期刊
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
卷 110, 期 4, 页码 1232-1236出版社
NATL ACAD SCIENCES
DOI: 10.1073/pnas.1109672110
关键词
high-dimensional chaos; statistical mechanics
资金
- National Science Foundation [0624351, 0965673]
- Research Councils United Kingdom Fellowship [EP/E500048/1]
- Engineering and Physical Sciences Research Council (United Kingdom) [EP/I019200/1]
- Direct For Social, Behav & Economic Scie
- Divn Of Social and Economic Sciences [0624351] Funding Source: National Science Foundation
- Divn Of Social and Economic Sciences
- Direct For Social, Behav & Economic Scie [0965673] Funding Source: National Science Foundation
Game theory is the standard tool used to model strategic interactions in evolutionary biology and social science. Traditionally, game theory studies the equilibria of simple games. However, is this useful if the game is complicated, and if not, what is? We define a complicated game as one with many possible moves, and therefore many possible payoffs conditional on those moves. We investigate two-person games in which the players learn based on a type of reinforcement learning called experience-weighted attraction (EWA). By generating games at random, we characterize the learning dynamics under EWA and show that there are three clearly separated regimes: (i) convergence to a unique fixed point, (ii) a huge multiplicity of stable fixed points, and (iii) chaotic behavior. In case (iii), the dimension of the chaotic attractors can be very high, implying that the learning dynamics are effectively random. In the chaotic regime, the total payoffs fluctuate intermittently, showing bursts of rapid change punctuated by periods of quiescence, with heavy tails similar to what is observed in fluid turbulence and financial markets. Our results suggest that, at least for some learning algorithms, there is a large parameter regime for which complicated strategic interactions generate inherently unpredictable behavior that is best described in the language of dynamical systems theory.
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