scholarly journals Human cooperation in the simultaneous and the alternating Prisoner's Dilemma: Pavlov versus Generous Tit-for-Tat.

1996 ◽  
Vol 93 (7) ◽  
pp. 2686-2689 ◽  
Author(s):  
C. Wedekind ◽  
M. Milinski
Keyword(s):  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Tit For Tat

Comparison of GRIT versus GRIT/TIT-FOR-TAT

1995 ◽  
Vol 76 (1) ◽  
pp. 322-322
Author(s):  
Brian Betz
Keyword(s):  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Communication Analysis ◽  
Prisoner’S Dilemma Game ◽  
Prisoner's Dilemma Game ◽  
Tit For Tat

120 subjects played a six-choice Prisoner's Dilemma game in which a simulated other employed either GRIT or GRIT/Tit-For-Tat with varying levels of communication. Analysis indicated that the addition of Tit-For-Tat to GRIT offers no advantages over the standard GRIT strategy.

scholarly journals Learning by pigeons playing against tit-for-tat in an operant prisoner’s dilemma

2003 ◽  
Vol 31 (4) ◽  
pp. 318-331 ◽  
Author(s):  
Federico Sanabria ◽  
Howard Rachlin ◽  
Forest Baker
Keyword(s):  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Tit For Tat

scholarly journals Iterated Prisoner's Dilemma among mobile agents performing 2D random walk

2021 ◽  
Vol 12 (2) ◽  
pp. 161-174
Author(s):  
Jurica Hižak
Keyword(s):  
Mobile Agents ◽  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Mixed Population ◽  
Expected Number ◽  
Iterated Prisoner's Dilemma ◽  
Tit For Tat ◽  
Detailed Derivation ◽  
Iterated Prisoner’S Dilemma ◽  
Better Than

When Iterated Prisoner's Dilemma takes place on a two-dimensional plane among mobile agents, the course of the game slightly differs from that one in a well-mixed population. In this paper we present a detailed derivation of the expected number of encounters required for Tit-for-tat strategy to get even with Always-Defect strategy in a Brownian-like population. It will be shown that in such an environment Tit-for-Tat can perform better than in a well-mixed population.

scholarly journals The excuse principle can maintain cooperation through forgivable defection in the Prisoner's Dilemma game

2013 ◽  
Vol 280 (1766) ◽  
pp. 20131475 ◽  
Author(s):  
Indrikis Krams ◽  
Hanna Kokko ◽  
Jolanta Vrublevska ◽  
Mikus Āboliņš-Ābols ◽  
Tatjana Krama ◽  
...  
Keyword(s):  
Prisoner's Dilemma ◽  
Decision Rules ◽  
Prisoner’S Dilemma ◽  
Short Term ◽  
Prisoner’S Dilemma Game ◽  
Prisoner's Dilemma Game ◽  
Tit For Tat ◽  
The Stability ◽  
Term Benefit ◽  
Behavioural Strategies

Reciprocal altruism describes a situation in which an organism acts in a manner that temporarily reduces its fitness while increasing another organism's fitness, but there is an ultimate fitness benefit based on an expectation that the other organism will act in a similar manner at a later time. It creates the obvious dilemma in which there is always a short-term benefit to cheating, therefore cooperating individuals must avoid being exploited by non-cooperating cheaters. This is achieved by following various decision rules, usually variants of the tit-for-tat (TFT) strategy. The strength of TFT, however, is also its weakness—mistakes in implementation or interpretation of moves, or the inability to cooperate, lead to a permanent breakdown in cooperation. We show that pied flycatchers ( Ficedula hypoleuca ) use a TFT with an embedded ‘excuse principle’ to forgive the neighbours that were perceived as unable to cooperate during mobbing of predators. The excuse principle dramatically increases the stability of TFT-like behavioural strategies within the Prisoner's Dilemma game.

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.

PIGEONS' CHOICE BETWEEN SHARED AND UNSHARED FEEDING SITES IN GAME SITUATIONS.

2019 ◽  
Vol 45 (2) ◽  
pp. 434-453
Author(s):  
Shoko Kitano ◽  
Tetsuo Yamaguchi ◽  
Daisuke Saeki ◽  
Masato Ito
Keyword(s):  
Present Experiment ◽  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
The Other ◽  
Choice Situation ◽  
Prisoner’S Dilemma Game ◽  
Feeding Site ◽  
Feeding Sites ◽  
Choice Strategy ◽  
Tit For Tat

Cooperative behavior in nonhuman animals has been studied within the framework of game theory, typically by using the prisoner’s dilemma game. Previous studies on cooperation by pigeons using this game have revealed that, under these conditions, the animals did not learn the tit-for-tat strategy played by their opponents. In many cases, animals fail to choose cooperation and in so doing do not maximize their gains. The present experiment examined pigeons’ cooperative choices in the prisoner’s dilemma game situation by using a different type of apparatus than that used in previous studies: Subjects moved to choose one of two feeding sites, one of which was shared by another, stooge, pigeon whose choices were controlled by a computer and the other of which was not shared by other pigeons. In this choice situation, the presence of the stooge pigeon increased the subjects’ choices of the shared feeding site significantly. Further, the pigeons learned the other player’s choice strategy (tit-for-tat and random), showing that choice proportions for the shared feeding site were significantly higher in the tit-for-tat condition than in the random condition. These results suggest that the presence of a conspecific at the feeding site is a reinforcer for choosing it and that the choice situation constituted by the apparatus used in the present experiment could promote learning of the opponent’s choice strategy.

