The spatial struggle of tit-for-tat and defect

1995 ◽  
Vol 348 (1326) ◽  
pp. 393-404 ◽  
Keyword(s):  
Game Theory ◽  
Stationary State ◽  
Evolution Of Cooperation ◽  
Space And Time ◽  
Stable Coexistence ◽  
Spatially Inhomogeneous ◽  
Biological Reality ◽  
Tit For Tat ◽  
Spatially Homogeneous ◽  
Homogeneous Environment

The pioneering work by Trivers (1971), Axelrod (1984) and Axelrod & Hamilton (1981) has stimulated continuing interest in explaining the evolution of cooperation by game theory, in particular, the iterated prisoner’s dilemma and the strategy of tit-for-tat. However these models suffer from a lack of biological reality, most seriously because it is assumed that players meet opponents at random from the population and, unless the population is very small, this excludes the repeated encounters necessary for tit-for-tat to prosper. To meet some of the objections, we consider a model with two types of players, defectors (D) and tit-for-tat players (T), in a spatially homogeneous environment with player densities varying continuously in space and time. Players only encounter neighbours but move at random in space. The analysis demonstrates major new conclusions, the three most important being as follows. First, stable coexistence with constant densities of both players is possible. Second, stable coexistence in a pattern (a spatially inhomogeneous stationary state) may be possible when it is impossible for constant distributions (even unstable ones) to exist. Third, invasion by a very small number of T-players is sometimes possible (in contrast with the usual predictions) and so a mutation to tit-for-tat may lead to a population of defectors being displaced by the T-players.

scholarly journals Variation and the response to variation as a basis for successful cooperation

2010 ◽  
Vol 365 (1553) ◽  
pp. 2627-2633 ◽  
Author(s):  
John M. McNamara ◽  
Olof Leimar
Keyword(s):  
Game Theory ◽  
Environmental Influences ◽  
Evolution Of Cooperation ◽  
Trait Variation ◽  
Social Sensitivity ◽  
Good Reputation ◽  
Contingent Behaviour

In applying game theory to problems in biology, differences between individuals are often ignored. In particular, when analysing the evolution of cooperation it is often implicitly assumed that ignoring variation will produce predictions that approximate the solution when differences are included. This need not be true. As we demonstrate, differences are not innocuous noise, but can fundamentally change the nature of a game. Even small amounts of variability can stabilize cooperation by, for example, maintaining the need to deal with cheaters. Differences promote the need to learn about others in an interaction, leading to contingent behaviour that can reduce conflict, and to negotiated outcomes that may or may not be more cooperative than unconditional actions. Once there are mechanisms such as mutation and environmental influences that maintain variation within populations, whether cooperation evolves may depend on the variation in the cooperativeness trait. Variation means that it may be worth taking a chance that a partner is cooperative by being cooperative. When there are markets, so that individuals can break off interactions to seek a better partner, variation promotes choosiness and hence penalizes those uncooperative individuals, who are rejected. Variation promotes the need to monitor the previous behaviour of others, and once this social sensitivity exists, the need to maintain a good reputation can promote cooperation.

TIT FOR TAT in sticklebacks and the evolution of cooperation

Nature ◽  
1987 ◽  
Vol 325 (6103) ◽  
pp. 433-435 ◽  
Author(s):  
Manfred Milinski
Keyword(s):  
Evolution Of Cooperation ◽  
Tit For Tat

scholarly journals Dynamic utility: the sixth reciprocity mechanism for the evolution of cooperation

2020 ◽  
Vol 7 (8) ◽  
pp. 200891 ◽  
Author(s):  
Hiromu Ito ◽  
Jun Tanimoto
Keyword(s):  
Game Theory ◽  
Dynamic Game ◽  
Evolutionary Games ◽  
Evolution Of Cooperation ◽  
Current Status ◽  
Cooperative Behaviour ◽  
Evolutionary Mechanism ◽  
Static Game ◽  
Chicken Game ◽  
The Difference

Game theory has been extensively applied to elucidate the evolutionary mechanism of cooperative behaviour. Dilemmas in game theory are important elements that disturb the promotion of cooperation. An important question is how to escape from dilemmas. Recently, a dynamic utility function (DUF) that considers an individual's current status (wealth) and that can be applied to game theory was developed. The DUF is different from the famous five reciprocity mechanisms called Nowak's five rules. Under the DUF, cooperation is promoted by poor players in the chicken game, with no changes in the prisoner's dilemma and stag-hunt games. In this paper, by comparing the strengths of the two dilemmas, we show that the DUF is a novel reciprocity mechanism (sixth rule) that differs from Nowak's five rules. We also show the difference in dilemma relaxation between dynamic game theory and (traditional) static game theory when the DUF and one of the five rules are combined. Our results indicate that poor players unequivocally promote cooperation in any dynamic game. Unlike conventional rules that have to be brought into game settings, this sixth rule is universally (canonical form) applicable to any game because all repeated/evolutionary games are dynamic in principle.

