[Paper Review] Metamimetic Games : Modeling Metadynamics in Social Cognition

David Chavalarias|arXiv (Cornell University)|Aug 1, 2005

Evolutionary Game Theory and Cooperation57 references16 citations

TL;DR

This paper introduces metamimetic games, a formal framework that endogenizes the selection of imitation rules in social cognition by modeling agents' reflexive capacity to choose among different mimetic strategies. It proposes counterfactually stable states and attractors as equilibria, enabling a cultural co-evolutionary view of social differentiation that departs from pre-existing optimization criteria.

ABSTRACT

Imitation is fundamental in the understanding of social system dynamics. But the diversity of imitation rules employed by modelers proves that the modeling of mimetic processes cannot avoid the traditional problem of endogenization of all the choices, including the one of the mimetic rules. Starting from the remark that human reflexive capacities are the ground for a new class of mimetic rules, I propose a formal framework, metamimetic games, that enable to endogenize the distribution of imitation rules while being human specific. The corresponding concepts of equilibrium - counterfactually stable state - and attractor are introduced. Finally, I give an interpretation of social differentiation in terms of cultural co-evolution among a set of possible motivations, which departs from the traditional view of optimization indexed to criteria that exist prior to the activity of agents.

Motivation & Objective

• To address the endogenization problem in modeling mimetic processes, where imitation rules are typically exogenous.
• To formalize human-specific reflexive decision-making in social imitation, moving beyond standard models of behavioral imitation.
• To develop a framework that captures the dynamics of how agents select among different mimetic strategies based on internal reasoning.
• To redefine social equilibrium not as a fixed point, but as a counterfactually stable state emerging from strategic rule selection.
• To model social differentiation as a co-evolutionary process among competing motivations, rather than optimization toward pre-defined goals.

Proposed method

• Proposes a game-theoretic framework—metamimetic games—where agents choose from a set of imitation rules based on reflexive evaluation of outcomes.
• Introduces the concept of a 'counterfactually stable state' as a new equilibrium notion, where no agent would prefer to deviate even under hypothetical changes.
• Uses attractor dynamics to model long-term behavioral patterns emerging from rule selection and interaction.
• Models the distribution of mimetic rules as endogenous, evolving through agent interactions rather than being externally imposed.
• Applies the framework to social cognition by embedding reflexive cognition into the strategic choice of imitation rules.
• Employs concepts from nonlinear dynamics and self-organizing systems to analyze stability and convergence in social systems.

Experimental results

Research questions

• RQ1 How can the selection of imitation rules be modeled as an endogenous process in social cognition?
• RQ2 What constitutes a stable equilibrium in a system where agents reflexively choose among different mimetic strategies?
• RQ3 How does social differentiation emerge not from optimization toward fixed criteria, but from co-evolution among competing motivations?
• RQ4 In what way does reflexive decision-making alter the dynamics of social imitation compared to standard models?
• RQ5 Can attractor states in such systems be characterized as counterfactually stable, and what does this imply for long-term social behavior?

Key findings

• The framework successfully endogenizes the distribution of imitation rules by modeling agents' reflexive choice among them.
• Counterfactually stable states emerge as a new equilibrium concept, capturing stability under hypothetical deviations.
• Attractor dynamics in metamimetic games reflect long-term social patterns shaped by evolving rule preferences.
• Social differentiation is reinterpreted as cultural co-evolution among motivations, rather than optimization toward pre-existing criteria.
• The model demonstrates that social cognition dynamics cannot be reduced to simple optimization, but require modeling rule selection as a strategic, reflexive process.
• The approach provides a formal basis for understanding how social systems self-organize through internal rule adaptation, not just external incentives.