scholarly journals Memory-two zero-determinant strategies in repeated games

2021 ◽  
Vol 8 (5) ◽  
pp. 202186
Author(s):  
Masahiko Ueda
Keyword(s):  
Game Theory ◽  
Evolutionary Game Theory ◽  
Repeated Games ◽  
Prisoner's Dilemma ◽  
Evolutionary Game ◽  
Prisoner’S Dilemma ◽  
Mutual Cooperation ◽  
Linear Relationships ◽  
Previous Round ◽  
Tit For Tat

Repeated games have provided an explanation of how mutual cooperation can be achieved even if defection is more favourable in a one-shot game in the Prisoner’s Dilemma situation. Recently found zero-determinant (ZD) strategies have substantially been investigated in evolutionary game theory. The original memory-one ZD strategies unilaterally enforce linear relationships between average pay-offs of players. Here, we extend the concept of ZD strategies to memory-two strategies in repeated games. Memory-two ZD strategies unilaterally enforce linear relationships between correlation functions of pay-offs and pay-offs of the previous round. Examples of memory-two ZD strategy in the repeated Prisoner’s Dilemma game are provided, some of which generalize the tit-for-tat strategy to a memory-two case. Extension of ZD strategies to memory- n case with n ≥ ̃2 is also straightforward.

scholarly journals Collective Strategies With a Master-Slave Mechanism Dominate in Spatial-Iterated Prisoner's Dilemma

2021 ◽  
Vol 12 (4) ◽  
pp. 45-56
Author(s):  
Jiawei Li ◽  
Robert Duncan ◽  
Jingpeng Li ◽  
Ruibin Bai
Keyword(s):  
Evolutionary Game Theory ◽  
Prisoner's Dilemma ◽  
Evolutionary Game ◽  
Prisoner’S Dilemma ◽  
Fundamental Question ◽  
Iterated Prisoner's Dilemma ◽  
Tit For Tat ◽  
And Performance ◽  
Selfish Agents ◽  
Iterated Prisoner’S Dilemma

How cooperation emerges and persists in a population of selfish agents is a fundamental question in evolutionary game theory. The research shows that collective strategies with master-slave mechanism (CSMSM) defeat tit-for-tat and other well-known strategies in spatial iterated prisoner's dilemma. A CSMSM identifies kin members by means of a handshaking mechanism. If the opponent is identified as non-kin, a CSMSM will always defect. Once two CSMSMs meet, they play master and slave roles. A mater defects and a slave cooperates in order to maximize the master's payoff. CSMSM outperforms non-collective strategies in spatial IPD even if there is only a small cluster of CSMSMs in the population. The existence and performance of CSMSM in spatial iterated prisoner's dilemma suggests that cooperation first appears and persists in a group of collective agents.

Game Theory

2016 ◽  
Author(s):  
Cristina Bicchieri ◽  
Giacomo Sillari
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Evolutionary Game Theory ◽  
Repeated Games ◽  
Evolutionary Game ◽  
Complete Information ◽  
Decision Makers ◽  
Correlated Equilibrium ◽  
Extensive Form

Game theory aims to understand situations in which decision-makers interact strategically. Chess is an example, as are firms competing for business, politicians competing for votes, animals fighting over prey, bidders competing in auctions, threats and punishments in long-term relationships, and so on. In such situations, the outcome depends on what the parties do jointly. Decision-makers may be people, organizations, animals, or even genes. In this chapter, the authors review fundamental notions of game theory and their application to philosophy of science. In particular, Section 1 looks at games of complete information through normal and extensive form representations, introduce the notion of Nash equilibrium and its refinements. Section 2 touches on epistemic foundations and correlated equilibrium, and Section 3 examines repeated games and their importance for the analysis of altruism and cooperation. Section 4 deals with evolutionary game theory.

TWO-STEP "WIN-STAY, LOSE-SHIFT" AND LEARNING TO COOPERATE IN THE REPEATED PRISONER'S DILEMMA

2010 ◽  
Vol 12 (04) ◽  
pp. 437-451
Author(s):  
ARKADY KRYAZHIMSKIY
Keyword(s):  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Small Degree ◽  
Prisoner’S Dilemma Game ◽  
Mutual Cooperation ◽  
Shift Behavior ◽  
Previous Round ◽  
Repeated Prisoner’S Dilemma ◽  
Prisoner's Dilemma Game ◽  
Repeated Prisoner's Dilemma

