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Indicators of order

Simulations generate a large number of data about individual transactions such as which shop was visited, purchased quantities, and agents' profits. The organization process itself, involving the dynamics of vectors of buyers 's is harder to monitor. We used two methods to do this.

Firstly, adapting a measure used in (Derrida [1986]) for instance, we defined an order parameter y by


In the organized regime, when the customer is faithful to only one shop, gets close to 1 (all except one being close to zero). On the other hand, when a buyer visits n shops with equal probability , is of order . More generally, can be interpreted as the inverse number of shops visited. We usually monitor y, the average of over all buyers.

Secondly, when the number of shops is small, 2 or 3, a simplex plot can be used to monitor on line the fidelity of every single buyer. Figures 2a and 3a, for instance, display simplex plots at different steps of a simulation. Each agent is represented by a small circle whose colour or shade is specific to the agent. The circle's position is the barycenter of the triangle for a choice of weights proportional to the fidelity of the agent to the 3 shops each of which corresponds to one of the 3 apexes of the triangle. Proximity to one corner is an indication of fidelity to the shop corresponding to that corner. Agents represented by circles which are close to the center are undecided.

Mon Feb 10 13:26:18 GMT+0100 1997