Determination of equilibrium points in non-zero sum non-cooperative games†

1975 ◽  
Vol 6 (1) ◽  
pp. 67-80
Author(s):  
RANGASWAMY MUKUNDAN ◽  
RANGASAMI L. KASHYAP
Keyword(s):  
Cooperative Games ◽  
Equilibrium Points ◽  
Zero Sum ◽  
Non Cooperative Games

scholarly journals A computational model of outguessing in two-player non-cooperative games

2014 ◽  
Vol 6 (1) ◽  
pp. 71-88
Author(s):  
Tamás László Balogh ◽  
János Kormos
Keyword(s):  
Numerical Simulation ◽  
Computational Model ◽  
Cooperative Games ◽  
Behavioral Game Theory ◽  
Equilibrium Concept ◽  
Zero Sum Games ◽  
Simulation Based ◽  
Behavioral Game ◽  
Zero Sum ◽  
Non Cooperative Games

Abstract Several behavioral game theory models aim at explaining why “smarter“ people win more frequently in simultaneous zero-sum games, a phanomenon, which is not explained by the Nash equilibrium concept. We use a computational model and a numerical simulation based on Markov chains to describe player behavior and predict payoffs.

scholarly journals Ergodic and thermodynamic games

2016 ◽  
Vol 16 (02) ◽  
pp. 1660008 ◽  
Author(s):  
Rafael Rigão Souza
Keyword(s):  
Nash Equilibrium ◽  
Cooperative Games ◽  
Invariant Measures ◽  
Equilibrium Points ◽  
Thermodynamic Formalism ◽  
Usual Sense ◽  
Compact Sets ◽  
Nash Equilibrium Points ◽  
Ergodic Optimization ◽  
Non Cooperative Games

Let [Formula: see text] and [Formula: see text] be compact sets, and [Formula: see text], [Formula: see text] be continuous maps. Let [Formula: see text] where [Formula: see text] is [Formula: see text]-invariant and [Formula: see text] is [Formula: see text]-invariant, be payoff functions for a game (in the usual sense of game theory) between players that have the set of invariant measures for [Formula: see text] (player 1) and [Formula: see text] (player 2) as possible strategies. Our goal here is to establish the notion of Nash equilibrium for the game defined by these payoffs and strategies. The main tools come from ergodic optimization (as we are optimizing over the set of invariant measures) and thermodynamic formalism (when we add to the integrals above the entropy of measures in order to define a second case to be explored). Both cases are ergodic versions of non-cooperative games. We show the existence of Nash equilibrium points with two independent arguments. One of the arguments deals with the case with entropy, and uses only tools of thermodynamical formalism, while the other, that works in the case without entropy but can be adapted to deal with both cases, uses the Kakutani fixed point. We also present examples and briefly discuss uniqueness (or lack of uniqueness). In the end, we present a different example where players are allowed to collaborate. This final example shows connections between cooperative games and ergodic transport.

Evaluation of Non-Cooperative Games as a Tool for Analyzing Political and Policy Behaviors

2001 ◽  
Vol 16 (1) ◽  
pp. 65-73
Author(s):  
Sung-bok Park
Keyword(s):  
Public Administration ◽  
Cooperative Game ◽  
Cooperative Games ◽  
Actual Behavior ◽  
Extensive Form ◽  
Collective Action Problem ◽  
The Public ◽  
Zero Sum ◽  
Non Cooperative Games ◽  
Existence Of Equilibria

This study evaluates the limitations and relevance of non-cooperative games as a tool for analyzing political and policy behavior. It aims to answer the questions, “for what situations are such non-cooperative games appropriate, and for what do they fail to predict actual behavior?” To answer these questions, we are going to look into the assumptions underlying the existence of equilibria developed by this non-cooperative game model. This model uses two types of situations: extensive form and normal form. Each of them is evaluated in terms of its underlying assumptions and their relevance to real behaviors in the public sector. The several theorems concerning non-cooperative game are introduced and evaluated in terms of its meaning and relevance to the real public arena. In particular, we see that the zero sum assumption is a restriction that precludes modeling many other situations central to politics and public administration, and that the prisoner dilemma models important processes, including collective action problem.