A Cross-cultural Analysis of Two China-US Game Cases and Tobacco Control Compliance

2021 ◽  
Vol 7 (6) ◽  
pp. 5087-5102
Author(s):  
Yuan Lingyu ◽  
Dexin Tian
Keyword(s):  
Game Theory ◽  
Tobacco Control ◽  
Intercultural Communication ◽  
Communication Strategies ◽  
Cultural Analysis ◽  
Cross Cultural ◽  
Diplomatic Relations ◽  
Cultural Roots ◽  
The Us ◽  
Tit For Tat

Objectives: This paper aims at exploring the China-US relations by analyzing the communication strategies and game intentions in two case studies and the cultural roots herein. Guided by the water and game theory for intercultural communication (WGICC) and cultural analyses, this study has found that in Case 1, China and the US have established initial win-win ties because of a mutually-beneficial trade system, the US intention to gain international recognition, and the romantic expectations of each other. In Case 2, both countries have suffered great losses due to the US pursuit of reinforced national identity and revitalized conservatism which set the stage for an endless line of plots to contain China. In return, China has been practicing a tit-for-tat strategy backed up with its grand ambition to forge a community with a shared future for mankind and ready to fight against containment and suppression from both the US and its allies. This study suggests an interactive pattern of win-win cooperation based on common needs and similar interests, and loss-loss confrontation based on real and imaginary fear while manifesting that the greatest Dao is expressed in the simplest terms. The findings can shed lighton appreciating China’s efforts in such domestic campaigns as tobacco control compliance and Covid-19 prevention and its diplomatic relations with other nations.

scholarly journals Evolution of Groupwise Cooperation: Generosity, Paradoxical Behavior, and Non-Linear Payoff Functions

Games ◽  
2018 ◽  
Vol 9 (4) ◽  
pp. 100 ◽  
Author(s):  
Shun Kurokawa ◽  
Joe Yuichiro Wakano ◽  
Yasuo Ihara
Keyword(s):  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Evolutionary Model ◽  
Repeated Game ◽  
Evolution Of Cooperation ◽  
Fixation Probability ◽  
Non Linear ◽  
Repeated Prisoner’S Dilemma ◽  
Tit For Tat ◽  
Repeated Prisoner's Dilemma

Evolution of cooperation by reciprocity has been studied using two-player and n-player repeated prisoner’s dilemma games. An interesting feature specific to the n-player case is that players can vary in generosity, or how many defections they tolerate in a given round of a repeated game. Reciprocators are quicker to detect defectors to withdraw further cooperation when less generous, and better at maintaining a long-term cooperation in the presence of rare defectors when more generous. A previous analysis on a stochastic evolutionary model of the n-player repeated prisoner’s dilemma has shown that the fixation probability of a single reciprocator in a population of defectors can be maximized for a moderate level of generosity. However, the analysis is limited in that it considers only tit-for-tat-type reciprocators within the conventional linear payoff assumption. Here we extend the previous study by removing these limitations and show that, if the games are repeated sufficiently many times, considering non-tit-for-tat type strategies does not alter the previous results, while the introduction of non-linear payoffs sometimes does. In particular, under certain conditions, the fixation probability is maximized for a “paradoxical” strategy, which cooperates in the presence of fewer cooperating opponents than in other situations in which it defects.

scholarly journals The influence of heterogeneous learning ability on the evolution of cooperation

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Xiaogang Li ◽  
Yini Geng ◽  
Chen Shen ◽  
Lei Shi
Keyword(s):  
Game Theory ◽  
Numerical Simulations ◽  
Prisoner’S Dilemma ◽  
Learning Ability ◽  
Evolution Of Cooperation ◽  
Game Dynamics ◽  
Potential Reason ◽  
Heterogeneous Learning ◽  
Spatial Prisoner’S Dilemma

Abstract In this paper, we design a simple coevolution model to investigate the role of heterogeneous learning ability on the evolution of cooperation. The model weakens the winner’s learning ability in order to keep its current advantage. Conversely, it strengthens the loser’s learning ability for increasing the chance to update its strategy. In particular, we consider this coevolutionary model separately applying to both cooperators and defectors (rule I), only cooperators (rule II), as well as only defectors (rule III) in spatial prisoner’s dilemma game. Through numerical simulations, we find that cooperation can be promoted in rule II, whereas, cooperation is hampered in rule I and rule III. We reveal its potential reason from the viewpoint of enduring and expanding periods in game dynamics. Our results thus provide a deeper understanding regarding the heterogeneous learning ability on game theory.