In Defense of Moderate Envy

2000 ◽  
Vol 22 (1) ◽  
Author(s):  
Bernd Lahno
Keyword(s):  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Behavior Patterns ◽  
Degree Of Stability ◽  
Tit For Tat

AbstractIn contrast to Axelrod’s advice “don’t be envious” it is argued that the emotion of envy may enhance cooperation. TIT FOR TAT does exhibit a certain degree of envy. But, it does so in inconsistent ways. Two variants of TIT FOR TAT are introduced and their strategic properties are analyzed. Both generate the very same actual play as TIT FOR TAT in a computer tournament without noise. However, if noise is introduced they display some greater degree of stability. This is due to the fact that they form, in a prisoner’s dilemma supergame with suitable parameters, an equilibrium with themselves that is subgame perfect or (in case of the first strategy) close to subgame perfect. It is additionally argued that these strategies are exceptionally clear and comprehensible to others in that they conform to well known real live behavior patterns.

ON LOCAL PRISONER'S DILEMMA GAME WITH PARETO UPDATING RULE

2000 ◽  
Vol 11 (08) ◽  
pp. 1539-1544 ◽  
Author(s):  
E. AHMED ◽  
A. S. ELGAZZAR
Keyword(s):  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Small World ◽  
Small World Networks ◽  
Prisoner’S Dilemma Game ◽  
Regular Lattices ◽  
Prisoner's Dilemma Game ◽  
Tit For Tat ◽  
Updating Rule ◽  
Erratic Behavior

Prisoner's Dilemma games with two and three strategies are studied. The corresponding replicator equations, their steady states and their asymptotic stability are discussed. Local Prisoner's Dilemma games are studied using Pareto optimality. As in the case with Nash updating rule, the existence of tit for tat strategy is crucial to imply cooperation even in one dimension. Pareto updating implies less erratic behavior since the steady state configurations are mostly fixed points or at most 2-cycle. Finally, Prisoner's Dilemma game is simulated on small-world networks which are closer to real systems than regular lattices. There are no significant changes compared to the results of the regular lattice.

scholarly journals Iterated Economic Games, Logic Gates, and the Flow of Shared Information in Strategic Interactions

2017 ◽  
Author(s):  
Michael Harré
Keyword(s):  
Mutual Information ◽  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Logic Gates ◽  
Strategic Choices ◽  
Information Measures ◽  
Information Sets ◽  
Shared Information ◽  
Economic Interaction ◽  
Tit For Tat

Iterated games, in which the same economic interaction is repeatedly played between the same agents, are an important framework for understanding the effectiveness of strategic choices over time. To date very little work has applied information theory to the information sets used by agents in order to decide what action to take next in such strategic situations. This article looks at the mutual information between previous game states and an agent's next action by introducing two new classes of games: ’invertible games’ and ‘cyclical games'. By explicitly expanding out the mutual information between past states and the next action we show under what circumstances these expressions can be simplified. These information measures are then applied to the Traveler's Dilemma game and the Prisoner's Dilemma game, the Prisoner's Dilemma being invertible, to illustrate their use. In the Prisoner's Dilemma a novel connection is made between the computational principles of logic gates and both the structure of games and the agents' decision strategies. This approach is applied to the cyclical game Matching Pennies to analyse the foundations of a behavioural ambiguity between two well studied strategies: ‘Tit-for-Tat' and ’Win-Stay, Lose-Switch'.

The Moral and Ethical Significance of TIT FOR TAT

Dialogue ◽  
1986 ◽  
Vol 25 (3) ◽  
pp. 449-470 ◽  
Author(s):  
Peter Danielson
Keyword(s):  
Reinforcement Schedule ◽  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Choice Situation ◽  
Sermon On The Mount ◽  
Tit For Tat ◽  
Good For ◽  
Robert Axelrod ◽  
Ethical Significance

TIT FOR TAT (TFT) is the familiar strategy of returning like for like, good for good, bad for bad. Recently Robert Axelrod has shown this rule to be remarkably effective in promoting co-operation among egoists.1Nevertheless, it has been morally denigrated, most notably in the Sermon on the Mount but also by the modern patron of TFT, Anatol Rapoport:Of the contingent strategies, Tit-for-tat elicits consistently the most cooperation in the Prisoner's Dilemma. Obviously, it would be fatuous to interpret this result as a vindication of the “eye-for-an-eye” principle. The success of Tit-for-tat may be no more than that of a simple reinforcement schedule in à two-choice situation, devoid of ethical overtones.

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