Equilibrium Points for Open Acyclic Relations

1967 ◽  
Vol 19 ◽  
pp. 366-369 ◽  
Author(s):  
Bezalel Peleg
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Cooperative Games ◽  
Equilibrium Points ◽  
Real Functions ◽  
Disjoint Sets ◽  
Image Position ◽  
Non Cooperative Games

A formulation of a fixed point theorem, which can be applied conveniently to non-cooperative games and cooperative games, is suggested in this note.Let N1, … , Nm be m non-empty, finite disjoint sets. For k = 1, … , m we denote by Sk the simplex the coordinates of whose points are indexed by the members of Nk; thus Sk is the collection of all real functions xk defined on Nk which satisfy:1.11.2

Mathematical views of the fractional Chua's electrical circuit described by the Caputo-Liouville derivative

2021 ◽  
Vol 67 (1 Jan-Feb) ◽  
pp. 91
Author(s):  
N. Sene
Keyword(s):  
Caputo Derivative ◽  
Local Stability ◽  
Numerical Scheme ◽  
Equilibrium Points ◽  
Electrical Circuit ◽  
Maximal Lyapunov Exponent ◽  
Electrical Circuits ◽  
Adaptive Controls ◽  
Liouville Derivative

This paper revisits Chua's electrical circuit in the context of the Caputo derivative. We introduce the Caputo derivative into the modeling of the electrical circuit. The solutions of the new model are proposed using numerical discretizations. The discretizations use the numerical scheme of the Riemann-Liouville integral. We have determined the equilibrium points and study their local stability. The existence of the chaotic behaviors with the used fractional-order has been characterized by the determination of the maximal Lyapunov exponent value. The variations of the parameters of the model into the Chua's electrical circuit have been quantified using the bifurcation concept. We also propose adaptive controls under which the master and the slave fractional Chua's electrical circuits go in the same way. The graphical representations have supported all the main results of the paper.

scholarly journals Weak Berge Equilibrium in Finite Three-person Games: Conception and Computation

2020 ◽  
Vol 11 (1) ◽  
pp. 127-134
Author(s):  
Konstantin Kudryavtsev ◽  
Ustav Malkov
Keyword(s):  
Cooperative Games ◽  
Hippocratic Oath ◽  
The Other ◽  
Mixed Strategies ◽  
Finite Games ◽  
Moral Basis ◽  
Other Hand ◽  
Berge Equilibrium ◽  
Do No Harm ◽  
Non Cooperative Games

AbstractThe paper proposes the concept of a weak Berge equilibrium. Unlike the Berge equilibrium, the moral basis of this equilibrium is the Hippocratic Oath “First do no harm”. On the other hand, any Berge equilibrium is a weak Berge equilibrium. But, there are weak Berge equilibria, which are not the Berge equilibria. The properties of the weak Berge equilibrium have been investigated. The existence of the weak Berge equilibrium in mixed strategies has been established for finite games. The weak Berge equilibria for finite three-person non-cooperative games are computed.

scholarly journals A Control Based Mathematical Model for the Evaluation of Intervention Lines in COVID-19 Epidemic Spread: The Italian Case Study

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 890
Author(s):  
Paolo Di Giamberardino ◽  
Rita Caldarella ◽  
Daniela Iacoviello
Keyword(s):  
Mathematical Model ◽  
Equilibrium Points ◽  
Italian Case ◽  
Control Actions ◽  
Containment Measures ◽  
Asymptomatic Subjects ◽  
The Impact

This paper addresses the problem of describing the spread of COVID-19 by a mathematical model introducing all the possible control actions as prevention (informative campaign, use of masks, social distancing, vaccination) and medication. The model adopted is similar to SEIQR, with the infected patients split into groups of asymptomatic subjects and isolated ones. This distinction is particularly important in the current pandemic, due to the fundamental the role of asymptomatic subjects in the virus diffusion. The influence of the control actions is considered in analysing the model, from the calculus of the equilibrium points to the determination of the reproduction number. This choice is motivated by the fact that the available organised data have been collected since from the end of February 2020, and almost simultaneously containment measures, increasing in typology and effectiveness, have been applied. The characteristics of COVID-19, not fully understood yet, suggest an asymmetric diffusion among countries and among categories of subjects. Referring to the Italian situation, the containment measures, as applied by the population, have been identified, showing their relation with the government's decisions; this allows the study of possible scenarios, comparing the impact of different possible choices.

A positive approach to non-cooperative games

1986 ◽  
Vol 7 (3) ◽  
pp. 235-251 ◽  
Author(s):  
James W. Friedman ◽  
Robert W. Rosenthal
Keyword(s):  
Cooperative Games ◽  
Positive Approach ◽  
Non Cooperative Games
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