel and Fudenberg in J Econ Theory 52:243–267, 1990).

scholarly journals The Game Theory of Politeness in Language: A Formal Model of Polite Requests

2019 ◽  
Author(s):  
Roland Muehlenbernd ◽  
Przemyslaw Zywiczynski ◽  
Sławomir Wacewicz
Keyword(s):  
Game Theory ◽  
Social Behavior ◽  
Formal Model ◽  
Mathematical Proof ◽  
Signaling Theory ◽  
Order Theory ◽  
Higher Order ◽  
The Game Theory ◽  
Human Social Behavior ◽  
Higher Order Theory

Linguistic Politeness (LP) is a fascinating domain of language, as it directly interfaces with human social behavior. Here, we show how game theory, as a higher-order theory of behavior, can provide the tools to understand and model LP phenomena. We show this for the specific case of requests, where the magnitude of request and the resultant Rate of Imposition are subsumed under a more powerful explanatory principle: alignment of interests. We put forward the Politeness Equilibrium Principle (PEP), whereby the more disalignment there is between the interests of Speaker and Hearer, the more LP Speaker needs to offset the imbalance. In the second part of our paper, we flesh out our ideas by means of a formal model inspired by evolutionary signaling theory, and provide a mathematical proof showing that the model follows the PEP. We see this work as an important first step in the direction of reconciling theories of language with signaling theory, by incorporating language into more general models of communication.

Reputation and Gossip in Game Theory

2019 ◽  
pp. 213-229
Author(s):  
Charles Roddie
Keyword(s):  
Game Theory ◽  
Strategic Behavior ◽  
Third Party ◽  
The Past ◽  
Past Behavior ◽  
Future Behavior ◽  
The Game Theory ◽  
Shed Light

When interacting with others, it is often important for you to know what they have done in similar situations in the past: to know their reputation. One reason is that their past behavior may be a guide to their future behavior. A second reason is that their past behavior may have qualified them for reward and cooperation, or for punishment and revenge. The fact that you respond positively or negatively to the reputation of others then generates incentives for them to maintain good reputations. This article surveys the game theory literature which analyses the mechanisms and incentives involved in reputation. It also discusses how experiments have shed light on strategic behavior involved in maintaining reputations, and the adequacy of unreliable and third party information (gossip) for maintaining incentives for cooperation.

scholarly journals The Superiority of Quantum Strategy in 3-Player Prisoner’s Dilemma

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1443
Author(s):  
Zhiyuan Dong ◽  
Ai-Guo Wu
Keyword(s):  
Game Theory ◽  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Quantum Game ◽  
Final State ◽  
The Game Theory ◽  
Initial States ◽  
Quantum Strategy ◽  
Selection Of

In this paper, we extend the quantum game theory of Prisoner’s Dilemma to the N-player case. The final state of quantum game theory of N-player Prisoner’s Dilemma is derived, which can be used to investigate the payoff of each player. As demonstration, two cases (2-player and 3-player) are studied to illustrate the superiority of quantum strategy in the game theory. Specifically, the non-unique entanglement parameter is found to maximize the total payoff, which oscillates periodically. Finally, the optimal strategic set is proved to depend on the selection of initial states.

An inhomogeneous problem for an elastic half-strip: An exact solution

2021 ◽  
pp. 108128652199641
Author(s):  
Mikhail D Kovalenko ◽  
Irina V Menshova ◽  
Alexander P Kerzhaev ◽  
Guangming Yu
Keyword(s):  
Exact Solution ◽  
Boundary Conditions ◽  
Exact Solutions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Theory Of Elasticity ◽  
Orthogonality Relation ◽  
Infinite Strip ◽  
Inhomogeneous Problem ◽  
Half Strip

We construct exact solutions of two inhomogeneous boundary value problems in the theory of elasticity for a half-strip with free long sides in the form of series in Papkovich–Fadle eigenfunctions: (a) the half-strip end is free and (b) the half-strip end is firmly clamped. Initially, we construct a solution of the inhomogeneous problem for an infinite strip. Subsequently, the corresponding solutions for a half-strip are added to this solution, whereby the boundary conditions at the end are satisfied. The Papkovich orthogonality relation is used to solve the inhomogeneous problem in a strip.

scholarly journals Exact solutions for the total variation denoising problem of piecewise constant images in dimension one

