scholarly journals Designing Strategic Games with Preestablished Nash Equilibrium through Artificial Inference and Global Learning

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Hime A. e Oliveira Jr.
Keyword(s):  
Global Optimization ◽  
Nash Equilibrium ◽  
Solution Concept ◽  
Optimization Method ◽  
Optimization Techniques ◽  
Strategic Games ◽  
Global Learning ◽  
Finite State ◽  
Payoff Functions ◽  
Game Designer

Abstract This work presents novel results obtained by the application of global optimization techniques to the design of finite, normal form games with mixed strategies. To that end, the Fuzzy ASA global optimization method is applied to several design examples of strategic games, demonstrating its effectiveness in obtaining payoff functions whose corresponding games present a previously established Nash equilibrium. In other words, the game designer becomes able to choose a convenient Nash equilibrium for a generic finite state strategic game and the proposed method computes payoff functions that will realize the desired equilibrium, making it possible for the players to reach the favorable conditions represented by the chosen equilibrium. Considering that game theory is a very useful approach for modeling interactions between competing agents and Nash equilibrium represents a powerful solution concept, it is natural to infer that the proposed method may be very useful for strategists in general. In summary, it is a genuine instance of artificial inference of payoff functions after a process of global machine learning, applied to their numerical components.

scholarly journals Designing Strategic Games With Preestablished Nash Equilibrium Through Artificial Inference and Global Learning

2019 ◽  
Author(s):  
Hime A. e Oliveira Jr.
Keyword(s):  
Global Optimization ◽  
Nash Equilibrium ◽  
Solution Concept ◽  
Optimization Method ◽  
Optimization Techniques ◽  
Strategic Games ◽  
Global Learning ◽  
Finite State ◽  
Payoff Functions ◽  
Game Designer

This work presents significant results obtained by the application of global optimization techniques to the design of finite, normal form games with mixed strategies. To that end, the Fuzzy ASA global optimization method is applied to several design examples of strategic games, demonstrating its effectiveness in obtaining payoff functions whose corresponding games present a previously established Nash equilibrium. In other words, the game designer becomes able to choose a convenient Nash equilibrium for a generic finite state strategic game and the proposed method computes payoff functions that will realize the desired equilibrium, making it possible for the players to reach the favorable conditions represented by the chosen equilibrium. Considering that game theory is a very significant approach for modeling interactions between competing agents, and Nash equilibrium represents a powerful solution concept, portraying situations in which joint strategies are optimal in the sense that players cannot benefit from individually modifying their current strategies provided that other players do not change their strategies as well, it is natural to infer that the proposed method may be very useful for strategists in general. In summary, it is a genuine instance of artificial inference of payoff functions after a process of global machine learning, applied to their numerical components.

scholarly journals Designing Strategic Games With Preestablished Nash Equilibrium Through Artificial Inference and Global Learning

2019 ◽  
Author(s):  
Hime A. e Oliveira Jr.
Keyword(s):  
Global Optimization ◽  
Nash Equilibrium ◽  
Solution Concept ◽  
Optimization Method ◽  
Optimization Techniques ◽  
Strategic Games ◽  
Global Learning ◽  
Finite State ◽  
Payoff Functions ◽  
Game Designer

This work presents significant results obtained by the application of global optimization techniques to the design of finite, normal form games with mixed strategies. To that end, the Fuzzy ASA global optimization method is applied to several design examples of strategic games, demonstrating its effectiveness in obtaining payoff functions whose corresponding games present a previously established Nash equilibrium. In other words, the game designer becomes able to choose a convenient Nash equilibrium for a generic finite state strategic game and the proposed method computes payoff functions that will realize the desired equilibrium, making it possible for the players to reach the favorable conditions represented by the chosen equilibrium. Considering that game theory is a very significant approach for modeling interactions between competing agents, and Nash equilibrium represents a powerful solution concept, portraying situations in which joint strategies are optimal in the sense that players cannot benefit from individually modifying their current strategies provided that other players do not change their strategies as well, it is natural to infer that the proposed method may be very useful for strategists in general. In summary, it is a genuine instance of artificial inference of payoff functions after a process of global machine learning, applied to their numerical components.

scholarly journals Synthesis of Strategic Games with Multiple Nash Equilibria - A Global Optimization Approach

2019 ◽  
Author(s):  
Hime Oliveira
Keyword(s):  
Global Optimization ◽  
Nash Equilibrium ◽  
Nash Equilibria ◽  
Optimization Method ◽  
Optimization Techniques ◽  
Optimization Approach ◽  
Strategic Games ◽  
Finite State ◽  
Payoff Functions ◽  
Multiple Nash Equilibria

