Partially Specified Probabilities: Decisions and Games

2012 ◽  
Vol 4 (1) ◽  
pp. 70-100 ◽  
Author(s):  
Ehud Lehrer
Keyword(s):  
Decision Making ◽  
Nash Equilibrium ◽  
Axiomatic Approach ◽  
Concave Integral ◽  
Interactive Models

The paper develops a theory of decision making based on partially specified probabilities. It takes an axiomatic approach using Anscombe and Aumann's (1963) setting, and is based on the concave integral for capacities. This theory is then expanded to interactive models in order to extend Nash equilibrium by introducing the concept of partially specified equilibrium. (JEL C70, D81, D83)

scholarly journals Mehanizmi odlucivanja i strateske manipulacije

2004 ◽  
Vol 44 (161) ◽  
pp. 123-134
Author(s):  
Dragan Azdejkovic
Keyword(s):  
Decision Making ◽  
Social Choice ◽  
Mechanism Design ◽  
Axiomatic Approach ◽  
Collective Decision ◽  
Design Approach ◽  
Collective Decision Making

The theory of social choice deals with both the processes and results of collective decision making. In this paper, we explore some issues in the theory of social choice and mechanism design. We examine the premises of this theory, the axiomatic approach, and the mechanism design approach.

scholarly journals Axiomatic approach of measurement and decision making

2014 ◽  
Vol 78 (0) ◽  
pp. SS-064-SS-064
Author(s):  
Kazuhisa Takemura ◽  
Ryozo Yoshino ◽  
Yutaka Matsushita ◽  
Takayuki Sakagami ◽  
Kenpei Shiina
Keyword(s):  
Decision Making ◽  
Axiomatic Approach

New expected impact functions and algorithms for modeling games under soft sets

2020 ◽  
Vol 39 (3) ◽  
pp. 4463-4472
Author(s):  
Irfan Deli ◽  
Hoang Viet Long ◽  
Le Hoang Son ◽  
Raghvendra Kumar ◽  
Arindam Dey
Keyword(s):  
Decision Making ◽  
Nash Equilibrium ◽  
Model Theory ◽  
Saddle Points ◽  
Soft Set ◽  
Soft Sets ◽  
Matrix Games ◽  
Soft Matrix ◽  
Dominated Strategies

Soft set is the power tool to deal with uncertainty in a parametric manner. In applications of soft set, one of the most important steps is to define mappings on soft sets. In this study, we model theory of game under theory of soft set which is an effective tool for handling uncertainties events and problems that may exist in a game. To this end, we first define some expected impact functions of players in soft games. Then, we propose three new decision making algorithms to solve the 2.2 × p, 2 . n × p and m . 2 × p soft matrix games, which cannot be settled by the relevant soft methods such as saddle points, lover and upper values, dominated strategies and Nash equilibrium. The proposed soft game algorithms are illustrated by examples.

scholarly journals Dynamic Pricing Based on Strategic Consumers and Substitutes in a Duopoly Setting

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Gongbing Bi ◽  
Lechi Li ◽  
Feng Yang ◽  
Liang Liang
Keyword(s):  
Decision Making ◽  
Nash Equilibrium ◽  
Product Differentiation ◽  
Dynamic Pricing ◽  
Dynamic Game ◽  
Solution Concept ◽  
Expected Value ◽  
Decision Making Process ◽  
Pricing Model ◽  
Strategic Consumers

Based on the rational strategic consumers, we construct a dynamic game to build a two-period dynamic pricing model for two brands of substitutes which are sold by duopoly. The solution concept of the dynamic game is Nash equilibrium. In our model, consumers have been clearly segmented into several consumption classes, according to their expected value of the products. The two competing firms enter a pricing game and finally reach the state of Nash equilibrium. In addition, decision-making process with only myopic consumers existing in the market is analyzed. To make the paper more practical and realistic, the condition, in which the myopic and strategic consumers both exist in the market, is also considered and studied. In order to help the readers understand better and make it intuitively more clearly, a numerical example is given to describe the influence of the main parameters to the optimal prices. The result indicates that, to maintain the firms’ respective optimal profits, the prices of the products should be adjusted appropriately with the changes of product differentiation coefficient.

scholarly journals A program to find all pure Nash equilibria in games with n-players and m-strategies: the Nash Equilibria Finder – NEFinder

2021 ◽  
Vol 28 (3) ◽  
Author(s):  
Renan Henrique Cavicchioli Sugiyama ◽  
Alexandre Bevilacqua Leoneti
Keyword(s):  
Decision Making ◽  
Nash Equilibrium ◽  
Group Decision Making ◽  
Operations Research ◽  
Nash Equilibria ◽  
Group Decision ◽  
Microsoft Excel ◽  
Computational Tools ◽  
Practical Applications ◽  
Decision Making Problem

Abstract: Nash equilibrium is an important concept for studying human behavior in group decision making process. Given the complexity of finding Nash equilibria, computational tools are necessary to find them. Several programs were developed for this task. However, available programs are either not comprehensive or might be of difficult installation and handling, creating a “barrier of entry” to non-specialists. The aims of this research are twofold: (i) firstly, it was to identify and to discuss about the available programs for finding Nash equilibria; and (ii) secondly, based on the theoretical proprieties of a Nash equilibrium, to develop a program capable of finding all pure Nash equilibria in games with “n” players and “m” strategies (“n” and “m” being finite numbers) as a Macro tool for Microsoft Excel®. It is expected that the program can contributed to the area of Operations Research by providing a new tool that facilitate the use of game theory concepts within group decision-making problem-solving scenarios enabling practical applications using a widespread software.

Applied Game Theory in Business Analytics

2014 ◽  
pp. 156-167 ◽  
Author(s):  
William P. Fox
Keyword(s):  
Game Theory ◽  
Decision Making ◽  
Nash Equilibrium ◽  
Pure Strategy ◽  
Business Analytics ◽  
Competitive Situation ◽  
Present Solution ◽  
Different Types ◽  
Applied Game Theory ◽  
Decision Making Tool

In this chapter we introduce the concept of game theory and its use as a decision making tool in a competitive situation among players. We define and describe some different types of games and solution methodologies. We present the assumptions regarding these different types of game. We define and represent the different types of games between two players as either total conflict or partial conflict. We present solution techniques to both total conflict and partial conflict games. We present both pure strategy and mixed strategy solutions. We discuss the Nash equilibrium.

Problem Solving in Geometry

1972 ◽  
Vol 65 (7) ◽  
pp. 595-600
Author(s):  
Arthur A. Hiatt
Keyword(s):  
Decision Making ◽  
Problem Solving ◽  
Creative Thinking ◽  
Axiomatic Approach ◽  
Decision Making Process ◽  
Creative Problem Solving ◽  
Teaching Of Mathematics ◽  
Creative Problem

One of the most important tasks of education is to develop the decision-making process of each individual. If mathematics is to aid in this process, its presentation must elicit from the student creative, problem-solving abilities. A strictly axiomatic approach to the teaching of mathematics often stifles this creative thinking. Although axiomatics and structure are important, they are secondary considerations in problem solving.

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