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Riccardo Cristoferi
Keyword(s):  
Exact Solution ◽  
Exact Solutions ◽  
Total Variation ◽  
Piecewise Constant ◽  
Geometrical Properties ◽  
Total Variation Denoising ◽  
Fidelity Term ◽  
Dimension One

AbstractA method for obtaining the exact solution for the total variation denoising problem of piecewise constant images in dimension one is presented. The validity of the algorithm relies on some results concerning the behavior of the solution when the parameter λ in front of the fidelity term varies. Albeit some of them are well-known in the community, here they are proved with simple techniques based on qualitative geometrical properties of the solutions.

scholarly journals Multi-Robot Searching using Game-Theory Based Approach

10.5772/6232 ◽  
2008 ◽  
Vol 5 (4) ◽  
pp. 44 ◽  
Author(s):  
Yan Meng
Keyword(s):  
Game Theory ◽  
Dynamic Programming ◽  
Utility Function ◽  
Real Time ◽  
Dynamic Environment ◽  
Equilibrium Solutions ◽  
Strategy Equilibrium ◽  
The Game Theory ◽  
Target Searching ◽  
Multi Robot

This paper proposes a game-theory based approach in a multi–target searching using a multi-robot system in a dynamic environment. It is assumed that a rough priori probability map of the targets' distribution within the environment is given. To consider the interaction between the robots, a dynamic-programming equation is proposed to estimate the utility function for each robot. Based on this utility function, a cooperative nonzero-sum game is generated, where both pure Nash Equilibrium and mixed-strategy Equilibrium solutions are presented to achieve an optimal overall robot behaviors. A special consideration has been taken to improve the real-time performance of the game-theory based approach. Several mechanisms, such as event-driven discretization, one-step dynamic programming, and decision buffer, have been proposed to reduce the computational complexity. The main advantage of the algorithm lies in its real-time capabilities whilst being efficient and robust to dynamic environments.

THE TYPES OF AXISYMMETRIC EXACT SOLUTIONS CLOSELY RELATED TO n-SOLITONS FOR YANG–MILLS–HIGGS THEORY

1999 ◽  
Vol 14 (08n09) ◽  
pp. 585-592
Author(s):  
ZAI ZHE ZHONG
Keyword(s):  
Exact Solution ◽  
Exact Solutions ◽  
Inverse Scattering ◽  
Real Matrix ◽  
Zakharov Equation ◽  
Yang Mills ◽  
Scattering Technique

In this letter, we point out that if a symmetric 2×2 real matrix M(ρ,z) obeys the Belinsky–Zakharov equation and | det (M)|=1, then an axisymmetric Bogomol'nyi field exact solution for the Yang–Mills–Higgs theory can be given. By using the inverse scattering technique, some special Bogomol'nyi field exact solutions, which are closely related to the true solitons, are generated. In particular, the Schwarzschild-like solution is a two-soliton-like solution.

scholarly journals Cosmological constant in chameleon Brans–Dicke theory

2019 ◽  
Vol 28 (01) ◽  
pp. 1950022 ◽  
Author(s):  
Yousef Bisabr
Keyword(s):  
Exact Solution ◽  
Scalar Field ◽  
Cosmological Constant ◽  
Exact Solutions ◽  
Effective Mass ◽  
Potential Function ◽  
Power Law ◽  
Exponential Form ◽  
First Case ◽  
Different Types

We consider a generalized Brans–Dicke model in which the scalar field has a self-interacting potential function. The scalar field is also allowed to couple nonminimally with the matter part. We assume that it has a chameleon behavior in the sense that it acquires a density-dependent effective mass. We consider two different types of matter systems which couple with the chameleon, dust and vacuum. In the first case, we find a set of exact solutions when the potential has an exponential form. In the second case, we find a power-law exact solution for the scale factor. In this case, we will show that the vacuum density decays during expansion due to coupling with the chameleon.

scholarly journals Exact solution of fractional Nizhnik-Novikov-Veselov equation

2014 ◽  
Vol 18 (5) ◽  
pp. 1716-1717 ◽  
Author(s):  
Sui-Min Jia ◽  
Ming-Sheng Hu ◽  
Qiao-Ling Chen ◽  
Zhi-Juan Jia
Keyword(s):  
Exact Solution ◽  
Exact Solutions ◽  
Function Method

The fractional Nizhnik-Novikov-Veselov equation is converted to its differential partner, and its exact solutions are successfully established by the exp-function method.

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