scholarly journals The Superiority of Quantum Strategy in 3-Player Prisoner’s Dilemma

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1443
Author(s):  
Zhiyuan Dong ◽  
Ai-Guo Wu
Keyword(s):  
Game Theory ◽  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Quantum Game ◽  
Final State ◽  
The Game Theory ◽  
Initial States ◽  
Quantum Strategy ◽  
Selection Of

In this paper, we extend the quantum game theory of Prisoner’s Dilemma to the N-player case. The final state of quantum game theory of N-player Prisoner’s Dilemma is derived, which can be used to investigate the payoff of each player. As demonstration, two cases (2-player and 3-player) are studied to illustrate the superiority of quantum strategy in the game theory. Specifically, the non-unique entanglement parameter is found to maximize the total payoff, which oscillates periodically. Finally, the optimal strategic set is proved to depend on the selection of initial states.

scholarly journals Cooperative n-person Prisoner's Dilemma on a Network

2021 ◽  
Vol 14 ◽  
pp. 122-126
Author(s):  
Aleksandra L. Grinikh ◽  
◽  
Leon A. Petrosyan ◽  
Keyword(s):  
Game Theory ◽  
Cooperative Game ◽  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Pairwise Interaction ◽  
Network Interaction ◽  
The Game Theory

In the paper n-person prisoner's dilemma on the network is investigated. A cooperative game with the pairwise interaction of players is constructed. The model is a modification of the classic 2-person prisoner's dilemma problem in the game theory. Network interaction provide an ability to take into account the in uence only to the adjacent players from the whole set of players. The feature of the game is found that allows to make a decision about necessity of playing dominated strategy by a few players. This solution is based on the number of the adjacent players. The work is a continuation of the paper published earlier by Grinikh A.L. and Petrosyan L.A. in 2021.

The Social Contract in Leviathan and the Prisoner's Dilemma Supergame

1981 ◽  
Vol 29 (3) ◽  
pp. 339-351 ◽  
Author(s):  
Iain McLean
Keyword(s):  
Game Theory ◽  
Social Contract ◽  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
The State ◽  
Theory Approach ◽  
Prisoner’S Dilemma Game ◽  
State Of Nature ◽  
The Social ◽  
The Game Theory

The familiar problem of whether Hobbesian men in the state of nature would ever abide by an agreement to obey a Sovereign is a version of the puzzle now known as ‘Prisoner's Dilemma’. The present paper has the following aims: (1) To establish that the game-theory approach is a legitimate way to study Hobbes. (2) To see whether a proposed ‘solution’ to the paradox of Prisoner's Dilemma applies to this example. The paradox is that individually rational self-interested calculations sum to an outcome that is suboptimal not only for society but also for every single member of it. The solution is the Supergame which consists of indefinitely repeated plays of the simple Prisoner's Dilemma game. (3) To compare the results of the above with the similar conclusions reached by a different route by recent arguments in sociobiology.

scholarly journals PLAYING PRISONER'S DILEMMA WITH QUANTUM RULES

2002 ◽  
Vol 02 (04) ◽  
pp. R189-R203 ◽  
Author(s):  
JIANGFENG DU ◽  
XIAODONG XU ◽  
HUI LI ◽  
XIANYI ZHOU ◽  
RONGDIAN HAN
Keyword(s):  
Game Theory ◽  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Quantum Game ◽  
Quantum Games ◽  
Physical Research ◽  
Strategic Space

Quantum game theory is a recently developing field of physical research. In this paper, we investigate quantum games in a systematic way. With the famous instance of the Prisoner's Dilemma, we present the fascinating properties of quantum games in different conditions, i.e. different number of the players, different strategic space of the players and different amount of the entanglement involved.

A Game Research on the Integration between Xi’an and Xian Yang

2011 ◽  
Vol 368-373 ◽  
pp. 1763-1766
Author(s):  
Jing Zhu ◽  
Pei Zhang ◽  
Hai Jun Sun
Keyword(s):  
Game Theory ◽  
European Union ◽  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Game Model ◽  
The European Union ◽  
Strategic Option ◽  
Two Cities ◽  
The Game Theory ◽  
Angle Of View

The prisoner’s dilemma is applied to make the new game model between Xi’an and Xian Yang from Game Theory angle of view. In this new model, the profits inequality is taken into account when both sides face the same strategic option, which can make the model to approach more actual situations. The prisoner’s dilemma is the main handicap. Furthermore, the author built the interpretation framework of the two cities’ integration on the basis of the Game Theory and the inspirations of the European Union benefits gained by its members.

The Prisoner's Dilemma Game and Cooperation in the Rat

1984 ◽  
Vol 55 (3) ◽  
pp. 687-696 ◽  
Author(s):  
Rick M. Gardner ◽  
Terry L. Corbin ◽  
Janelle S. Beltramo ◽  
Gary S. Nickell
Keyword(s):  
Game Theory ◽  
Visual Communication ◽  
Prisoner's Dilemma ◽  
Human Subjects ◽  
Cooperative Behavior ◽  
Prisoner’S Dilemma ◽  
The Other ◽  
Prisoner’S Dilemma Game ◽  
Prisoner's Dilemma Game ◽  
Cooperative Behaviors

Cooperation in pairs of rats playing the prisoner's dilemma game was investigated. Six pairs of animals were taught to make either cooperative or uncooperative responses by running to one or the other end of a T-maze. Two T-mazes were joined together such that animals could respond simultaneously. Animals were run under conditions in which visual communication was present and absent. Mutually uncooperative responses were the most common and mutually cooperative behaviors the least preferred. Introduction of a barrier between the mazes, which removed visual communication between pairs, sharply accentuated uncooperative behavior. Similarities of the present findings to results with human subjects and the implications of using game theory for studying cooperative behavior in animals are discussed.

Designing Practices, Institutions, and Processes

2018 ◽  
pp. 193-220
Author(s):  
Barry Hoffmaster ◽  
Cliff Hooker
Keyword(s):  
Game Theory ◽  
Prisoner's Dilemma ◽  
Institutional Design ◽  
Prisoner’S Dilemma ◽  
The Third ◽  
Ethical Design ◽  
Design Solutions

Ethics is embedded in the practices and institutions of society. Three examples illustrate the communal importance of ethical design. First is the distinction between Fights, Games, and Debates as successively more ethical and more intelligent institutional designs for handling conflict. The second is the Prisoner’s Dilemma in game theory, whose best solution is to step outside the game and change the surrounding institutional design. The third is an account of the ethical and effective institutional design solutions for various situations, especially of mediation for those that invoke the notion of ‘polycentric’ problems.

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