Repeated Sequential Prisoner's Dilemma: The Stackleberg Variant

2015 ◽  
Vol 32 (01) ◽  
pp. 1540009
Author(s):  
Xing-Long Qu ◽  
Zhi-Gang Cao ◽  
Yi-Fen Mu ◽  
Xiao-Guang Yang
Keyword(s):  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Subgame Perfect Equilibrium ◽  
Optimal Strategies ◽  
Equilibrium Analysis ◽  
Equilibrium Payoff ◽  
Second Stage ◽  
Usual Equilibrium ◽  
Great Contrast ◽  
Two Stages

We study the Stackleberg variant of the repeated Sequential Prisoner's Dilemma (SPD). The game goes in two stages, and the two players, the leader and the follower, are asymmetric in both stages. In the first stage of the game, the leader chooses a strategy (for the repeated SPD of the second stage), which is immediately known to the follower. In the second stage, they play repeated SPD: In each round the follower moves after observing the leader's action. Assuming complete rationality, we find some extraordinary properties of this model. (i) The (subgame perfect) equilibrium payoff profile is unique, which lies on the corner of the region predicted by classical folk theorems: It is best for the leader and at the same time worst for the follower, (ii) the leader has simple optimal strategies that are one-step memory and stationary. These features are in great contrast with classical results, where either uniqueness cannot be guaranteed and equilibrium strategies are often quite complicated, or bounded rationality is required. Although full cooperation, i.e., the outcome is always (cooperate, cooperate), is not attainable in our model, at least a half of the optimal social welfare can be guaranteed. We also do a non-equilibrium analysis which makes the usual equilibrium analysis more convincing.

In What Sense is “the Prisoner’s Dilemma Game” a Dilemma for a Human or a Programmed Agent?

2007 ◽  
Vol 11 (7) ◽  
pp. 833-841
Author(s):  
Shihomi Wada ◽  
◽  
Keiji Suzuki
Keyword(s):  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Experimental Results ◽  
Double Bind ◽  
Prisoner’S Dilemma Game ◽  
Equal Distribution ◽  
Second Stage ◽  
Human Agent ◽  
Prisoner's Dilemma Game ◽  
Similarities And Differences

In this paper, we compare the experimental results of human agents with that of programmed agents using the double-bind prisoner’s dilemma game, in which an ordinary prisoner’s dilemma game is nested into another dilemma; that is, a player has to decide firstly if s/he will play prisoner’s dilemma or not. Comparing human-agent experimental results with programmed agent experimental results, we found remarkable similarities and differences as follows: (1) when cooperation is chosen in the second stage, both human and programmed agents show similar distributions of the first choices, (2) in the case when agents choose defection in the second stage, human agents have a tendency to play an ordinary prisoner’s dilemma game, (3) in the case when agents choose defection in the second stage, programmed agents show almost equal distribution. These results suggest that programmed agents may be cooperators and get close to the Pareto optimal equilibrium in an appropriate setting.

scholarly journals Strong and Safe Nash Equilibrium in Some Repeated 3-Player Games

2019 ◽  
Vol 65 (3) ◽  
pp. 271-295 ◽  
Author(s):  
Tadeusz Kufel ◽  
Sławomir Plaskacz ◽  
Joanna Zwierzchowska
Keyword(s):  
Nash Equilibrium ◽  
Normal Form ◽  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Repeated Game ◽  
Equilibrium Payoff ◽  
Equilibrium Strategies ◽  
Strong Nash Equilibrium ◽  
Player Game ◽  
Stage Game

The paper examines an infinitely repeated 3-player extension of the Prisoner’s Dilemma game. We consider a 3-player game in the normal form with incomplete information, in which each player has two actions. We assume that the game is symmetric and repeated infinitely many times. At each stage, players make their choices knowing only the average payoffs from previous stages of all the players. A strategy of a player in the repeated game is a function defined on the convex hull of the set of payoffs. Our aim is to construct a strong Nash equilibrium in the repeated game, i.e. a strategy profile being resistant to deviations by coalitions. Constructed equilibrium strategies are safe, i.e. the non-deviating player payoff is not smaller than the equilibrium payoff in the stage game, and deviating players’ payoffs do not exceed the nondeviating player payoff more than by a positive constant which can be arbitrary small and chosen by the non-deviating player. Our construction is inspired by Smale’s good strategies described in Smale’s paper (1980), where the repeated Prisoner’s Dilemma was considered. In proofs we use arguments based on approachability and strong approachability type results.

