Robert Axelrod

An Evolutionary Approach to Norms

Iorms provide a powerful mechanism for regulating conflict in groups, even when there are more than two people and no central authority. This paper investigates the emergence and stability of behavioral norms in the context of a game played by people of limited rationality. The dynamics of this new norms game are analyzed with a computer simulation based upon the evolutionary principle that strategies shown to be relatively effective will be used more in the future than less effective strategies. The results show the conditions under which norms can evolve and prove stable. One interesting possibility is the employment of metanorms, the willingness to punish someone who did not enforce a norm. Many historical examples of domestic and international norms are used to illustrate the wide variety of mechanisms that can support norms, including metanorms, dominance, internalization, deterrence, social proof, membership in groups, law, and reputation.

The Dissemination of Culture A MODEL WITH LOCAL CONVERGENCE AND GLOBAL POLARIZATION

Despite tendencies toward convergence, differences between individuals and groups continue to exist in beliefs, attitudes, and behavior. An agent-based adaptive model reveals the effects of a mechanism of convergent social influence. The actors are placed at fixed sites. The basic premise is that the more similar an actor is to a neighbor, the more likely that that actor will adopt one of the neighbors traits. Unlike previous models of social influence or cultural change that treat features one at a time, the proposed model takes into account the interaction between different features. The model illustrates how local convergence can generate global polarization. Simulations show that the number of stable homogeneous regions decreases with the number of features, increases with the number of alternative traits per feature, decreases with the range of interaction, and (most surprisingly) decreases when the geographic territory grows beyond a certain size.

Advancing the art of simulation in the social sciences

Advancing the state of the art of simulation in the social sciences requires appreciating the unique value of simulation as a third way of doing science, in contrast to both induction and deduction. This essay offers advice for doing simulation research, focusing on the programming of a simulation model, analyzing the results and sharing the results with others. Replicating other people’s simulations gets special emphasis, with examples of the procedures and difficulties involved in the process of replication. Finally, suggestions are offered for building of a community of social scientists who do simulation.

the Further Evolution of Cooperation

Axelrods model of the evolution of cooperation was based on the iterated Prisoners Dilemma. Empirical work following this approach has helped establish the prevalence of cooperation based on reciprocity. Theoretical work has led to a deeper understanding of the role of other factors in the evolution of cooperation: the number of players, the range of possible choices, variation in the payoff structure, noise, the shadow of the future, population dynamics, and population structure.

The Emergence of Cooperation among Egoists

This article investigates the conditions under which cooperation will emerge in a world of egoists without central authority. This problem plays an important role in such diverse fields as political philosophy, international politics, and economic and social exchange. The problem is formalized as an iterated Prisoners Dilemma with pairwise interaction among a population of individuals.Results from three approaches are reported: the tournament approach, the ecological approach, and the evolutionary approach. The evolutionary approach is the most general since all possible strategies can be taken into account. A series of theorems is presented which show: (1) the conditions under which no strategy can do any better than the population average if the others are using the reciprocal cooperation strategy of TIT FOR TAT, (2) the necessary and sufficient conditions for a strategy to be collectively stable, and (3) how cooperation can emerge from a small cluster of discriminating individuals even when everyone else is using a strategy of unconditional defection.

Evolution of cooperation without reciprocity

A long-standing problem in biological and social sciences is to understand the conditions required for the emergence and maintenance of cooperation in evolving populations. For many situations, kin selection is an adequate explanation, although kin-recognition may still be a problem. Explanations of cooperation between non-kin include continuing interactions that provide a shadow of the future (that is, the expectation of an ongoing relationship) that can sustain reciprocity, possibly supported by mechanisms to bias interactions such as embedding the agents in a two-dimensional space or other context-preserving networks. Another explanation, indirect reciprocity, applies when benevolence to one agent increases the chance of receiving help from others. Here we use computer simulations to show that cooperation can arise when agents donate to others who are sufficiently similar to themselves in some arbitrary characteristic. Such a characteristic, or ‘tag’, can be a marking, display, or other observable trait. Tag-based donation can lead to the emergence of cooperation among agents who have only rudimentary ability to detect environmental signals and, unlike models of direct or indirect reciprocity, no memory of past encounters is required.

