Some games are just too complicated.

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Equilibrium is the point of optimal exchange, and the strategies of rational agents have long fascinated game-theorists. However, many games are just too complex for human players as a recently published scholarly paper demonstrates. Mark Buchanan, a columnist for "Bloomberg" and author of the forthcoming book "Forecast", noticed its practical value early in his blog "The physics of finance".
 
In a simulation experiment, Tobias Galla from The University of Manchester and Professor Doyne Farmer from Oxford University and the Santa Fe Institute, analyzed the strategies in two-player games in which success is based on experience. Simple games with a few moves such as Noughts and Crosses become uninteresting fast because the strategy is easy to guess. The strategies of the players converge at fixed points. In complex games like Chess, Go, and some cardgames, however, the players act less rational, and it is hard for them to identify optimal strategies. The games follow limited cycles, are random or chaotic. The findings challenge the classical equilibrium theories, and may explain phenomena like the volatility of stock markets. Preliminary results with a multi-player variant indicate that the chances of establishing equilibrium decreases as the number of players increases.
 
Computer simulation studies are by their very nature abstract, but convincing in their conceptualization. To prove that there is equilibrium is one thing, but to develop the strategies leading to it another. In complex environments with many options, individuals seem to be overcharged given the limits of memory and motivation. Therefore, the study may be a milestone for physics entering economics, but is certainly comforting for anyone not having found the optimal path to equilibrium in complex social situations.