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3. Evolutionarily stable strategies

In the population dynamics simulations, a population number is associated with each strategy, to indicate how many "organisms" in the overall population are following the strategy. In each generation, the score received by an organism is the score it would receive in playing a series of one-on-one games with every organism in a representative sample of the total pop- ulation. At the end of each generation, the total score accumulated by organisms using a given strategy determines how many organisms of that type will exist in the next generation. (A process of this sort-in which success in one round determines influence or existence in the next-distinguishes evolutionary game theory from conventional game theory. Evolutionary game theory need make no assumptions about motives or values, though it is natural to think in terms of a "survival motive" which generates a "success motive".)

As Figure 2 shows, in a population dominated by suckers, a small population of con men have a great advantage, rising to temporary dominance. But in doing so, they drive down the population of suckers and so lose their advantage; they are then driven to extinction by TIT FOR TAT. As shown in the diagram, an environment with enough TIT FOR TAT players to fight off an invasion of con men can support a stable population of suckers.

In this ecosystem, TIT FOR TAT can be termed an evolutionarily stable strategy, or ESS. An ESS is a strategy which, given that it dominates an ecology, cannot be invaded by any other strategy [10,7]. In Maynard Smith's terminology, "ESS" refers to a specific detailed strategy (such as TIT FOR TAT); here, the term will refer to general classes of strategies that share basic characteristics, such as being "nice and retaliatory". The rules governing a given ecology determine the success of different strategic characteristics, and therefore the ESS.

As shown, suckers are not an ESS in Axelrod's system because they can be invaded by con men. Con men are not an ESS except in a trivial sense-a population consisting purely of con men cannot be invaded by a small, scattered group of TIT FOR TAT players. A small but significant number of invaders, however, can cooperate, expand, and completely replace a population of con men. A population dominated by any strategy that is both nice and sufficiently retaliatory cannot be invaded by any strategy that is not. Any population dominated by a strategy that is not both nice and sufficiently retaliatory can be invaded. Therefore, the ESS of the Axelrod tournament is to be nice and retaliatory.

A single population-dynamics process can be described as an ecosystem, but not as an evolutionary ecosystem, since there is no source of variation. Axelrod's series of two tournaments included variation from one to the next, and hence qualifies. To transform it into a better example of an evolutionary ecosystem, imagine a continuing tournament open to outside contestants able to create new strategies and introduce them in small numbers. In any such open, evolving ecosystem, given no special restrictions on allowable variations, one should expect the ecosystem to become populated primarily by an ESS. The properties of such an ESS will often indicate emergent properties of the system. For example, in any open Axelrod ecosystem most moves will be cooperative.

The above discussion of Axelrod's system benefits from hindsight. The original game-theory experts who submitted the original strategies knew the rules, and those who submitted strategies for the second tournament even had the benefit of a bit of hindsight from the first tournament. Nevertheless, in both cases most of the strategies submitted were not nice, and so were not ESSs. The analyses which follow cover much more complex ecosystems, in which the nature of strategies and payoffs are much more subtle.

As a result, many of the points made in the rest of this paper are not settled conclusions, but merely initial hypotheses to be tested. The best testing methodology is that used by Axelrod: run a system and open it to outside contributors. The goal is to understand what properties of a computational ecosystem will result in useful system behavior.

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