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 The Frequency of Convergent Games under Best-Response Dynamics

2021 ◽  
Author(s):  
Samuel C. Wiese ◽  
Torsten Heinrich
Keyword(s):  
Nash Equilibrium ◽  
Nash Equilibria ◽  
Pure Strategy ◽  
Response Dynamics ◽  
Novel Approach ◽  
Best Response ◽  
Random Games ◽  
Payoff Matrices ◽  
Best Response Dynamic ◽  
Strategy Nash Equilibrium

AbstractWe calculate the frequency of games with a unique pure strategy Nash equilibrium in the ensemble of n-player, m-strategy normal-form games. To obtain the ensemble, we generate payoff matrices at random. Games with a unique pure strategy Nash equilibrium converge to the Nash equilibrium. We then consider a wider class of games that converge under a best-response dynamic, in which each player chooses their optimal pure strategy successively. We show that the frequency of convergent games with a given number of pure Nash equilibria goes to zero as the number of players or the number of strategies goes to infinity. In the 2-player case, we show that for large games with at least 10 strategies, convergent games with multiple pure strategy Nash equilibria are more likely than games with a unique Nash equilibrium. Our novel approach uses an n-partite graph to describe games.

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.

On the Foundations of Nash Equilibrium

1996 ◽  
Vol 12 (1) ◽  
pp. 67-88 ◽  
Author(s):  
Hans Jørgen Jacobsen
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Cooperative Game Theory ◽  
Mixed Strategy ◽  
Pure Strategy ◽  
Mixed Strategies ◽  
Positive Theory ◽  
Equilibrium Concept ◽  
Strategy Equilibrium ◽  
Pure Strategies

The most important analytical tool in non-cooperative game theory is the concept of a Nash equilibrium, which is a collection of possibly mixed strategies, one for each player, with the property that each player's strategy is a best reply to the strategies of the other players. If we do not go into normative game theory, which concerns itself with the recommendation of strategies, and focus instead entirely on the positive theory of prediction, two alternative interpretations of the Nash equilibrium concept are predominantly available.In the more traditional one, a Nash equilibrium is a prediction of actual play. A game may not have a Nash equilibrium in pure strategies, and a mixed strategy equilibrium may be difficult to incorporate into this interpretation if it involves the idea of actual randomization over equally good pure strategies. In another interpretation originating from Harsanyi (1973a), see also Rubinstein (1991), and Aumann and Brandenburger (1991), a Nash equilibrium is a ‘consistent’ collection of probabilistic expectations, conjectures, on the players. It is consistent in the sense that for each player each pure strategy, which has positive probability according to the conjecture about that player, is indeed a best reply to the conjectures about others.

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.

scholarly journals Non-decreasing Payment Rules for Combinatorial Auctions

2018 ◽  
Author(s):  
Vitor Bosshard ◽  
Ye Wang ◽  
Sven Seuken
Keyword(s):  
Nash Equilibrium ◽  
Nash Equilibria ◽  
State Of The Art ◽  
Combinatorial Auctions ◽  
Desirable Property ◽  
Limited Success ◽  
Multiple Orders ◽  
Auction Game

Combinatorial auctions are used to allocate resources in domains where bidders have complex preferences over bundles of goods. However, the behavior of bidders under different payment rules is not well understood, and there has been limited success in finding Bayes-Nash equilibria of such auctions due to the computational difficulties involved. In this paper, we introduce non-decreasing payment rules. Under such a rule, the payment of a bidder cannot decrease when he increases his bid, which is a natural and desirable property. VCG-nearest, the payment rule most commonly used in practice, violates this property and can thus be manipulated in surprising ways. In contrast, we show that many other payment rules are non-decreasing. We also show that a non-decreasing payment rule imposes a structure on the auction game that enables us to search for an approximate Bayes-Nash equilibrium much more efficiently than in the general case. Finally, we introduce the utility planes BNE algorithm, which exploits this structure and outperforms a state-of-the-art algorithm by multiple orders of magnitude.

scholarly journals Invariant Representations through Adversarial Forgetting

2020 ◽  
Vol 34 (04) ◽  
pp. 4272-4279
Author(s):  
Ayush Jaiswal ◽  
Daniel Moyer ◽  
Greg Ver Steeg ◽  
Wael AbdAlmageed ◽  
Premkumar Natarajan
Keyword(s):  
Neural Networks ◽  
Deep Neural Networks ◽  
State Of The Art ◽  
Empirical Results ◽  
Information Bottleneck ◽  
Novel Approach ◽  
Adversarial Training ◽  
Invariant Representations ◽  
Art Performance ◽  
Forgetting Mechanism

We propose a novel approach to achieving invariance for deep neural networks in the form of inducing amnesia to unwanted factors of data through a new adversarial forgetting mechanism. We show that the forgetting mechanism serves as an information-bottleneck, which is manipulated by the adversarial training to learn invariance to unwanted factors. Empirical results show that the proposed framework achieves state-of-the-art performance at learning invariance in both nuisance and bias settings on a diverse collection of datasets and tasks.

scholarly journals ECG Denoising Using Artificial Neural Networks and Complete Ensemble Empirical Mode Decomposition

2021 ◽  
Vol 12 (2) ◽  
pp. 2382-2389
Author(s):  
Rajesh Birok, Et. al.
Keyword(s):  
Neural Networks ◽  
Empirical Mode Decomposition ◽  
State Of The Art ◽  
Signal To Noise Ratio ◽  
Low Frequency ◽  
Ensemble Empirical Mode Decomposition ◽  
Novel Approach ◽  
Mode Decomposition ◽  
The Neural Network ◽  
Art Methods

Electrocardiogram (ECG) is a documentation of the electrical activities of the heart. It is used to identify a number of cardiac faults such as arrhythmias, AF etc.  Quite often the ECG gets corrupted by various kinds of artifacts, thus in order to gain correct information from them, they must first be denoised. This paper presents a novel approach for the filtering of low frequency artifacts of ECG signals by using Complete Ensemble Empirical Mode Decomposition (CEED) and Neural Networks, which removes most of the constituent noise while assuring no loss of information in terms of the morphology of the ECG signal. The contribution of the method lies in the fact that it combines the advantages of both EEMD and ANN. The use of CEEMD ensures that the Neural Network does not get over fitted. It also significantly helps in building better predictors at individual frequency levels. The proposed method is compared with other state-of-the-art methods in terms of Mean Square Error (MSE), Signal to Noise Ratio (SNR) and Correlation Coefficient. The results show that the proposed method has better performance as compared to other state-of-the-art methods for low frequency artifacts removal from EEG.  

Nash Equilibrium in Discontinuous Games

2020 ◽  
Vol 12 (1) ◽  
pp. 439-470
Author(s):  
Philip J. Reny
Keyword(s):  
Nash Equilibrium ◽  
Nash Equilibria ◽  
Mixed Strategy ◽  
Discontinuous Games ◽  
Bayesian Games ◽  
Sharp Focus

We review the discontinuous games literature, with a sharp focus on conditions that ensure the existence of pure and mixed strategy Nash equilibria in strategic form games and of Bayes-Nash equilibria in Bayesian games.

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