AN APPROACH FOR SOLVING FUZZY GAMES

2006 ◽  
Vol 14 (03) ◽  
pp. 277-292 ◽  
Author(s):  
WEI YI LIU ◽  
JIN LI ◽  
KUN YUE ◽  
NING SONG ◽  
HONG YAO
Keyword(s):  
Genetic Algorithm ◽  
Nash Equilibrium ◽  
Mixed Strategies ◽  
Fuzzy Environment ◽  
Approximate Nash Equilibrium ◽  
Fuzzy Games ◽  
The Relationship

This paper is to compute a Nash equilibrium in a fuzzy environment, which is represented by a fuzzy approximate Nash equilibrium in a space of discrete mixed strategies. For discrete mixed strategies, the relationship between the discrete degree and the approximate degree is discussed. Based on the fuzzy regret degree, a genetic algorithm for computing a fuzzy Nash equilibrium is given.

scholarly journals Sampling Individually Fundamental Simplexes as Sets of Players’ Mixed Strategies in Finite Noncooperative Game for Applicable Approximate Nash Equilibrium Situations with Possible Concessions

2016 ◽  
Vol 40 (1) ◽  
pp. 105-143
Author(s):  
Vadim Romanuke
Keyword(s):  
Nash Equilibrium ◽  
Nash Equilibria ◽  
Finite Lattice ◽  
Noncooperative Game ◽  
Mixed Strategies ◽  
Approximate Equilibrium ◽  
Approximate Nash Equilibrium ◽  
Universal Approach ◽  
Finite Lattices

In finite noncooperative game, a method for finding approximate Nash equilibrium situations is developed. The method is prior-based on sampling fundamental simplexes being the sets of players’ mixed strategies. Whereas the sampling is exercised, the sets of players’ mixed strategies are mapped into finite lattices. Sampling steps are envisaged dissimilar. Thus, each player within every dimension of its simplex selects and controls one’s sampling individually. For preventing approximation low quality, however, sampling steps are restricted. According to the restricted sampling steps, a player acting singly with minimal spacing over its lattice cannot change payoff of any player more than by some predetermined magnitude, being specific for each player. The finite lattice is explicitly built by the represented routine, where the player’s mixed strategies are calculated and arranged. The product of all the players’ finite lattices approximates the product of continuous fundamental simplexes. This re-defines the finite noncooperative game in its finite mixed extension on the finite lattices’ product. In such a finite-mixed-extension-defined game, the set of Nash equilibrium situations may be empty. Therefore, approximate Nash equilibrium situations are defined by the introduced possible payoff concessions. A routine for finding approximate equilibrium situations is represented. Approximate strong Nash equilibria with possible concessions are defined, and a routine for finding them is represented as well. Acceleration of finding approximate equilibria is argued also. Finally, the developed method is discussed to be a basis in stating a universal approach for the finite noncooperative game solution approximation implying unification of the game solvability, applicability, realizability, and adaptability.

scholarly journals Inventory model of deteriorating items with two-warehouse and stock dependent demand using genetic algorithm in fuzzy environment

2012 ◽  
Vol 22 (1) ◽  
pp. 51-78 ◽  
Author(s):  
Dharmendra Yadav ◽  
S.R. Singh ◽  
Rachna Kumari
Keyword(s):  
Genetic Algorithm ◽  
Inventory Model ◽  
Deteriorating Items ◽  
Market Place ◽  
Time Value Of Money ◽  
Fuzzy Environment ◽  
Purchase Cost ◽  
Stock Dependent Demand ◽  
Fuzzy Goal ◽  
Dependent Demand

Multi-item inventory model for deteriorating items with stock dependent demand under two-warehouse system is developed in fuzzy environment (purchase cost, investment amount and storehouse capacity are imprecise ) under inflation and time value of money. For display and storage, the retailers hire one warehouse of finite capacity at market place, treated as their own warehouse (OW), and another warehouse of imprecise capacity which may be required at some place distant from the market, treated as a rented warehouse (RW). Joint replenishment and simultaneous transfer of items from one warehouse to another is proposed using basic period (BP) policy. As some parameters are fuzzy in nature, objective (average profit) functions as well as some constraints are imprecise in nature, too. The model is formulated so to optimize the possibility/necessity measure of the fuzzy goal of the objective functions, and the constraints satisfy some pre-defined necessity. A genetic algorithm (GA) is used to solve the model, which is illustrated on a numerical example.

scholarly journals The Method for Product Design Selection with Incomplete Linguistic Weight Information Based on Quality Function Deployment in a Fuzzy Environment