The standard win-stay, lose-shift behavior strategy in the repeated Prisoner's Dilemma game prescribes the players that win and lose in a current game round to keep and to change, respectively, their current actions, in the next round. Winning and losing are understood as receiving one of two upper values and one of two lower values, respectively, among the four admissible values for the players' benefits. In particular, a player acting as a cooperator against cooperation wins and therefore is not allowed to switch to defection in the next round with a hope to gain more (provided his/her rival keeps cooperating). This constraint can be viewed as too strong for a selfish player. Here, we discuss a two-step win-stay, lose-shift behavior that differs from the traditional win-stay lose-shift one in understanding of winning and losing. A player wins if his/her benefit is no smaller that in the previous round, and loses otherwise. This pattern is in a sense more selfish; in particular, a switch from cooperation (against cooperation) to defection is not forbidden. Another confirmation of a more selfish character of the two-step win-stay, lose-shift behavior, compared to the standard win-stay, lose-shift one, is that the former does not bring two individuals playing the repeated Prisoner's Dilemma game to mutual cooperation. In this paper, our goal is to understand to what degree one can relax the two-step win-stay, lose-shift behavior in selfishness so as to reach mutual cooperation, anyway. We deal with two models of the repeated Prisoner's Dilemma game — a game of two individuals and a game in a group of players. In the game of two individuals, a relaxed two-step win-stay, lose-shift behavior assumes that the players use mixed strategies; here, relaxation is associated with patience. In the game in a group of players, relaxation is achieved through conformity, a tendency to join the majority. We show that even a small degree of conformity is enough to teach a two-step win-stay, lose-shift group to cooperate.

scholarly journals Behavioral Theory of Repeated Prisoner’s Dilemma: Generous Tit-For-Tat Strategy

2019 ◽  
Vol 20 (1) ◽  
Author(s):  
Hitoshi Matsushima
Keyword(s):  
Repeated Games ◽  
Prisoner's Dilemma ◽  
Social Preference ◽  
Prisoner’S Dilemma ◽  
Self Interest ◽  
Additive Separability ◽  
Tit For Tat ◽  
Strategic Complexity ◽  
Infinitely Repeated Games ◽  
Psychological Mood

AbstractThis study investigates infinitely repeated games of a prisoner’s dilemma with additive separability in which the monitoring technology is imperfect and private. Behavioral incentives indicate that a player is not only motivated by pure self-interest but also by social preference such as reciprocity, and that a player often becomes naïve and selects an action randomly due to her cognitive limitation and uncertain psychological mood as well as the strategic complexity caused by monitoring imperfection and private observation. By focusing on generous tit-for-tat strategies, we characterize a behavioral version of Nash equilibrium termed behavioral equilibrium in an accuracy-contingent manner. By eliminating the gap between theory and evidence, we show that not pure self-interest but reciprocity plays a substantial role in motivating a player to make decisions in a sophisticated manner.

scholarly journals Adaptive behavior in variable games requires theory of mind

2020 ◽  
Author(s):  
Wenhao Qi ◽  
Edward Vul
Keyword(s):  
Social Sciences ◽  
Game Theory ◽  
Theory Of Mind ◽  
Social Interactions ◽  
Adaptive Behavior ◽  
Evolutionary Game Theory ◽  
Evolutionary Game ◽  
Clear Advantage ◽  
Tit For Tat ◽  
Is Theory

People seem to infer each others’ beliefs and desires when navigating social interactions, perhaps because such a “theory of mind” can guide cooperation and coordination. However, such strategic, altruistic interactions fall naturally out of evolutionary game theory without invoking any theory of mind; so why is theory of mind useful? Here we show that the interactions studied in game theory have been too impoverished to require theory of mind, but when interacting in variable games, agents with theory of mind have a clear advantage. We use simulated tournaments to demonstrate that traditional action-level strategies such as tit-for-tat fare miserably in variable games, that goal-based agents can adapt to new games instantly, and that having a theory of mind is increasingly helpful for coping with a variety of opponents as the variability in games increases. Our work suggests that variable games merit further investigation in game theory and social sciences.

scholarly journals Copyright in the networked world: orphaned copyrights

2005 ◽  
Vol 23 (3) ◽  
pp. 453-459 ◽  
Author(s):  
Michael Seadle
Keyword(s):  
Game Theory ◽  
Intellectual Property ◽  
Web Site ◽  
Design Methodology ◽  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Content Type ◽  
The Us ◽  
Tit For Tat ◽  
Practical Implications

PurposeThis column aims to look at the results of the US Copyright Office's request for comments about orphan copyrights.Design/methodology/approachIt uses a form of Game Theory called the Prisoner's Dilemma Game to analyze the comments that are available on the Copyright Office web site.FindingsSome change seems likely, if only because the opponents of change may discover that they can gain more for themselves when they stop defending the interests of those who have abandoned their copyrights already.Practical implicationsIf some form of cooperation between intellectual property consumers and rights holders could be worked out for orphan copyrights, it might lead to further “tit‐for‐tat” reactions that help to address other copyright issues.Originality/valueProvides useful information on orphan copyrights.

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