This paper presents an extension of the resuts obtained in previous work by the author concerning the application of global optimization techniques to the design of finite strategic games with mixed strategies. In that publication the Fuzzy ASA global optimization method was applied to many examples of synthesis of strategic games with one previously specified Nash equilibrium, evidencing its ability in finding payoff functions whose respective games present those equilibria, possibly among others. That is to say, it was shown it is possible to establish in advance a Nash equilibrium for a generic finite state strategic game and to compute payoff functions that will make it feasible to reach the chosen equilibrium, allowing players to converge to the desired profile, considering that it is an equilibrium of the game as well. Going beyond this state of affairs, the present article shows that it is possible to "impose" multiple Nash equilibria to finite strategic games by following the same reasoning as before, but with a slight change: using the same fundamental theorem of Richard D. McKelvey, modifying the original prescribed objective function and globally minimizing it. The proposed method, in principle, is able to find payoff functions that result in games featuring an arbitrary number of Nash equiibria, paving the way to a substantial number of potential applications.

scholarly journals Calibration of the modified Bartlett-Lewis model using global optimization techniques and alternative objective functions

2012 ◽  
Vol 16 (3) ◽  
pp. 873-891 ◽  
Author(s):  
W. J. Vanhaute ◽  
S. Vandenberghe ◽  
K. Scheerlinck ◽  
B. De Baets ◽  
N. E. C. Verhoest
Keyword(s):  
Global Optimization ◽  
Optimization Methods ◽  
Optimization Method ◽  
Optimization Techniques ◽  
Objective Functions ◽  
Local Search Algorithms ◽  
Stochastic Point Process ◽  
Shuffled Complex Evolution ◽  
Global Optimization Methods ◽  
Downhill Simplex

Abstract. The calibration of stochastic point process rainfall models, such as of the Bartlett-Lewis type, suffers from the presence of multiple local minima which local search algorithms usually fail to avoid. To meet this shortcoming, four relatively new global optimization methods are presented and tested for their ability to calibrate the Modified Bartlett-Lewis Model. The list of tested methods consists of: the Downhill Simplex Method, Simplex-Simulated Annealing, Particle Swarm Optimization and Shuffled Complex Evolution. The parameters of these algorithms are first optimized to ensure optimal performance, after which they are used for calibration of the Modified Bartlett-Lewis model. Furthermore, this paper addresses the choice of weights in the objective function. Three alternative weighing methods are compared to determine whether or not simulation results (obtained after calibration with the best optimization method) are influenced by the choice of weights.

scholarly journals Calibration of the modified Bartlett-Lewis model using global optimization techniques and alternative objective functions

2011 ◽  
Vol 8 (6) ◽  
pp. 9707-9756 ◽  
Author(s):  
W. J. Vanhaute ◽  
S. Vandenberghe ◽  
K. Scheerlinck ◽  
B. De Baets ◽  
N. E. C. Verhoest
Keyword(s):  
Time Series ◽  
Global Optimization ◽  
Optimization Methods ◽  
Optimization Method ◽  
Optimization Techniques ◽  
Rainfall Time Series ◽  
Stochastic Point Process ◽  
Shuffled Complex Evolution ◽  
Global Optimization Methods ◽  
Downhill Simplex

Abstract. The use of rainfall time series for various applications is widespread. However, in many cases historical rainfall records lack in length or quality for certain practical purposes, resulting in a reliance on rainfall models to supply simulated rainfall time series, e.g., in the design of hydraulic structures. One way to obtain such simulations is by means of stochastic point process rainfall models, such as the Bartlett-Lewis type of model. It is widely acknowledged that the calibration of such models suffers from the presence of multiple local minima which local search algorithms usually fail to avoid. To meet this shortcoming, four relatively new global optimization methods are presented and tested for their abilities to calibrate the Modified Bartlett-Lewis Model (MBL). The list of tested methods consists of: the Downhill Simplex Method (DSM), Simplex-Simulated Annealing (SIMPSA), Particle Swarm Optimization (PSO) and Shuffled Complex Evolution (SCE-UA). The parameters of these algorithms are first optimized to ensure optimal performance, after which they are used for calibration of the MBL model. Furthermore, this paper addresses the issue of subjectivity in the choice of weights in the objective function. Three alternative weighing methods are compared to determine whether or not simulation results (obtained after calibration with the best optimization method) are influenced by the choice of weights.

