Modeling cultural dynamics with metamimetic games : a multi-scale approach?

Modeling cultural dynamics with metamimetic games : a multi-scale approach?

David Chavalarias

CREA, Ecole Polytechnique, Paris


Workshop "Scaling in Biological and Social Networks", SFI, July 9-13, 2007

Some Question

What are the main differences between biological and cultural evolution ?

Are social systems maximizing something ?

Are current formal approach adapted ?


Co-evolution between social Networks and agents' identities


Toward endogenous preferences and endogenous networks social modelling

Changing identities

The interplay between imitation and preferences : two different perspectives

  • Imitation is at the origin of preferences formation : Tarde (1890), Baldwin (1890), Girard (1961), ...
Imitative desire is always a desire to be Another. There is only one metaphysical desire but the particular desires which instantiate this primordial desire are of infinite variety.René Girard 1961

  • Preferences are at the origin of (rational) imitation acts : a position often adopted by economics modellers (cf. Orléan 2002).
Social causes are of two kinds : logical or not logical. Distinction is of highest importance. Logical causes act when an innovation is chosen by a man because it is judged by him more useful or more true than other, i.e. more in line than these latters with the goals already adopted by him (by imitation always). Tarde 1890

Imitation can change its own form

We imitate after some personal criteria


as reflexive entities we can imitate criteria of others and change the way we imitate.

Jaan Valsiner (2004)
The maker becomes the made and moves on to be the maker for the something new.

Metamimetic games

Changing reflexively one's strategy : basic example


Chavalarias (2006)

Metamimetic games: Modeling Metadynamics in Social Cognition, Journal of Artificial Societies and Social Simulations (JASSS) Vol. 9 Issue 2.

Counterfactual equilibrium

Counterfactual equilibrium

Social situations such that each agent from his own point of view and with his own values, feels as well or better off than when he imagines himself in the place of one of his neighbors.

When some agents are still frustrated, we can still have counterfactual attractors. Frustrated people are found at the border of social groups.

In case of stochastic dynamics we have counterfactual stochastically stable sets.

The rules' space

The set of rules


Simple MMG

A simple metamimetic game

  • Consider a population of agents in situation of dyadic social interactions with two opportunities of actions.
  • Each interaction yields some material payoffs for each protagonists
  • Agents can view the worlds through different imitation rules:
    • Conformist
    • Non-conformist
    • Payoffs maximization
    • Payoffs minimization

Chavalarias, D., Cooperation as an outcome of a social differentiation process in a metamimetic game (Forthcoming 2007) In : Social Simulation: Technologies, Advances and New Discoveries, Bruce Edmonds, Cesáreo Hernández Iglesias, et Klaus G. Troitzsch (ed).

Metamimetic games
Some slides off line

Phase transition

Metamimetic SPD between conformists and maxi agents

  • The behavioral attractor is all D.
  • Noise on rule favors maximizing behaviors
  • Noise on actions favors conformism.
Phase transition with non linear dependancy.



  • Cultural evolution through a differentiation process discarding reference to a global criteria,
  • Agent's heterogeneity in behaviours and goals/preferences/values
  • Emergence of social groups with specific configurations
  • Interplay between the individual level and the group level dynamics
  • Social dynamics depend agent's possible cognitive contents and the structure of noise.

Open questions
  • How to compute counterfactual attractors and the geometry of social groups from agent's cognitives capacities ?
  • If innovation = new rule that spreads, what do we miss when modelling innovation as the exploration of a predefined (infinite) space?
  • Endogenization of some noise's component : perturbations due to some behaviours, stabilizing effects due to some institutions.

The end

Thanks for your attention!

papers ans slides : http://chavalarias.com