Effective Choice in the Prisoner's Dilemma

This is a “primer” on how to play the iterated Prisoners Dilemma game effectively. Existing research approaches offer the participant limited help in understanding how to cope effectively with such interactions. To gain a deeper understanding of how to be effective in such a partially competitive and partially cooperative environment, a computer tournament was conducted for the iterated Prisoners Dilemma. Decision rules were submitted by entrants who were recruited primarily from experts in game theory from a variety of disciplines: psychology, political science, economics, sociology, and mathematics. The results of the tournament demonstrate that there are subtle reasons for an individualistic pragmatist to cooperate as long as the other side does, to be somewhat for-giving, and to be optimistic about the other sides responsiveness.

More Effective Choice in the Prisoner's Dilemma

This study reports and analyzes the results of the second round of the computer tournament for the iterated Prisoners Dilemma. The object is to gain a deeper understanding of how to perform well in such a setting. The 62 entrants were able to draw lessons from the results of the first round and were able to design their entries to take these lessons into account. The results of the second round demonstrate a number of subtle pitfalls which specific types of decision rules can encounter. The winning rule was once again TIT FOR TAT, the rule which cooperates on the first move and then does what the other player did on the previous move. The analysis of the results shows the value of not being the first to defect, of being somewhat forgiving, but also the importance of being provocable. An analysis of hypothetical alternative tournaments demonstrates the robustness of the results.

Aligning simulation models: A case study and results

This paper develops the concepts and methods of a process we will call “alignment of computational models” or “docking” for short. Alignment is needed to determine whether two models can produce the same results, which in turn is the basis for critical experiments and for tests of whether one model can subsume another. We illustrate our concepts and methods using as a target a model of cultural transmission built by Axelrod. For comparison we use the Sugarscape model developed by Epstein and Axtell.The two models differ in many ways and, to date, have been employed with quite different aims. The Axelrod model has been used principally for intensive experimentation with parameter variation, and includes only one mechanism. In contrast, the Sugarscape model has been used primarily to generate rich “artificial histories”, scenarios that display stylized facts of interest, such as cultural differentiation driven by many different mechansims including resource availability, migration, trade, and combat.The Sugarscape model was modified so as to reproduce the results of the Axelrod cultural model. Among the questions we address are: what does it mean for two models to be equivalent, how can different standards of equivalence be statistically evaluated, and how do subtle differences in model design affect the results? After attaining a “docking” of the two models, the richer set of mechanisms of the Sugarscape model is used to provide two experiments in sensitivity analysis for the cultural rule of Axelrods model.Our generally positive experience in this enterprise has suggested that it could be beneficial if alignment and equivalence testing were more widely practiced among computational modelers.

Evolution of cooperation among tumor cells

The evolution of cooperation has a well established theoretical framework based on game theory. This approach has made valuable contributions to a wide variety of disciplines, including political science, economics, and evolutionary biology. Existing cancer theory suggests that individual clones of cancer cells evolve independently from one another, acquiring all of the genetic traits or hallmarks necessary to form a malignant tumor. It is also now recognized that tumors are heterotypic, with cancer cells interacting with normal stromal cells within the tissue microenvironment, including endothelial, stromal, and nerve cells. This tumor cell–stromal cell interaction in itself is a form of commensalism, because it has been demonstrated that these nonmalignant cells support and even enable tumor growth. Here, we add to this theory by regarding tumor cells as game players whose interactions help to determine their Darwinian fitness. We marshal evidence that tumor cells overcome certain host defenses by means of diffusible products. Our original contribution is to raise the possibility that two nearby cells can protect each other from a set of host defenses that neither could survive alone. Cooperation can evolve as by-product mutualism among genetically diverse tumor cells. Our hypothesis supplements, but does not supplant, the traditional view of carcinogenesis in which one clonal population of cells develops all of the necessary genetic traits independently to form a tumor. Cooperation through the sharing of diffusible products raises new questions about tumorigenesis and has implications for understanding observed phenomena, designing new experiments, and developing new therapeutic approaches.