scholarly journals Direct Evolutionary Search for Nash Equilibria Detection

2016 ◽  
Vol 11 (4) ◽  
pp. 472
Author(s):  
Rodica Ioana Lung
Keyword(s):  
Normal Form ◽  
Evolutionary Algorithm ◽  
Numerical Experiments ◽  
Nash Equilibria ◽  
Search Algorithm ◽  
Direct Method ◽  
Evolutionary Search ◽  
Normal Form Game ◽  
Tournament Selection ◽  
A Direct Method

<p>A Direct method of computing mixed form Nash equilibria of a normal form game by using a simple evolutionary algorithm is proposed. The Direct Evolutionary Search algorithm (DES) uses a generative relation for Nash equilibria with binary tournament selection and uniform mutation. Numerical experiments are used to illustrate the efficiency of the method.</p>

On modeling column crystallizers and a Hermite predictor–corrector scheme for a system of integro-differential equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Khaldoun El Khaldi ◽  
Nima Rabiei ◽  
Elias G. Saleeby
Keyword(s):  
Numerical Experiments ◽  
Main Part ◽  
Direct Method ◽  
Particle Agglomeration ◽  
Volterra Type ◽  
Type Method ◽  
Method Of Solution ◽  
System Of Integrodifferential Equations ◽  
Predictor Corrector ◽  
A Direct Method

Abstract Multistaged crystallization systems are used in the production of many chemicals. In this article, employing the population balance framework, we develop a model for a column crystallizer where particle agglomeration is a significant growth mechanism. The main part of the model can be reduced to a system of integrodifferential equations (IDEs) of the Volterra type. To solve this system simultaneously, we examine two numerical schemes that yield a direct method of solution and an implicit Runge–Kutta type method. Our numerical experiments show that the extension of a Hermite predictor–corrector method originally advanced in Khanh (1994) for a single IDE is effective in solving our model. The numerical method is presented for a generalization of the model which can be used to study and simulate a number of possible operating profiles of the column.

Quantifying Commitment in Nash Equilibria

2019 ◽  
Vol 21 (02) ◽  
pp. 1940011
Author(s):  
Thomas A. Weber
Keyword(s):  
Nash Equilibrium ◽  
Normal Form ◽  
Nash Equilibria ◽  
Dynamic Game ◽  
Subgame Perfect Equilibrium ◽  
Canonical Extension ◽  
Perfect Equilibrium ◽  
Form Game ◽  
Normal Form Game ◽  
The Given

To quantify a player’s commitment in a given Nash equilibrium of a finite dynamic game, we map the corresponding normal-form game to a “canonical extension,” which allows each player to adjust his or her move with a certain probability. The commitment measure relates to the average overall adjustment probabilities for which the given Nash equilibrium can be implemented as a subgame-perfect equilibrium in the canonical extension.

COALITION-PROOF NASH EQUILIBRIA IN A NORMAL-FORM GAME AND ITS SUBGAMES

2010 ◽  
Vol 12 (03) ◽  
pp. 253-261
Author(s):  
RYUSUKE SHINOHARA
Keyword(s):  
Normal Form ◽  
Nash Equilibria ◽  
Sufficient Condition ◽  
Form Game ◽  
Normal Form Game ◽  
Aggregative Games ◽  
The Relationship ◽  
Coalition Proof

The relationship between coalition-proof (Nash) equilibria in a normal-form game and those in its subgame is examined. A subgame of a normal-form game is a game in which the strategy sets of all players in the subgame are subsets of those in the normal-form game. In this paper, focusing on a class of aggregative games, we provide a sufficient condition for the aggregative game under which every coalition-proof equilibrium in a subgame is also coalition-proof in the original normal-form game. The stringency of the sufficient condition means that a coalition-proof equilibrium in a subgame is rarely a coalition-proof equilibrium in the whole game.

Applications of Algebra for Some Game Theoretic Problems

2015 ◽  
Vol 26 (01) ◽  
pp. 51-78
Author(s):  
Ratnik Gandhi ◽  
Samaresh Chatterji
Keyword(s):  
Normal Form ◽  
Group Action ◽  
Nash Equilibria ◽  
Polynomial Algebra ◽  
Algebraic Method ◽  
Polynomial Equations ◽  
Form Game ◽  
Normal Form Game ◽  
Game Theoretic ◽  
System Of Polynomial Equations

In this paper we present applications of polynomial algebra for the problem of computing Nash equilibria of a subclass of finite normal form games.We characterize Nash equilibria of a normal form game as solutions to a system of polynomial equations and define the subclass of games under consideration. We present an algebraic method for deciding membership decision to the subclass of games. A method based on group action to compute all Nash equilibria of the subclass of games is presented with examples to show working of the methods. We also present some related results and discuss properties of the subclass of games.

A Non-Monotone Line Search Combination Technique for Unconstrained Optimization

2014 ◽  
Vol 8 (1) ◽  
pp. 218-221 ◽  
Author(s):  
Ping Hu ◽  
Zong-yao Wang
Keyword(s):  
Global Convergence ◽  
Unconstrained Optimization ◽  
Numerical Experiments ◽  
Line Search ◽  
Optimization Problems ◽  
Search Algorithm ◽  
New Combination ◽  
Combination Rule ◽  
Combination Technique ◽  
Unconstrained Optimization Problems

We propose a non-monotone line search combination rule for unconstrained optimization problems, the corresponding non-monotone search algorithm is established and its global convergence can be proved. Finally, we use some numerical experiments to illustrate the new combination of non-monotone search algorithm’s effectiveness.

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