Calibration of the Parameters of a Model of an Engineering System Using the Global Optimization Method

2014 ◽  
Vol 5 (3) ◽  
pp. 14-41 ◽  
Author(s):  
Marwa Elhajj ◽  
Rafic Younes ◽  
Sebastien Charles ◽  
Eric Padiolleau
Keyword(s):  
Genetic Algorithm ◽  
Global Optimization ◽  
Optimization Technique ◽  
Optimization Method ◽  
Simulation Software ◽  
Optimization Techniques ◽  
Engineering System ◽  
Global Optimization Method ◽  
Unknown Parameters ◽  
Simulated Model

The calibration of the model is one of the most important steps in the development of models of engineering systems. A new approach is presented in this study to calibrate a complex multi-domain system. This approach respects the real characteristics of the circuit, the accuracy of the results, and minimizes the cost of the experimental phase. This paper proposes a complete method, the Global Optimization Method for Parameter Calibration (GOMPC). This method uses an optimization technique coupled with the simulated model on simulation software. In this paper, two optimization techniques, the Genetic Algorithm (GA) and the two-level Genetic Algorithm, are applied and then compared on two case studies: a theoretical and a real hydro-electromechanical circuit. In order to optimize the number of measured outputs, a sensitivity analysis is used to identify the objective function (OBJ) of the two studied optimization techniques. Finally, results concluded that applying GOMPC by combining the two-level GA with the simulated model was an efficient solution as it proves its accuracy and efficiency with less computation time. It is believed that this approach is able to converge to the expected results and to find the system's unknown parameters faster and with more accuracy than GA.

Global Optimization Method Based on Incremental Radial Basis Functions

2011 ◽  
Vol 121-126 ◽  
pp. 3950-3954
Author(s):  
Xin Wei ◽  
Yi Zhong Wu ◽  
Li Ping Chen
Keyword(s):  
Global Optimization ◽  
Global Minimum ◽  
Optimization Method ◽  
Optimization Techniques ◽  
Global Optimization Method ◽  
Latin Hypercube Design ◽  
Sampling Step ◽  
Method Base ◽  
Engineering Problems ◽  
Complex Engineering

Global optimization techniques have been used extensively due to their capability in handling complex engineering problems. Metamodel becomes effective method to enhance global optimization. In this paper, we propose a new global optimization method base on incremental metamodel. At each sampling step, we adopt inherited Latin HyperCube design to sample points step by step, and propose a new incremental metamodel to update the cofficient matrix gradually. Experiments proved that the global optimization method has highest efficiency and can be finding global minimum fastly.

Optimization Design of Finger Seal Performances Based on Game Theory

2010 ◽  
Vol 156-157 ◽  
pp. 1275-1280
Author(s):  
Yan Chao Zhang ◽  
Guo Ding Chen
Keyword(s):  
Mathematical Model ◽  
Game Theory ◽  
Nash Equilibrium ◽  
Optimization Design ◽  
Optimization Method ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Equilibrium Method ◽  
Wear Ratio ◽  
Payoff Functions

To reach the expecting goal of lower leakage ratio and longer operation life(lower wear ratio) for finger seal, great efforts have been made continuously to obtain good structure of finger seal with advanced optimization design technology. A cooperation Nash equilibrium mathematical model of multi-objective optimization for finger seal is presented in current work based on Nash equilibrium of game theory. In this solution, the reciprocal of leakage ratio and the wear ratio value for finger seal are thought as the payoff functions and the game is solved by genetic algorithm. The numerical simulation in the paper shows that the finger seal with better performances can be achieved by using Nash equilibrium method. This means Nash equilibrium method can be used as a new multi-objective optimization method for finger seal performances optimization.

SOLUTION CONCEPT FOR A NON-COOPERATIVE GAME WITH FUZZY PARAMETERS

2006 ◽  
Vol 08 (03) ◽  
pp. 489-498 ◽  
Author(s):  
FATIHA KACHER ◽  
MOUSSA LARBANI
Keyword(s):  
Decision Making ◽  
Nash Equilibrium ◽  
Cooperative Game ◽  
Sufficient Conditions ◽  
Solution Concept ◽  
Decision Making Under Uncertainty ◽  
Unknown Parameters ◽  
Complete Ignorance ◽  
Payoff Functions ◽  
Fuzzy Parameters

In this paper, we study a non cooperative game with payoff functions involving fuzzy parameters. We introduce a concept of solution for this game that we call α-N-S- equilibrium. Our definition is derived from the concept of N-S equilibrium introduced by Zhukovskii for a non cooperative game with payoffs involving unknown parameters in the case of complete ignorance of their behavior. The α-N-S- equilibrium takes into account both the aspect of conflict and the aspect of decision making under uncertainty related to the presence of fuzzy parameters. For the aspect of conflict we adopted the Nash equilibrium, for the aspect of uncertainty we adopted the maximin approach through weak Pareto optimality. Furthermore, we give sufficient conditions for its existence.

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