Foundational Papers in Complexity Science pp. 2285–2309
DOI: 10.37911/9781947864559.73
Simple Dynamics with Rich Implications
Author: W. Brian Arthur, SRI International; Santa Fe Institute
Excerpt
Every so often a paper comes along with a simple setup but a richness of implications. Kristian Lindgren’s (1991) is such a paper. It appeared thirty years ago, and I still find it striking.
Lindgren constructed a computerized tournament where strategies compete in pairs to play an iterated prisoner’s dilemma game. Players play one-against-one in a repeated sequence of rounds, and each time they have two options: “cooperate” or “defect.” There’s a tension here. Neither player knows what the other will choose. If you and your opponent choose to cooperate, both will do quite well. But if you choose to defect—take advantage—you can do a bit better. However, if your opponent defects as well, you will both be harmed. Cooperating, defecting, and retaliating are all possible; and you need to choose judiciously if you want to do well.
The number of players in the tournament is kept fixed, and each plays a given strategy in the repeated game, a set of fixed instructions for how to act given its own and its opponent strategy’s immediate past actions. All strategies play all strategies in a given round or “generation.” If a strategy performs well over its encounters, it gets to replicate; if it does poorly, it dies and is removed. Existing strategies can mutate their instructions with a small probability, thus creating new ones. Lindgren adds two important ingredients to the mix: strategies can make occasional mistakes, so there is some “noise,” and they can occasionally “deepen”—that is, mutate by using deeper memory of their opponent’s immediate past moves and their own. This allows them to “read” their opponents’ moves better, anticipate them, and become smarter.
Bibliography
Arthur, W. B. 1994. “Inductive Reasoning and Bounded Rationality: the El Farol Problem.” American Economic Review 84:406–411. https://www.jstor.org/stable/2117868.
― . 2021. “Foundations of Complexity Economics.” Nature Reviews Physics 3:136–45.
Lindgren, K. 1991. “Evolutionary Phenomena in Simple Dynamics.” In Artificial Life II, edited by C. G. Langton, C. Taylor, J. D. Farmer, and S. Rasmussen, 295–312. Reading, MA: Addison-Wesley.
Lindgren, K., and M. G. Nordahl. 1994. “Evolutionary Dynamics of Spatial Games.” Physica D: Nonlinear Phenomena 75 (1–3): 292–309. https://doi.org/10.1016/0167-2789(94)90289-5.