International Cooperation: Testing Evolution of Cooperation Theories

2017 ◽  
Vol 23 (1) ◽  
Author(s):  
Jeremy Bowling
Keyword(s):  
International Cooperation ◽  
Evolution Of Cooperation ◽  
Indirect Reciprocity ◽  
Cooperative Action ◽  
Tit For Tat

AbstractThe evolution of cooperation scholarship develops evolutionary stable theories that explain the presence of cooperation when there are many reasons to defect from cooperation. In this analysis, these theories are tested using the relations between states. Focusing on the direct reciprocity strategies of Tit-for-Tat and Win-stay/Lose-shift and the indirect reciprocity strategies of Cooperative Reputation and Tag, Tit-for-Tat and Cooperative Reputation are found to be robust, while Tags have mixed results. In the end, it is the direct cooperative action by states and their cooperative reputation and not shared characteristics that are most likely to elicit cooperative action in return.

scholarly journals The interplay of cognition and cooperation

2010 ◽  
Vol 365 (1553) ◽  
pp. 2699-2710 ◽  
Author(s):  
Sarah F. Brosnan ◽  
Lucie Salwiczek ◽  
Redouan Bshary
Keyword(s):  
Cognitive Abilities ◽  
Cognitive Complexity ◽  
Convincing Evidence ◽  
The Other ◽  
Evolution Of Cooperation ◽  
Social Environments ◽  
Average Gain ◽  
Central Nervous Systems ◽  
Tit For Tat ◽  
Key Variables

Cooperation often involves behaviours that reduce immediate payoffs for actors. Delayed benefits have often been argued to pose problems for the evolution of cooperation because learning such contingencies may be difficult as partners may cheat in return. Therefore, the ability to achieve stable cooperation has often been linked to a species' cognitive abilities, which is in turn linked to the evolution of increasingly complex central nervous systems. However, in their famous 1981 paper, Axelrod and Hamilton stated that in principle even bacteria could play a tit-for-tat strategy in an iterated Prisoner's Dilemma. While to our knowledge this has not been documented, interspecific mutualisms are present in bacteria, plants and fungi. Moreover, many species which have evolved large brains in complex social environments lack convincing evidence in favour of reciprocity. What conditions must be fulfilled so that organisms with little to no brainpower, including plants and single-celled organisms, can, on average, gain benefits from interactions with partner species? On the other hand, what conditions favour the evolution of large brains and flexible behaviour, which includes the use of misinformation and so on? These questions are critical, as they begin to address why cognitive complexity would emerge when ‘simple’ cooperation is clearly sufficient in some cases. This paper spans the literature from bacteria to humans in our search for the key variables that link cooperation and deception to cognition.

scholarly journals THE SINGULARITY IN GENERIC GRAVITATIONAL COLLAPSE IS SPACELIKE, LOCAL AND OSCILLATORY

1998 ◽  
Vol 13 (19) ◽  
pp. 1565-1573 ◽  
Author(s):  
B. K. BERGER ◽  
D. GARFINKLE ◽  
J. ISENBERG ◽  
V. MONCRIEF ◽  
M. WEAVER
Keyword(s):  
Numerical Simulations ◽  
Gravitational Collapse ◽  
Evolution Equations ◽  
Oscillatory Behavior ◽  
Einstein’S Equations ◽  
Einstein's Equations ◽  
Spatial Point ◽  
Spatially Inhomogeneous ◽  
Homogeneous Universe ◽  
Spatially Homogeneous

A longstanding conjecture by Belinskii, Khalatnikov and Lifshitz that the singularity in generic gravitational collapse is spacelike, local and oscillatory is explored analytically and numerically in spatially inhomogeneous cosmological space–times. With a convenient choice of variables, it can be seen analytically how nonlinear terms in Einstein's equations control the approach to the singularity and cause oscillatory behavior. The analytic picture requires the drastic assumption that each spatial point evolves toward the singularity as an independent spatially homogeneous universe. In every case, detailed numerical simulations of the full Einstein evolution equations support this assumption.

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