Boltzmann-like and Boltzmann-Fokker-Planck equations as a foundation of behavioral models

Punishment of free-riders is generally viewed as an important factor in promoting cooperation. But since it is often costly to sanction exploiters, the emergence of such a behavior and its stability raise interesting problems. Players who do not contribute to the sanctions, but profit from the increased level of cooperation caused by them, act as "second-order exploiters" and threaten the joint enterprise. In this paper, we review the role of voluntary participation in establishing and upholding cooperation with or without punishment. In particular, we deal with two distinct forms of punishment, namely peer punishment and pool punishment, and compare their stability and their efficiency. The emergence and upkeep of collaborative undertakings can strongly depend on whether participation is voluntary or mandatory. The possibility to opt out of a joint enterprise often helps in curbing exploiters and boosting pro-social behavior.Keywords Evolutionary game theory · Public goods games · Cooperation · Costly punishment · Social dilemma · Voluntary interactions For online experimentation, we refer to http://www.hanneloredesilva.at/sanctions and the VirtualLabs at

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“…In the case of weak imitation (s very small), we obtain, up to a change in velocity, the well known replicator equation (cf. [53,54,102] and [61]…”

Section: Evolutionary Dynamics Of Social Learningmentioning

confidence: 99%

Social Control and the Social Contract: The Emergence of Sanctioning Systems for Collective Action

et al. 2010

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“…Social individua deciding in economic situations [7,8,9,10, 11,12,13] can fall into oscillatory cycles, e.g. when loners, not participating in the game, are added as a third strategy to a Prisoner's Dilemma [14,15].…”

Section: Introductionmentioning

confidence: 99%

Drift reversal in asymmetric coevolutionary conflicts: influence of microscopic processes and population size

Claussen

2007

Eur. Phys. J. B

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Abstract. The coevolutionary dynamics in finite populations currently is investigated in a wide range of disciplines, as chemical catalysis, biological evolution, social and economic systems. The dynamics of those systems can be formulated within the unifying framework of evolutionary game theory. However it is not a priori clear which mathematical description is appropriate when populations are not infinitely large. Whereas the replicator equation approach describes the infinite population size limit by deterministic differential equations, in finite populations the dynamics is inherently stochastic which can lead to new effects. Recently, an explicit mean-field description in the form of a Fokker-Planck equation was derived for frequency-dependent selection in finite populations based on microscopic processes. In asymmetric conflicts between two populations with a cyclic dominance, a finite-size dependent drift reversal was demonstrated, depending on the underlying microscopic process of the evolutionary update. Cyclic dynamics appears widely in biological coevolution, be it within a homogeneous population, or be it between disjunct populations as female and male. Here explicit analytic address is given and the average drift is calculated for the frequency-dependent Moran process and for different pairwise comparison processes. It is explicitely shown that the drift reversal cannot occur if the process relies on payoff differences between pairs of individuals. Further, also a linear comparison with the average payoff does not lead to a drift towards the internal fixed point. Hence the nonlinear comparison function of the frequency-dependent Moran process, together with its usage of nonlocal information via the average payoff, is the essential part of the mechanism.

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“…The author is not the first to make use of collective phenomena from physics in social theory, and the reader is guided to Helbing (1993) for an earlier such perspective. For a book on the physics of phase transitions the reader is recommended Stanley (1971), for a review of crowd behavior see McPhail (1991).…”

Section: Introductionmentioning

confidence: 99%

Like water and vapor—conformity and independence in the large group

Tarnow¹

1996

Syst. Res.

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Behavioral Science v41, 136-151 (1996). AbstractConformity and independence in the large group may, in part, be due to collective phenomena analogous to those producing different physical phases like solid, liquid and vapor. This phase model of the large group explains several previous anecdotal observations: It predicts a suddenness in the decision making, it explains the apparent contradiction between crowd suggestibility on the one hand and the difficulty of controlling a crowd on the other hand, and it provides a new rationalization for the phenomenon of splitting. The model is of use to both leaders and members of the large group. For example, it suggests what social parameters to change to disperse a violent crowd, and why crowd crystals, a concept examined by the writer Canetti, can suddenly make the large group conform.

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Boltzmann-like and Boltzmann-Fokker-Planck equations as a foundation of behavioral models

Cited by 58 publications

References 27 publications

Social Control and the Social Contract: The Emergence of Sanctioning Systems for Collective Action

Social Control and the Social Contract: The Emergence of Sanctioning Systems for Collective Action

Drift reversal in asymmetric coevolutionary conflicts: influence of microscopic processes and population size

Like water and vapor—conformity and independence in the large group

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