Characterization of optimal strategies in matrix games with convexity properties

2000 ◽  
Vol 29 (2) ◽  
pp. 211-227 ◽  
Author(s):  
Tadeusz Radzik
Keyword(s):  
Optimal Strategies ◽  
Matrix Games ◽  
Convexity Properties

A Combinatorial method for a class of matrix games

1966 ◽  
Vol 3 (2) ◽  
pp. 495-511
Author(s):  
Rodrigo A. Restrepo
Keyword(s):  
Optimal Strategies ◽  
Matrix Game ◽  
Combinatorial Method ◽  
Matrix Games ◽  
Finite Matrix ◽  
Special Relations ◽  
Class Of Matrices

The optimal strategies of any finite matrix game can be characterized by means of the Snow-Shapley Theorem [1]. However, in order to use this theorem to compute the optimal strategies, it may be necessary to invert a large number of matrices, most of which are not related to the solutions of the game. The present paper will show that when the columns of the pay-off matrix satisfy some special relations, it is possible to enumerate a much smaller class of matrices from which the optimal strategies may be obtained. Furthermore, the maximizing strategies that are determined by these matrices can be written down by inspection as soon as the matrices are specified.

scholarly journals A Stochastic Characterization of the Capture Zone in Pursuit-Evasion Games

Games ◽  
2020 ◽  
Vol 11 (4) ◽  
pp. 54
Author(s):  
Simone Battistini
Keyword(s):  
Optimal Strategies ◽  
Capture Zone ◽  
Pursuit Evasion ◽  
Guidance Strategies ◽  
Stochastic Characterization ◽  
Evasion Game ◽  
Multi Agent ◽  
Planning Problems ◽  
Insight Into

Pursuit-evasion games are used to define guidance strategies for multi-agent planning problems. Although optimal strategies exist for deterministic scenarios, in the case when information about the opponent players is imperfect, it is important to evaluate the effect of uncertainties on the estimated variables. This paper proposes a method to characterize the game space of a pursuit-evasion game under a stochastic perspective. The Mahalanobis distance is used as a metric to determine the levels of confidence in the estimation of the Zero Effort Miss across the capture zone. This information can be used to gain an insight into the guidance strategy. A simulation is carried out to provide numerical results.

A Stochastic Model for Service Contract

1998 ◽  
Vol 05 (01) ◽  
pp. 29-45 ◽  
Author(s):  
D. N. P. Murthy ◽  
E. Asgharizadeh
Keyword(s):  
Sensitivity Analysis ◽  
Simple Model ◽  
Single Agent ◽  
Optimal Strategies ◽  
Complete Characterization ◽  
Viable Option ◽  
Service Contract ◽  
External Agent ◽  
Maintenance Service

When it is not economical to carry out maintenance in-house, out-sourcing to an external agent is an alternate viable option. In this paper, we study a simple maintenance service contract involving a single agent (providing the maintenance service) and a single customer (owner of the equipment and recipient of the maintenance service). We develop a simple model to obtain the optimal strategies for both the customer and the agent. We give a complete characterization of the strategies along with some sensitivity analysis and discuss some extensions.

A novel method for solving constrained matrix games with fuzzy payoffs

2021 ◽  
Vol 40 (1) ◽  
pp. 191-204
Author(s):  
Tina Verma
Keyword(s):  
Mathematical Programming ◽  
Programming Problem ◽  
Complete Solution ◽  
Optimal Strategies ◽  
New Method ◽  
Mathematical Programming Problem ◽  
Expected Loss ◽  
Matrix Games ◽  
Expected Gain ◽  
Novel Method

In last few years, lots of researchers have proposed different methods to solve the constrained matrix games with fuzzy payoffs. In this paper, it has been shown that the mathematical programming problem of constrained matrix games with fuzzy payoffs, considered by researchers, is mathematically invalid and hence the method, proposed by researchers to obtain the complete solution (minimum expected gain of Player I, maximum expected loss of Player II and their corresponding optimal strategies) of constrained matrix games with fuzzy payoffs by solving the mathematical programming problem with fuzzy payoffs, are also invalid. Further, in the present paper, a new method has been proposed to find the complete solution of matrix games with fuzzy payoffs. To illustrate the proposed method, some existing numerical problems of constrained matrix games with fuzzy payoffs have been solved by the proposed method.

Game models for economic problems

2019 ◽  
Author(s):  
Виктор Невежин ◽  
Victor Nevezhin ◽  
Александр Богомолов ◽  
Aleksandr Bogomolov
Keyword(s):  
Game Theory ◽  
Strategic Behavior ◽  
Optimal Strategies ◽  
Federal State ◽  
Mixed Strategies ◽  
Mathematical Methods ◽  
Design Work ◽  
Matrix Games ◽  
Analytical Services ◽  
State Educational

The tutorial examines the theoretical and practical aspects of game theory, which are included in such studied disciplines as “Game Theory”, “Elements of Game Theory”, “Game Theory and Strategic Behavior of Firms”, “Mathematical Methods and Models of Operations Research”, etc. Examples and tasks for performing design work on topics are presented: solving matrix games in pure strategies; solving 2 × 2 matrix games in mixed strategies and modeling results; methods for solving m × n matrix games in mixed strategies; bimatrix games, games with nature, finding equilibrium and optimal strategies according to Nash and Pareto. The topics considered are accompanied by a brief theory, the solution of typical examples, as well as tasks for independent work by students. The theoretical and practical material set out in the textbook complies with the requirements of the Federal State Educational Standard of Higher Education of the last generation in the areas of training 38.03.01 and 38.04.01. The manual is intended for bachelors, masters and graduate students of economic specialties, university professors, researchers and specialists of analytical services

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