OPINION DYNAMICS:

AGENT BASED MODELS AND OPINION DYNAMICS AS MARKOV CHAINS
Sven BANISCH, Ricardo LIMA AND Tanya ARAUJO

(the pdf version of the paper is here)

Abstract. This paper introduces a Markov chain approach that allows a rigorous analysis of agent based opinion dynamics as well as other related agent based models (ABM). By viewing the ABM dynamics as a micro description of the process, we show how the corresponding macro description is obtained by a projection construction. Then, well known conditions for lumpability make it possible to establish the cases where the macro model is still Markov. In this case we obtain a complete picture of the dynamics including the transient stage, the most interesting phase in applications. For such a purpose a crucial role is played by the type of probability distribution used to implement the stochastic part of the model which defines the updating rule and governs the dynamics. In addition,
we show how restrictions in communication leading to the co–existence of different opinions follow from the emergence of new absorbing states. We describe our analysis in detail with some specific models of opinion dynamics. Generalizations concerning different opinion representations as well as opinion models with other interaction mechanisms are also discussed. We find that our method may be an attractive alternative to mean–field approaches and that this approach provides new perspectives on the modeling of opinion exchange dynamics, and more generally of other ABM.

Keywords: Agent Based Models, Opinion Dynamics, Markov chains, Micro Macro, Lumpability , Transient Dynamics .

MSC: 37L60, 37N25, 05C69.

NEW!

Aggregation and Emergence in Agent-Based
Models: A Markov Chain Approach

Sven BANISCH, Ricardo LIMA AND Tanya ARAUJO

(the pdf version of the paper is here)

Abstract. We analyze the dynamics of agent based models (ABMs) from a Markovian
perspective and derive explicit statements about the possibility of linking a
microscopic agent model to the dynamical processes of macroscopic observables
that are useful for a precise understanding of the model dynamics. In this
way the dynamics of collective variables may be studied, and a description of
macro dynamics as emergent properties of micro dynamics, in particular during
transient times, is possible.

NEW!

Interplay of turbulence bursts and transport barriers
analyzed in term of combined stochastic processes

E. Floriani1 , G. Ciraolo2,3 , Ph. Ghendrih4 , R. Lima5,6 , Y. Sarazin4

1) Aix-Marseille Univ, Centre de Physique Théorique, 13009 Marseille, France.
2) Centrale Marseille, 13451 Marseille, France.
3) Aix Marseille Univ, Mécanique, Modélisation et Procédés Propres (M2P2) - 13451 Marseille, France.
4) CEA, IRFM, F-13108 Saint-Paul-lez-Durance, France.
5) Dream & Science Factory, Marseille, France.
6) Institute for Complexity Sciences (ICC), Lisbon, Portugal.

(the pdf version of the article is here)

Abstract.

The interplay of large bursts of turbulent transport or blobs with regions of vanishing turbulence is a complex system that can eventually generate transport barriers when the majority of blobs are trapped in these weak turbulence regions. We present 2 models where stochastic processes are combined to recover the physics of this interaction. The main stochastic variables are the barrierwidth and the spreading distance of the blobs within the barrier together with their level of correlation.

We predict that for a class of Probability Distribution Function of these stochastic variables, the PDF of the escaping blobs will exhibit heavy tails, either exponential for a leaky barrier, or with power laws, for a tight barrier. Two-dimensional nonlinear fluid simulations of edge turbulence in tokamak plasmas bearing analogy with Rayleigh-Benard turbulence in neutral fluids – are used to supporte these stochastic models. The PDF of the blob penetration into the barrier is estimated as well as that of the barrier width for two different barriers generated in the plasma boundary layer. One can show that in the case of a barrier generated by external biasing – leading to an external radial electric field shear – the stochastic model predicts a leaky barrier with an exponential PDF of escaping blobs in agreement with the simulation data.