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Ming Li
Keyword(s):  
Product Design ◽  
Quality Function Deployment ◽  
Design Development ◽  
Quality Function ◽  
Advantages And Disadvantages ◽  
Fuzzy Environment ◽  
Design Requirements ◽  
Design Selection ◽  
The Given ◽  
The Relationship

The selection of a design for the given product is a critical problem in product design development. Focuses of the designers and customers on the design are not identical. In order to bridge the gap and provide a more relaxing way to select the design, a new method based on quality function deployment (QFD) is proposed. In such a method, customers are required to give their linguistic preferences on the design with respect to the customer requirements (CRs). In the rating of the weight of CRs, they are allowed to provide incomplete linguistic weight information and the objective optimization model is proposed to derive the exact linguistic weight information. Designers are required to rate the correlation between design requirements (DRs) and the relationship between the CRs and DRs to construct the house of quality. Opinions given by the customers are translated into the opinions with respect to the DRs based on the QFD. Afterwards, the priorities of the designs and design requirements are determined. The assessment results not only show the contribution of each design requirement to the customer satisfaction but also show the advantages and disadvantages of each design from the designers’ perspective clearly and directly. An example is provided to validate the applicability of the proposed method.

scholarly journals Operant Matching as a Nash Equilibrium of an Intertemporal Game

2009 ◽  
Vol 21 (10) ◽  
pp. 2755-2773 ◽  
Author(s):  
Yonatan Loewenstein ◽  
Drazen Prelec ◽  
H. Sebastian Seung
Keyword(s):  
Nash Equilibrium ◽  
Matching Law ◽  
Single Subject ◽  
Multiple Selves ◽  
The Past ◽  
Aggregate Behavior ◽  
The Subject ◽  
Individual Choices ◽  
The Relationship ◽  
Mutual Defection

Over the past several decades, economists, psychologists, and neuroscientists have conducted experiments in which a subject, human or animal, repeatedly chooses between alternative actions and is rewarded based on choice history. While individual choices are unpredictable, aggregate behavior typically follows Herrnstein's matching law: the average reward per choice is equal for all chosen alternatives. In general, matching behavior does not maximize the overall reward delivered to the subject, and therefore matching appears inconsistent with the principle of utility maximization. Here we show that matching can be made consistent with maximization by regarding the choices of a single subject as being made by a sequence of multiple selves—one for each instant of time. If each self is blind to the state of the world and discounts future rewards completely, then the resulting game has at least one Nash equilibrium that satisfies both Herrnstein's matching law and the unpredictability of individual choices. This equilibrium is, in general, Pareto suboptimal, and can be understood as a mutual defection of the multiple selves in an intertemporal prisoner's dilemma. The mathematical assumptions about the multiple selves should not be interpreted literally as psychological assumptions. Human and animals do remember past choices and care about future rewards. However, they may be unable to comprehend or take into account the relationship between past and future. This can be made more explicit when a mechanism that converges on the equilibrium, such as reinforcement learning, is considered. Using specific examples, we show that there exist behaviors that satisfy the matching law but are not Nash equilibria. We expect that these behaviors will not be observed experimentally in animals and humans. If this is the case, the Nash equilibrium formulation can be regarded as a refinement of Herrnstein's matching law.

Inflation shocks and income inequality

2019 ◽  
Vol 10 (2) ◽  
pp. 226-240
Author(s):  
Rolando Gonzales ◽  
Andrea Rojas-Hosse
Keyword(s):  
Genetic Algorithm ◽  
Methodological Approach ◽  
Mena Region ◽  
Content Type ◽  
Core Inflation ◽  
Research Gap ◽  
Using Data ◽  
The Impact ◽  
The Relationship ◽  
Detrimental Impact

Purpose The purpose of this paper is to analyze the effects of inflationary shocks on inequality, using data of selected countries of the Middle East and North Africa (MENA). Design/methodology/approach Inflationary shocks were measured as deviations from core inflation, based on a genetic algorithm. Bayesian quantile regression was used to estimate the impact of inflationary shocks in different levels of inequality. Findings The results showed that inflationary shocks substantially affect countries with higher levels of inequality, thus suggesting that the detrimental impact of inflation is exacerbated by the high division of classes in a country. Originality/value The study contributes to the literature about the relationship between inflation and inequality by proposing that not only the sustained increase in prices but also the inflationary shocks – the deviations from core inflation – contribute to the generation of inequality. Also, to the best of the authors knowledge, the relationship between inflation shocks and inequality in the MENA region has never been analyzed before, thus creating a research gap to provide additional empirical evidence about the sources of inequality. Additionally, the authors contribute with a methodological approach to measure inflationary shocks, based on a semelparous genetic algorithm.

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