EVOLUTION AND THE COMPLEXITY OF FINITE AUTOMATA

2007 ◽  
Vol 09 (04) ◽  
pp. 731-743 ◽  
Author(s):  
MOEZ KILANI
Keyword(s):  
Prisoner's Dilemma ◽  
Finite Automata ◽  
Limit Equilibrium ◽  
Prisoner’S Dilemma ◽  
Second Stage ◽  
Repeated Interaction

Prisoner's dilemma played by finite automata is reviewed again using a slightly modified measure of complexity. At a first step, an equilibrium with a large number of possible outcomes is shown to hold. At a second stage, we consider a game of repeated interaction, and show that on (limit) equilibrium only cooperative actions are played. We conclude that cooperation is the result of a (complex) long interaction.

Altered Fine Structure of B Lymphocytes Correlated with Defective Terminal Differentiation

1973 ◽  
Vol 31 ◽  
pp. 386-387
Author(s):  
Dale E. Bockman ◽  
L. Y. Frank Wu ◽  
Alexander R. Lawton ◽  
Max D. Cooper
Keyword(s):  
Immune Deficiency ◽  
B Lymphocytes ◽  
Plasma Cells ◽  
Present Report ◽  
Specific Antigen ◽  
Terminal Differentiation ◽  
Second Stage ◽  
Two Stages ◽  
Deficiency Diseases ◽  
Cell Line Generation

B-lymphocytes normally synthesize small amounts of immunoglobulin, some of which is incorporated into the cell membrane where it serves as receptor of antigen. These cells, on contact with specific antigen, proliferate and differentiate to plasma cells which synthesize and secrete large quantities of immunoglobulin. The two stages of differentiation of this cell line (generation of B-lymphocytes and antigen-driven maturation to plasma cells) are clearly separable during ontogeny and in some immune deficiency diseases. The present report describes morphologic aberrations of B-lymphocytes in two diseases in which second stage differentiation is defective.

Zu brav oder zu böse? Mobbing-Opfer und Abgelehnte im Prisoner's Dilemma-Paradigma

1999 ◽  
Vol 30 (2/3) ◽  
pp. 179-193 ◽  
Author(s):  
Beate Schuster
Keyword(s):  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma

Zusammenfassung: Der soziometrische Status und der Viktimisierungsstatus von 5. bis 11. Klässlern wurde ermittelt, der Status hypothetischer InteraktionspartnerInnen sowie deren angebliche Wahlen variiert, und die Reaktionen im Gefangenendilemma erfaßt. Die Reaktionen wurden sowohl durch die experimentell vorgegebenen als auch durch die erwarteten Wahlen der InteraktionspartnerInnen bestimmt: Kooperative Zuege wurden eher kooperativ, und kompetitive Zuege eher kompetitiv beantwortet. Darüber hinaus vermieden Mobbingopfer kompetitive Züge, während zwei Untergruppen der Abgelehnten gegensätzliche Strategiepräferenzen aufwiesen: Versuchspersonen, die sowohl Ablehnung als auch Mobbing erfahren («Viktimisiert-Abgelehnte») verhielten sich besonders kooperativ; abgelehnte ProbandInnen, die nicht viktimisiert werden («Nicht-viktimisiert-Abgelehnte») dagegen vergleichsweise kompetitiv. Die kooperativen Wahlen viktimisierter Versuchspersonen wurden nicht erwidert: Die Versuchspersonen reagierten gegenüber den Viktimisierten kompetitiver als sich die Viktimisierten ihrerseits gegenüber ihren InteraktionspartnerInnen verhielten. Diese Befunde bestätigen die Notwendigkeit, bei «Abgelehnten» zwei Untergruppen auf der Basis der Viktimisierungsdimension zu unterscheiden. Die Befunde werden ferner vor dem Hintergrund der Hypothese diskutiert, daß die Submissivität potentieller Opfer mit zu ihrer Viktimisierungs-Erfahrung beiträgt.

Facial Likability and Smiling Enhance Cooperation, but Have No Direct Effect on Moralistic Punishment

2016 ◽  
Vol 63 (5) ◽  
pp. 263-277 ◽  
Author(s):  
Laura Mieth ◽  
Raoul Bell ◽  
Axel Buchner
Keyword(s):  
Conditional Probability ◽  
Direct Effect ◽  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Prisoner’S Dilemma Game ◽  
Costly Punishment ◽  
Prisoner's Dilemma Game ◽  
Moralistic Punishment

Abstract. The present study serves to test how positive and negative appearance-based expectations affect cooperation and punishment. Participants played a prisoner’s dilemma game with partners who either cooperated or defected. Then they were given a costly punishment option: They could spend money to decrease the payoffs of their partners. Aggregated over trials, participants spent more money for punishing the defection of likable-looking and smiling partners compared to punishing the defection of unlikable-looking and nonsmiling partners, but only because participants were more likely to cooperate with likable-looking and smiling partners, which provided the participants with more opportunities for moralistic punishment. When expressed as a conditional probability, moralistic punishment did not differ as a function of the partners’ facial likability. Smiling had no effect on the probability of moralistic punishment, but punishment was milder for smiling in comparison to nonsmiling partners.

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