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

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 Learning Deviation Payoffs in Simulation-Based Games

2019 ◽  
Vol 33 ◽  
pp. 2173-2180 ◽  
Author(s):  
Samuel Sokota ◽  
Caleb Ho ◽  
Bryce Wiedenbeck
Keyword(s):  
Neural Networks ◽  
Nash Equilibrium ◽  
Nash Equilibria ◽  
Mixed Strategy ◽  
State Of The Art ◽  
Pure Strategy ◽  
Normal Form Games ◽  
Novel Approach ◽  
Simulation Based ◽  
Expected Values

We present a novel approach for identifying approximate role-symmetric Nash equilibria in large simulation-based games. Our method uses neural networks to learn a mapping from mixed-strategy profiles to deviation payoffs—the expected values of playing pure-strategy deviations from those profiles. This learning can generalize from data about a tiny fraction of a game’s outcomes, permitting tractable analysis of exponentially large normal-form games. We give a procedure for iteratively refining the learned model with new data produced by sampling in the neighborhood of each candidate Nash equilibrium. Relative to the existing state of the art, deviation payoff learning dramatically simplifies the task of computing equilibria and more effectively addresses player asymmetries. We demonstrate empirically that deviation payoff learning identifies better approximate equilibria than previous methods and can handle more difficult settings, including games with many more players, strategies, and roles.

Quasi-Transfer Continuity and Nash Equilibrium

2019 ◽  
Vol 21 (04) ◽  
pp. 1950004
Author(s):  
Rabia Nessah ◽  
Tarik Tazdait
Keyword(s):  
Nash Equilibrium ◽  
Nash Equilibria ◽  
Existence Result ◽  
Mixed Strategy ◽  
Existence Theorems ◽  
Pure Strategy ◽  
Econ Theory ◽  
Discontinuous Games ◽  
Normal Form Games ◽  
Existence Of Equilibria

We introduce a new notion of continuity, called quasi-transfer continuity, and show that it is enough to guarantee the existence of Nash equilibria in compact, quasiconcave normal form games. This holds true in a large class of discontinuous games. We show that our result strictly generalizes the pure strategy existence theorem of Carmona [Carmona, G. [2009] An existence result for discontinuous games, J. Econ. Theory 144, 1333–1340]. We also show that our result is neither implied by nor does it imply the existence theorems of Reny [Reny, J. P. [1999] On the existence of pure and mixed strategy Nash equilibria in discontinuous games, Econometrica 67, 1029–1056] and Baye et al. [Baye, M. R., Tian, G. and Zhou, J. [1993] Characterizations of the existence of equilibria in games with discontinuous and nonquasiconcave payoffs, Rev. Econ. Studies 60, 935–948].

scholarly journals A Mixed 0-1 Linear Programming Approach to the Computation of All Pure-Strategy Nash Equilibria of a Finiten-Person Game in Normal Form

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Zhengtian Wu ◽  
Chuangyin Dang ◽  
Hamid Reza Karimi ◽  
Changan Zhu ◽  
Qing Gao
Keyword(s):  
Linear Programming ◽  
Nash Equilibrium ◽  
Normal Form ◽  
Nash Equilibria ◽  
Selection Process ◽  
Pure Strategy ◽  
Programming Approach ◽  
Main Concern ◽  
Person Game ◽  
Strategy Nash Equilibrium

A main concern in applications of game theory is how to effectively select a Nash equilibrium, especially a pure-strategy Nash equilibrium for a finiten-person game in normal form. This selection process often requires the computation of all Nash equilibria. It is well known that determining whether a finite game has a pure-strategy Nash equilibrium is an NP-hard problem and it is difficult to solve by naive enumeration algorithms. By exploiting the properties of pure strategy and multilinear terms in the payoff functions, this paper formulates a new mixed 0-1 linear program for computing all pure-strategy Nash equilibria. To our knowledge, it is the first method to formulate a mixed 0-1 linear programming for pure-strategy Nash equilibria and it may work well for similar problems. Numerical results show that the approach is effective and this method can be easily distributed in a distributed way.

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.

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