CAR Project: Replication of Eight "Social Science" Simulation Models

Michael Cohen (
Robert Axelrod (
Rick Riolo (

This page under construction!

This page is referenced by the following article:
Robert Axelrod, "Advancing the Art of Simulation in the Social Sciences," in Rosario Conte, Rainer Hegselmann and Pietro Terna (eds.), Simulating Social Phenomena. (Berlin: Springer, 1997), pp. 21-40.

We selected a set of eight core models to replicate. We selected these models using six criteria: (1) their simplicity (for ease of implementation, explanation and understanding), (2) their relevance to the social sciences, (3) their diversity across disciplines and types of models, (4) their reasonably short run times, (5) their established heuristic value and (6) their accessibility through published accounts. Most of the eight models meet at least five of these six criteria. To be sure we included some models that we could completely understand, we selected one model from each of the three of us. The eight core models were:

Press the first link for more details about our replication; press the other links for references.

Cohen, Axelrod and Riolo implemented each of these models in the Swarm simulation system developed at Santa Fe Institute under the direction ofChris Langton. When carrying out experiments, we used Drone, a tool for automatically running batch jobs of a simulation program.

For each model, we identified the key results from the original simulations, and determined what comparisons would be needed to test for equivalence. After a good deal more work than we had expected would be necessary, we were able to attain relational equivalence on all eight models. In most cases, the results were so close that we probably attained distributional equivalence as well, although we did not perform the statistical tests to confirm this.

Summary Description of the Models and Key Results.

The following list includes brief comments on the key characteristics and results of the eight models we studied.

1. Conway's Game of Life, 1970 (see Poundstone 1985).
Comment: Although this is not a social science model, it is one of the earliest and most influential simulations of artificial life.
Metric: 2 dimensional cellular automata.
Rules: An agent stays alive if 2 or 3 neighbors are alive, otherwise it dies. New agent is born if exactly 3 neighbors are alive.
Results: Highly complex possibilities, such as gliders and R pentomino, arise from very simple rules.

2. Cohen, March and Olsen's Garbage Can Model (see Cohen etal, 1972).
Comment: This is one of the most widely cited social science simulations.
Metric: organizational relations
Rules: An organization is viewed as collections of choices looking for problems, issues and feelings looking for decision situations in which they might be aired, solutions looking for issues to which they might be an answer, and decision makers looking for work.
Results: The timing of issues, and the organizational structure both matter for outcomes.

3. Schelling's Tipping Model (see Schelling, 1974; Schelling, 1978).
Comment: This is an early and well known simulation of an artificial society.
Metric: 2 dimensions, 8 neighbors
Rule: A discontented agent moves to nearest empty location where it would be content. An agent is content if more than one-third of its neighbors are of the same color.
Result: Segregated neighborhoods form even though everyone is somewhat tolerant.
Note: Source codes for the Tipping model are available in Visual Basic and Pascal at Complexity of Cooperation, Appendix B, as part of the online collection of software for Axelrod, 1997.

4. Axelrod's Evolution of Prisoner's Dilemma Strategies (see Axelrod, 1987).
Comment: This study is widely cited in the genetic algorithms literature.
Metric: soup (anyone can meet anyone)
Rule: A population of agents play the iterated Prisoner's Dilemma with each other, using deterministic strategies based upon the three previous outcomes. (There are 2**70 such strategies.) A genetic algorithm is used to evolve a population of co-adapting agents.
Result: From a random start, most populations of agents first evolve to be un-cooperative, and then evolve further to cooperate based upon reciprocity.
Note: Additional information and software are available at Complexity of Cooperation, Chapter 1, as part of the online collection of software for Axelrod, 1997.

