Extreme punishments characterize weak Pareto optimality

2017 ◽  
Vol 25 (1) ◽  
pp. 24-29
Author(s):  
Patrick L. Leoni
Keyword(s):  
Normal Form ◽  
Pareto Optimality ◽  
Nash Equilibria ◽  
Weak Form ◽  
Pareto Optimal ◽  
Optimal Outcome ◽  
Normal Form Games ◽  
Psychological Phenomenon ◽  
Tit For Tat ◽  
The Cost

In normal form games, we model the largely observed psychological phenomenon of systematic and extreme punishment after a deviation, regardless of the cost. After establishing basic properties, we show that this notion characterizes a weak form of Pareto optimality. Every Pareto optimal outcome can also be sustained by the threat of extreme punishment, which cannot be achieved in general through Nash equilibria strategies, nor with tit-for-tat strategies.

scholarly journals Representing pure Nash equilibria in argumentation

2021 ◽  
pp. 1-14
Author(s):  
Bruno Yun ◽  
Srdjan Vesic ◽  
Nir Oren
Keyword(s):  
Normal Form ◽  
Nash Equilibria ◽  
Pure Strategy ◽  
Normal Form Games

In this paper we describe an argumentation-based representation of normal form games, and demonstrate how argumentation can be used to compute pure strategy Nash equilibria. Our approach builds on Modgil’s Extended Argumentation Frameworks. We demonstrate its correctness, showprove several theoretical properties it satisfies, and outline how it can be used to explain why certain strategies are Nash equilibria to a non-expert human user.

Neural networks as a unifying learning model for random normal form games

2011 ◽  
Vol 19 (6) ◽  
pp. 383-408 ◽  
Author(s):  
Leonidas Spiliopoulos
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Normal Form ◽  
Human Behavior ◽  
Nash Equilibria ◽  
Human Subjects ◽  
Correlation Coefficients ◽  
Normal Form Games ◽  
The Neural Network ◽  
Iterated Dominance

This article models the learning process of a population of randomly rematched tabula rasa neural network agents playing randomly generated 3 × 3 normal form games of all strategic types. Evidence was found of the endogenous emergence of a similarity measure of games based on the number and types of Nash equilibria, and of heuristics that have been found effective in describing human behavior in experimental one-shot games. The neural network agents were found to approximate experimental human behavior very well across various dimensions such as convergence to Nash equilibria, equilibrium selection, and adherence to principles of dominance and iterated dominance. This is corroborated by evidence from five studies of experimental one-shot games, because the Spearman correlation coefficients of the probability distribution over the neural networks’ and human subjects’ actions ranged from 0.49 to 0.89.

Further results on essential Nash equilibria in normal-form games

2014 ◽  
Vol 59 (2) ◽  
pp. 277-300 ◽  
Author(s):  
Oriol Carbonell-Nicolau
Keyword(s):  
Normal Form ◽  
Nash Equilibria ◽  
Normal Form Games

scholarly journals Pareto Efficiency of Mixed Quantum Strategy Equilibria

2021 ◽  
Author(s):  
Marek Szopa
Keyword(s):  
Pareto Optimality ◽  
Nash Equilibria ◽  
Pareto Optimal ◽  
Game Of Chicken ◽  
Battle Of The Sexes ◽  
Quantum Strategy ◽  
Correlated Equilibria ◽  
Relationship Of ◽  
The Relationship ◽  
Strategy Parameters

The aim of the paper is to investigate Nash equilibria and correlated equilibria of classical and quantum games in the context of their Pareto optimality. We study four games: the prisoner's dilemma, battle of the sexes and two versions of the game of chicken. The correlated equilibria usually improve Nash equilibria of games but require a trusted correlation device. We analyze the quantum extension of these games in the Eisert-Wilkens-Lewenstein formalism with the full SU(2) space of players’ strategy parameters. It has been shown that the Nash equilibria of these games in quantum mixed Pauli strategies are closer to Pareto optimal results than their classical counterparts. The relationship of mixed Pauli strategies equilibria and correlated equilibria is also analyzed.

DYNAMIC SELECTION IN NORMAL-FORM GAMES

2006 ◽  
Vol 08 (03) ◽  
pp. 395-416 ◽  
Author(s):  
MARC MEERTENS ◽  
JOS POTTERS ◽  
HANS REIJNIERSE
Keyword(s):  
Normal Form ◽  
Nash Equilibria ◽  
Potential Game ◽  
Asymptotically Stable ◽  
Connected Component ◽  
Von Neumann ◽  
Dynamic Selection ◽  
Normal Form Games ◽  
Selection Processes ◽  
Zero Sum

This paper investigates a class of dynamic selection processes for n-person normal-form games which includes the Brown-von Neumann-Nash dynamics. For (two-person) zero-sum games and for (n-person) potential games every limit set of these dynamics is a subset of the set of Nash-equilibria. Furthermore, under these dynamics the unique Nash-component of a zero-sum game is minimal asymptotically stable and for a potential game a smoothly connected component which is a local maximizer is minimal asymptotically stable.

A Theory of Patronized Goods: Inefficient and Efficient Equilibria

2011 ◽  
pp. 65-87 ◽  
Author(s):  
A. Rubinstein
Keyword(s):  
Nash Equilibrium ◽  
Social Policy ◽  
Nash Equilibria ◽  
Institutional Environment ◽  
Social Motivation ◽  
Pareto Optimal ◽  
Market Failures ◽  
Equilibrium Conditions ◽  
Policy Issues

The article considers some aspects of the patronized goods theory with respect to efficient and inefficient equilibria. The author analyzes specific features of patronized goods as well as their connection with market failures, and conjectures that they are related to the emergence of Pareto-inefficient Nash equilibria. The key problem is the analysis of the opportunities for transforming inefficient Nash equilibrium into Pareto-optimal Nash equilibrium for patronized goods by modifying the institutional environment. The paper analyzes social motivation for institutional modernization and equilibrium conditions in the generalized Wicksell-Lindahl model for patronized goods. The author also considers some applications of patronized goods theory to social policy issues.

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