Computational Simulation as Theoretical Experiment

ABSTRACT

Agent-based simulation can help establish the possibility and characteristics of emergent processes. However the simulation is meaningless without an accompanying interpretation. We argue that the original context needs to be carried with the simulation so as to limit excess generalization from such models. The simulation becomes a theoretical experiment which mediates between observations of the phenomena and natural language descriptions. Replication and exploration of simulations can start to identify the extent of their validity, and thus pave the way for cautions and limited generalization of results.

This is illustrated by reimplementing and re-examining two established models. Schelling's model of racial segregation is shown to give counter-intuitive results when pushed out of its intended context—the domain of valid interpretation is narrower than that covered by the whole the model. Takahashi's model of generalized exchange is shown to have included unnecessary assumptions. In this case the domain of valid interpretation is wider than the model (at least in this aspect). A tag-based variation is described where generalized exchange is shown to emerge without information about the past behavior of others.

Keywords:

• simulation
• experiment
• exchange
• context
• segregation
• agent-based

Notes

¹Even continuous quantites are represented in a computer by a finite and crisp approximation.

²Schelling did not use a computer but, in essence, it was a computational simulation.

³Takahashi's spatial model lpar;Takahashi,2000rpar; is less interesting since it presents results that have been well explored and reproduced elsewhere lpar;Nowak and May,1992 Axelrod, 1980 1998rpar;. Without going into details, we note that a 2D spatial layout of agents can resolve free-riding issues even without the need for fairness criteria-based giving.

⁴As noted by Takahashi the biological terminology is not to be taken literally in the interpretation of the model, rather, it is used for clarity in the explanation of its mechanics.

⁵If several gave the same highest amount then one of these is selected at random.

⁶As noted.by Takahashilpar;2000rpar; repeating Takagilpar;1996rpar;, this condition has been indicated as necessary condition for the emergence of generalised exchange.

⁷This population is adjusted to ensure it is the same size over each generation.

⁸To test if generalized exchange would emerge when, initially, all agents give nothing.

The values given are averages over 50 independent runs. The numbers in brackets are standard deviations.

⁹The results are not literally identical. This is to be expected due to differing implementation details lpar;e.g., different numeric precision, pseudo-random number generators, etc.rpar;. However, the results are well within the tolerances expected at this level of replication. More importantly, the replication gives us confidence that Takahashi's results are independent of such specifics.

¹⁰To understand this one can visualize a “roulette wheel” in which each agent occupies a number of spots on the wheel. The number of spots is proportional to the score of the agent. Reproduction involves “spinning” the wheel for each new offspring required; an agent with score P has half the chance of generating an offspring than one with a score of 2P lpar;Davis,1991rpar;.

¹¹One can imagine that this could have a dramatic effect on the results since an agent that does not give lpar;even if it has a high GG valuerpar; will be marked as a low giver in the subsequent trial and hence potentially not be identified by others as one worthy of a gift.

We feel this would be a very interesting line of future work, developing a theory relating various factors to the emergence of exchange without any increase factor.

¹³Indeed, so puzzling to us initially that we independently re-implemented the model in another computer language, and the results produced were identical.

¹⁴These might include any characteristic that can be observed and learned socially, including style of dress or manner of speech. Bowles and Gintis lpar;2000 use this representation in their analytical model of parochialism.

¹⁵When mutation is applied to a tag bit it is “flipped” lpar;i.e., 0 to 1 or 1 to 0rpar;.

¹⁶No significant difference was found when we increased the number of trials.

¹⁷The interpretations given by Sigmund and Nowak (2001) relate to Riolo et al.'s (20012001) tag model. However, on-going work (Edmonds and Hales, 2003 Roberts and Sherratt, 2002) has identified that this model (even when fixed) effectively collapses to the mechanism given here.

¹⁸Initial experimentation with individual runs for lower numbers of agents and numbers of tags has confirmed this. We found that with less than 80 agents and 25 tags, exchange disappeared in the current model. However, more runs needed to justify a more confident claim.