Stability of Mixed-Strategy-Based Iterative Logit Quantal Response Dynamics in Game Theory

Zhang, Qian; Di, Zengru; Wu, Jinshan

doi:10.1371/journal.pone.0105391

Cited by 9 publications

(9 citation statements)

References 33 publications

(69 reference statements)

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“…“The QRE has been compared with experimental observation and generally provides a better fit to the data than the NE” [ 35 ]. On this basis, we decided to evaluate the model using our experimental data.…”

Section: Methodsmentioning

confidence: 99%

From rationality to cooperativeness: The totally mixed Nash equilibrium in Markov strategies in the iterated Prisoner’s Dilemma

et al. 2017

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In this research, the social behavior of the participants in a Prisoner's Dilemma laboratory game is explained on the basis of the quantal response equilibrium concept and the representation of the game in Markov strategies. In previous research, we demonstrated that social interaction during the experiment has a positive influence on cooperation, trust, and gratefulness. This research shows that the quantal response equilibrium concept agrees only with the results of experiments on cooperation in Prisoner’s Dilemma prior to social interaction. However, quantal response equilibrium does not explain of participants’ behavior after social interaction. As an alternative theoretical approach, an examination was conducted of iterated Prisoner's Dilemma game in Markov strategies. We built a totally mixed Nash equilibrium in this game; the equilibrium agrees with the results of the experiments both before and after social interaction.

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Section: Methodsmentioning

confidence: 99%

From rationality to cooperativeness: The totally mixed Nash equilibrium in Markov strategies in the iterated Prisoner’s Dilemma

et al. 2017

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“…However, in contrast to the classical Nash equilibrium, the definition of QRE assumes that participants strive for the best answer only in the probabilistic sense: the better the answer, the more likely the participant will choose it 38 , 39 . A comparison of the QRE with experimental data indicated that this approach provided a better fit than the Nash equilibrium 40 . In practice, the QRE is dependent upon employing logistic distribution.…”

Section: Modelmentioning

confidence: 99%

Quantal response equilibrium for the Prisoner’s Dilemma game in Markov strategies

Kozitsina

Kozitsin

Menshikov

2022

Sci Rep

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Within the studies of human cooperation, there are gaps that require further investigation. One possible area for growth is developing theoretical concepts which describe high levels of cooperation. In this paper, we present a symmetrical quantal response equilibrium (QRE) in Prisoner’s Dilemma game (PD) constructed in Markov strategies (tolerance to defection and mutual cooperation). To prove the adequacy of the resulting equilibrium, we compare it with the previously found Nash equilibrium in PD in Markov strategies: the QRE converges with the Nash equilibrium that corresponds with the theory. Next, we investigate the properties of QRE in PD in Markov strategies by testing it against experimental data. For low levels of rationality, the found equilibrium manages to describe high cooperation. We derive the levels of rationality under which the intersection between Nash and QRE occurs. Lastly, our experimental data suggest that QRE serves as a dividing line between behavior with low and high cooperation.

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“…However, in contrast to the classical Nash equilibrium, the definition of QRE assumes that participants strive for the best answer only in the probabilistic sense: the better the answer, the more likely the participant will choose it 34,35 . The QRE was compared with experimental data, and determined that this approach provided better fit than the Nash equilibrium 36 . In practice, the QRE is built upon employing logistic distribution.…”

Section: Quantal Response Equilibrium (Qre)mentioning

confidence: 99%

Mutual Cooperation and Tolerance to Defection in the Context of Socialization: The Theoretical Model and Experimental Evidence

Kozitsina

Kozitsin

Menshikov

2021

Preprint

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The study of the nature of human cooperation still contains gaps needing investigation. Previous findings reveal that socialization effectively promotes cooperation in the well-known Prisoner’s dilemma (PD) game. However, theoretical concepts fail to describe high levels of cooperation (probability higher than 50%) that were observed empirically. In this paper, we derive a symmetrical quantal response equilibrium (QRE) in PD in Markov strategies and test it against experimental data. Our results indicate that for low levels of rationality, QRE manages to describe high cooperation. In contrast, for high rationality QRE converges to the Nash equilibrium and describes low-cooperation behavior of participants. In the area of middle rationality, QRE matches the curve that represents the set of Nash equilibrium in Markov strategies. Further, we find that QRE serves as a dividing line between behavior before and after socialization, according to the experimental data. Finally, we successfully highlight the theoretically-predicted intersection of the set of Nash equilibrium for PD in Markov strategies and the QRE curve.

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Stability of Mixed-Strategy-Based Iterative Logit Quantal Response Dynamics in Game Theory

Cited by 9 publications

References 33 publications

From rationality to cooperativeness: The totally mixed Nash equilibrium in Markov strategies in the iterated Prisoner’s Dilemma

From rationality to cooperativeness: The totally mixed Nash equilibrium in Markov strategies in the iterated Prisoner’s Dilemma

Quantal response equilibrium for the Prisoner’s Dilemma game in Markov strategies

Mutual Cooperation and Tolerance to Defection in the Context of Socialization: The Theoretical Model and Experimental Evidence

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