5. March's Organizational Code Model (see March, 1991).
Comment: An good example of learning in an organizational setting.
Metric: 2 level hierarchy
Rules: Mutual learning occurs between members of an organization and the organizational code. The organizational code learns from the members who are good at predicting the environment, while all members learn from the organizational code.
Result: There is a trade-off between exploration and exploitation. For example, there can be premature convergence of the organizational code and all the agents on incorrect beliefs

6. Alvin and Foley's Decentralized Market Model (see Alvin and Foley, 1992).
Comment: A good example of simulation used to study the robustness of markets.
Metric: 1 dimensional ring
Rules: Exchange is initiated by agents who broadcast costly messages indicating their interest in trade. Trade is accomplished by bilateral bargaining between pairs of agents. Agents use information from previous attempts at local trade to calculate their search strategies.
Result: Limited rationality with decentralized advertising and trade can do quite well, giving a substantial improvement in the allocation of resources and average welfare.

7. Kauffman, Macready and Dickenson's NK Patch Model
Kaufmann etal, 1994, and also Kauffman, 1995)
Comment: A very abstract model with an interesting result.
Metric: 2 dimensions
Rules: Each agent's energy depends on state of several agents, forming a rugged NK landscape. The entire 120x120 lattice is partitioned into rectangular patches. For each patch all possible single spin flips within the patch are examined, and one is randomly chosen which leads to lower energy within the patch.
Result: Ignoring some of the constraints (effects beyond the current patch) increases the energy temporarily, but is an effective way to avoid being trapped on poor local optima.

8. Riolo's Prisoner's Dilemma Tag Model (see Riolo, 1997).
Comment: A realization of John Holland's theme about the value of arbitrary tags on agents.
Metric: soup
Rules: Pairs of agents meet at random. If both agree, they play a 4 move Prisoner's Dilemma. An agent is more likely to agree to play with someone with a similar "color" (tag). Strategies use 2 parameters: probability of C after C, and probability of C after D. Genetic algorithm determines next generation's population.
Result: Tags provide a way for reciprocating agents to attain high interaction rates, but then their success is undermined by "mimics" with the same tag. Although the meaning and success of a particular tag is temporary, tags help sustain cooperation in the long run.


Alvin, P., & Foley. D. (1992). Decentralized, dispersed exchange without an auctioneer. Journal of economic behavior and organization, 18, 27-51.

Axtell, R., Axelrod, R., Epstein, J. & Cohen, M. D. (1996). Aligning simulation models: a case study and results. Computational and mathematical organization theory, 1, 123-141.

Axelrod, R. (1987). The evolution of strategies in the iterated Prisoner's Dilemma. In Genetic algorithms and simulated annealing, Lawrence Davis (ed.). London: Pitman; Los Altos, CA: Morgan Kaufman, 32-41.

Axelrod, R. (forthcoming in 1997). The Complexity of Cooperation: Agent-Based Models of Competition and Collaboration. To be published by Princeton University Press in the fall of 1997.

Cohen, M. D., March, J. G., & Olsen, J. (1972). A garbage can theory of organizational choice. Administrative science quarterly, 17, 1-25.

Kauffman, S., Macready, W. G., & Dickinson, E. (1994). Divide to coordinate: coevolutionary problem solving. Santa Fe Institute Working Paper, 94-06-031.

Kauffman, S., (1995). At home in the universe. Oxford and New York: Oxford University Press. See especially 252-64.

March, J. G. (1991). Exploration and exploitation in organizational learning, Organizational science, 2, 71-87.

Poundstone, W. (1985). The recursive universe. Chicago, IL: Contemporary Books.

Riolo, R. (1997). The effects of tag-mediated selection of partners in evolving populations playing the iterated Prisoner's Dilemma. Santa Fe Institute Working Paper, 97-02-016.

Schelling, T. (1974). On the ecology of micromotives. In The corporate society, Robert Morris (ed.). 19-64 (See especially 43-54).

Schelling, T (1978). Micromotives and macrobehavior. New York: W. W. Norton. (See especially 137-55.)

University of Michigan Center for the Study of Complex Systems
Revised April 4, 1997.