scholarly journals Discovering theorems in game theory: Two-person games with unique pure Nash equilibrium payoffs

2011 ◽  
Vol 175 (14-15) ◽  
pp. 2010-2020 ◽  
Author(s):  
Pingzhong Tang ◽  
Fangzhen Lin
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Pure Nash Equilibrium

scholarly journals Holding a group together: non-game-theory vs. game-theory

2021 ◽  
Author(s):  
Michael Richter ◽  
Ariel Rubinstein
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Competitive Equilibrium ◽  
Solution Concept ◽  
Equilibrium Concept

Abstract Each member of a group chooses a position and has preferences regarding his chosen position. The group’s harmony depends on the profile of chosen positions meeting a specific condition. We analyse a solution concept (Richter and Rubinstein, 2020) based on a permissible set of individual positions, which plays a role analogous to that of prices in competitive equilibrium. Given the permissible set, members choose their most preferred position. The set is tightened if the chosen positions are inharmonious and relaxed if the restrictions are unnecessary. This new equilibrium concept yields more attractive outcomes than does Nash equilibrium in the corresponding game.

scholarly journals Quantum Mean-Field Games with the Observations of Counting Type

Games ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 7
Author(s):  
Vassili N. Kolokoltsov
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Open Problem ◽  
Existence And Uniqueness ◽  
Existence Of Solutions ◽  
Mean Field ◽  
Mean Field Games ◽  
Quantum Game ◽  
Quantum Games ◽  
Interesting Open Problem

Quantum games and mean-field games (MFG) represent two important new branches of game theory. In a recent paper the author developed quantum MFGs merging these two branches. These quantum MFGs were based on the theory of continuous quantum observations and filtering of diffusive type. In the present paper we develop the analogous quantum MFG theory based on continuous quantum observations and filtering of counting type. However, proving existence and uniqueness of the solutions for resulting limiting forward-backward system based on jump-type processes on manifolds seems to be more complicated than for diffusions. In this paper we only prove that if a solution exists, then it gives an ϵ-Nash equilibrium for the corresponding N-player quantum game. The existence of solutions is suggested as an interesting open problem.

Research on the Connection between Game Theory and Cryptography

2021 ◽  
Author(s):  
S M Nazmuz Sakib
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Operation Condition ◽  
Message Transmission ◽  
State Of Affairs ◽  
Multiparty Interaction

As may be seen, cryptography and game theory are the 2 primary parts of the phrase. game theory thinks about with optimizing a result involving 2 or a lot of well-defined parties, every with well-defined behavior. Nash equilibrium could be a notion in game theory that emphasizes the participants' mutual profit. , the unpredictability of the operational state of affairs, don't seem to be laid out in game theory. The goal of cryptography is to produce safe message transmission between genuine and approved parties. Multiparty computing could be a cryptographical technique that enables 2 or a lot of participants to calculate a perform conjointly. this can be kind of like the concept of reciprocal profit in game theory. throughout the employment of the protocol, all parties have a precise set of behavior determined, kind of like game theory. The parties, as an example, a probabilistic polynomials in nature. Cryptography doesn't specify however AN assailant could use it to breach the system just like the operation condition. In cryptography, multiparty interaction is outlined as parties communication to judge a perform on their inputs.

Bayesian Rationality and Social Epistemology

2014 ◽  
Author(s):  
Herbert Gintis
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Social Norms ◽  
Social Epistemology ◽  
Correlated Equilibrium ◽  
Epistemic Game Theory ◽  
Famous Theorem ◽  
Rational Agents ◽  
Natural Equilibrium ◽  
Bayesian Rationality

This chapter uses epistemic game theory to expand on the notion of social norms as choreographer of a correlated equilibrium, and to elucidate the socio-psychological prerequisites for the notion that social norms implement correlated equilibria. The correlated equilibrium is a much more natural equilibrium criterion than the Nash equilibrium, because of a famous theorem of Aumann (1987), who showed that Bayesian rational agents in an epistemic game G with a common subjective prior play a correlated equilibrium of G. Thus, while rationality and common priors do not imply Nash equilibrium, these assumptions do imply correlated equilibrium and social norms act not only as choreographer, but also supply the epistemic conditions for common priors.

scholarly journals Over-supply in Public Transportation: Case Study of Bus and Metro Lines in Harbin City, China

2016 ◽  
Vol 28 (5) ◽  
pp. 471-477
Author(s):  
Shumin Feng ◽  
Xianghao Shen ◽  
Baoyu Hu
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Public Transportation ◽  
Operation Mode ◽  
Utility Model ◽  
Coordinated Development ◽  
Supply Problem ◽  
Harbin City ◽  
Fundamental Reason

As the two most important modes in public transportation, the coordinated development of bus and metro networks significantly influences the efficiency of public transportation. However, two parallel bus and metro lines belonging to different operators may lead to supply competition and consequently yield over-supply. Taking two parallel bus and metro lines in Harbin city, China as a case study, this paper, drawing on game theory, establishes a utility model based on the two lines’ frequencies, and reveals and explains the fundamental reason for the over-supply problem using a Nash equilibrium. In an attempt to resolve this issue, the study proposes a new operation mode: integrating frequencies of the two modes to obtain larger total profits then reallocating the total profits to the two modes. The case study shows that this new operation mode can effectively solve the over-supply problem while satisfying both operators of the two modes, and hence having practical value.

scholarly journals Nash versus coarse correlation

2020 ◽  
Vol 23 (4) ◽  
pp. 1178-1204 ◽  
Author(s):  
Konstantinos Georgalos ◽  
Indrajit Ray ◽  
Sonali SenGupta
Keyword(s):  
Nash Equilibrium ◽  
Correlated Equilibrium ◽  
Individual Choice ◽  
Pure Nash Equilibrium ◽  
Expected Payoff ◽  
Equilibrium Payoff ◽  
Payoff Dominance ◽  
Dominated Strategies ◽  
Person Game ◽  
Nash Point

Abstract We run a laboratory experiment to test the concept of coarse correlated equilibrium (Moulin and Vial in Int J Game Theory 7:201–221, 1978), with a two-person game with unique pure Nash equilibrium which is also the solution of iterative elimination of strictly dominated strategies. The subjects are asked to commit to a device that randomly picks one of three symmetric outcomes (including the Nash point) with higher ex-ante expected payoff than the Nash equilibrium payoff. We find that the subjects do not accept this lottery (which is a coarse correlated equilibrium); instead, they choose to play the game and coordinate on the Nash equilibrium. However, given an individual choice between a lottery with equal probabilities of the same outcomes and the sure payoff as in the Nash point, the lottery is chosen by the subjects. This result is robust against a few variations. We explain our result as selecting risk-dominance over payoff dominance in equilibrium.

EXISTENCE AND UNIQUENESS OF EQUILIBRIUM IN ASYMMETRIC CONTESTS WITH ENDOGENOUS PRIZES

2013 ◽  
Vol 15 (01) ◽  
pp. 1350005 ◽  
Author(s):  
SHUMEI HIRAI ◽  
FERENC SZIDAROVSZKY
Keyword(s):  
Nash Equilibrium ◽  
Existence And Uniqueness ◽  
Financial Constraints ◽  
Pure Nash Equilibrium ◽  
Asymmetric Contests ◽  
Uniqueness Of Equilibrium

This paper considers contests in which the efforts of the players determine the value of the prize. Players may have different valuations of the prize and different abilities to convert expenditures to productive efforts. In addition, players may face different financial constraints. This paper presents a proof for the existence and uniqueness of a pure Nash equilibrium in asymmetric contests with endogenous prizes.

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