scholarly journals A Nikaido Isoda-Based Hybrid Genetic Algorithm and Relaxation Method for Finding Nash Equilibrium

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 81
Author(s):  
Napat Harnpornchai ◽  
Wiriyaporn Wonggattaleekam
Keyword(s):  
Genetic Algorithm ◽  
Nash Equilibrium ◽  
Hybrid Genetic Algorithm ◽  
Relaxation Method ◽  
Generalized Nash Equilibrium Problem ◽  
Adaptive Penalty ◽  
Coupled Constraints ◽  
Optimum Response ◽  
Payoff Functions

Nash Equilibrium (NE) plays a crucial role in game theory. The relaxation method in conjunction with the Nikaido–Isoda (NI) function, namely the NI-based relaxation method, has been widely applied to the determination of NE. Genetic Algorithm (GA) with adaptive penalty is introduced and incorporated in the original NI-based relaxation method. The GA enhances the capability in the optimization step for computing the optimum response function. The optimization of the non-convex and non-concave NI function is made possible by GA. The proposed method thus combines the advantageous feature of the GA in its optimization capability and that of the relaxation method in its implementation simplicity together. The applicability of the method is shown through the illustrative examples, including the generalized Nash Equilibrium problem with nonlinear payoff functions and coupled constraints, the game with multiple strategic variables for individual players, and the non-differentiable payoff functions. All test example results suggest the appropriate crossover and mutation rate to be 0.05 and 0.002 for use in GA. These numbers are closed to the recommended values by DeJong. The proposed method shows its capability of finding correct NEs in all test examples.

scholarly journals The study of the set of Nash equilibrium points for one two-players game with quadratic payoff functions

2015 ◽  
Vol 25 (2) ◽  
pp. 291-297
Author(s):  
Mikhail Nikolskii ◽  
Aboubacar Moussa
Keyword(s):  
Nash Equilibrium ◽  
Graphical Method ◽  
Equilibrium Points ◽  
Nash Equilibrium Points ◽  
Payoff Functions

In this paper, the general two-players game on the square with quadratic payoff functions is considered. We have studied the problem of determination of the set of Nash equilibrium points, and here we present a constructive graphical method for determination of the required set which we have developed.

scholarly journals Exact Penalization of Generalized Nash Equilibrium Problems

2020 ◽  
Author(s):  
Qin Ba ◽  
Jong-Shi Pang
Keyword(s):  
Nash Equilibrium ◽  
Optimization Problems ◽  
Salient Feature ◽  
Generalized Nash Equilibrium Problem ◽  
Generalized Nash Equilibrium ◽  
Exact Penalization ◽  
Mathematical Economics ◽  
Decision Variables ◽  
Solution Methods ◽  
Coupled Constraints

This paper presents an exact penalization theory of the generalized Nash equilibrium problem (GNEP) that has its origin from the renowned Arrow–Debreu general economic equilibrium model. Whereas the latter model is the foundation of much of mathematical economics, the GNEP provides a mathematical model of multiagent noncooperative competition that has found many contemporary applications in diverse engineering domains. The most salient feature of the GNEP that distinguishes it from a standard noncooperative (Nash) game is that each player’s optimization problem contains constraints that couple all players’ decision variables. Extending results for stand-alone optimization problems, the penalization theory aims to convert the GNEP into a game of the standard kind without the coupled constraints, which is known to be more readily amenable to solution methods and analysis. Starting with an illustrative example to motivate the development, this paper focuses on two kinds of coupled constraints, shared (i.e., common) and finitely representable. Constraint residual functions and the associated error bound theory play an important role throughout the development.

FIDDLE. Simultaneous Indexing and Structure Solution from Powder Diffraction Data using a Genetic Algorithm and Correlation Functions

2019 ◽  
Author(s):  
Carmen Guguta ◽  
Jan M.M. Smits ◽  
Rene de Gelder
Keyword(s):  
Genetic Algorithm ◽  
Powder Diffraction ◽  
Diffraction Data ◽  
Correlation Functions ◽  
Cross Correlation ◽  
Simultaneous Optimization ◽  
Powder Diffraction Data ◽  
Structure Solution ◽  
Matching Technique

A method for the determination of crystal structures from powder diffraction data is presented that circumvents the difficulties associated with separate indexing. For the simultaneous optimization of the parameters that describe a crystal structure a genetic algorithm is used together with a pattern matching technique based on auto and cross correlation functions.<br>

Design of GA and Ontology based NLP Frameworks for Online Opinion Mining

2019 ◽  
Vol 13 (2) ◽  
pp. 159-165
Author(s):  
Manik Sharma ◽  
Gurvinder Singh ◽  
Rajinder Singh
Keyword(s):  
Genetic Algorithm ◽  
Natural Language Processing ◽  
Natural Language ◽  
Language Processing ◽  
Opinion Mining ◽  
Hybrid Genetic Algorithm ◽  
Online Reviews ◽  
Middle Tier ◽  
Complete Set ◽  
Mining Model

Background: For almost every domain, a tremendous degree of data is accessible in an online and offline mode. Billions of users are daily posting their views or opinions by using different online applications like WhatsApp, Facebook, Twitter, Blogs, Instagram etc. Objective: These reviews are constructive for the progress of the venture, civilization, state and even nation. However, this momentous amount of information is useful only if it is collectively and effectively mined. Methodology: Opinion mining is used to extract the thoughts, expression, emotions, critics, appraisal from the data posted by different persons. It is one of the prevailing research techniques that coalesce and employ the features from natural language processing. Here, an amalgamated approach has been employed to mine online reviews. Results: To improve the results of genetic algorithm based opining mining patent, here, a hybrid genetic algorithm and ontology based 3-tier natural language processing framework named GAO_NLP_OM has been designed. First tier is used for preprocessing and corrosion of the sentences. Middle tier is composed of genetic algorithm based searching module, ontology for English sentences, base words for the review, complete set of English words with item and their features. Genetic algorithm is used to expedite the polarity mining process. The last tier is liable for semantic, discourse and feature summarization. Furthermore, the use of ontology assists in progressing more accurate opinion mining model. Conclusion: GAO_NLP_OM is supposed to improve the performance of genetic algorithm based opinion mining patent. The amalgamation of genetic algorithm, ontology and natural language processing seems to produce fast and more precise results. The proposed framework is able to mine simple as well as compound sentences. However, affirmative preceded interrogative, hidden feature and mixed language sentences still be a challenge for the proposed framework.

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