Complex dynamics in learning complicated games

被引:87
作者
Galla, Tobias [1 ]
Farmer, J. Doyne [2 ,3 ,4 ]
机构
[1] Univ Manchester, Sch Phys & Astron, Manchester M13 9PL, Lancs, England
[2] Univ Oxford, Oxford Martin Sch, Institute New Econ Thinking, Oxford OX1 3LP, England
[3] Univ Oxford, Math Inst, Oxford OX1 3LP, England
[4] Santa Fe Inst, Santa Fe, NM 87501 USA
基金
英国工程与自然科学研究理事会; 美国国家科学基金会;
关键词
high-dimensional chaos; statistical mechanics; NORMAL-FORM GAMES; STATISTICAL MECHANICS; INFORMATION THEORY; NASH EQUILIBRIA; MODEL; CHAOS;
D O I
10.1073/pnas.1109672110
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
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.
引用
收藏
页码:1232 / 1236
页数:5
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