Sociodynamics––a systematic approach to mathematical modelling in the social sciences

Weidlich, Wolfgang

doi:10.1016/s0960-0779(02)00666-5

Cited by 161 publications

(202 citation statements)

References 5 publications

Supporting

Mentioning

195

Contrasting

Unclassified

Order By: Relevance

“…Actually, we need the other aspect of the full feedback: "Its order parameters strongly influence the individuals of the society by orienting (enslaving) their activities and by activating or deactivating their attitudes and capabilities." (Mainzer 2007a, p. 395) This is just the slaving principle as a whole elucidated as synergetics by Hermann Haken (Weidlich 2002(Weidlich , 2006(Weidlich , 2007. This dynamic thus is encompassed by critical values, outside of which the system falls into an unstable situation.…”

Section: Discussionmentioning

confidence: 99%

Non-self-averaging of a two-person game with only positive spillover: a new formulation of Avatamsaka’s dilemma

Aruka

Akiyama

2009

J Econ Interact Coord

View full text Add to dashboard Cite

In this game [Aruka in Avatamsaka game structure and experiment on the web. In: Aruka Y (ed) Evolutionary controversies in economics. Springer, Tokyo, pp 115-132, 2001], selfishness may not be determined even if an agent selfishly adopts the strategy of defection. Individual selfishness can only be realized if the other agent cooperates, therefore gain from defection can never be assured by defection alone. The sanction by defection as a reaction of the rival agent cannot necessarily reduce the selfishness of the rival. In this game, explicit direct reciprocity cannot be guaranteed. Now we introduce different spillovers or payoff matrices, so that each agent may then be faced with a different payoff matrix. A ball in the urn is interpreted as the number of cooperators, and the urn as a payoff matrix. We apply Ewens' sampling formula to our urn process in this game theoretic environment. In this case, there is a similar result as in the classic case, because there is "self-averaging" for the variances of the number who cooperate. Applying Pitman's sampling formula to the urn process, the invariance of the random partition vectors under the properties of exchangeability and size-biased permutation does not hold in general. Pitman's sampling formula depends on the two-parameter Poisson-Dirichlet distribution whose special case is just Ewens' formula. In the Ewens setting, only one probability α of a new entry matters. On the other hand, there is an additional probability θ of an unknown entry, as will be argued in the Pitman formula. More concretely, we will investigate the effects

show abstract

Section: Discussionmentioning

confidence: 99%

Non-self-averaging of a two-person game with only positive spillover: a new formulation of Avatamsaka’s dilemma

Aruka

Akiyama

2009

J Econ Interact Coord

View full text Add to dashboard Cite

show abstract

“…If, instead of having infinite populations, we consider a more realistic setting in which populations or sectors involve a finite number of individuals, then one must modify the dynamics in order to take into consideration stochastic effects that in some cases, may be important [44,45]. In this regime, one is typically concerned with the time evolution of the probability distribution over the phase space, which can be modeled by resorting to a master equation [46,47]. Under specific circumstances-large but finite population sizes-these equations can be approximated by a Fokker-Plank equation [48].…”

Section: Evolutionary Game Theorymentioning

confidence: 99%

An Evolutionary Game Theoretic Approach to Multi-Sector Coordination and Self-Organization

Santos

Encarnação

Santos

et al. 2016

Entropy

View full text Add to dashboard Cite

Coordination games provide ubiquitous interaction paradigms to frame human behavioral features, such as information transmission, conventions and languages as well as socio-economic processes and institutions. By using a dynamical approach, such as Evolutionary Game Theory (EGT), one is able to follow, in detail, the self-organization process by which a population of individuals coordinates into a given behavior. Real socio-economic scenarios, however, often involve the interaction between multiple co-evolving sectors, with specific options of their own, that call for generalized and more sophisticated mathematical frameworks. In this paper, we explore a general EGT approach to deal with coordination dynamics in which individuals from multiple sectors interact. Starting from a two-sector, consumer/producer scenario, we investigate the effects of including a third co-evolving sector that we call public. We explore the changes in the self-organization process of all sectors, given the feedback that this new sector imparts on the other two.

show abstract

“…The procedure of model design consists of the following steps: and there exist phase-transitions between these cases, which can be studied in terms of the model (for details see [8]). …”

Section: Migrationmentioning

confidence: 99%

“…The individual transition rates p ba can mathematically be represented in a standard form as proved in [8]:…”

Section: Introductionmentioning

confidence: 99%

Sociodynamics––a systematic approach to mathematical modelling in the social sciences

Cited by 161 publications

References 5 publications

Non-self-averaging of a two-person game with only positive spillover: a new formulation of Avatamsaka’s dilemma

Non-self-averaging of a two-person game with only positive spillover: a new formulation of Avatamsaka’s dilemma

An Evolutionary Game Theoretic Approach to Multi-Sector Coordination and Self-Organization

Thirty years of sociodynamics.An integrated strategy of modelling in the social sciences: applications to migration and urban evolution

Contact Info

Product

Resources

About