X. H. Li, and J. P. Huang Department of Physics, Fudan University, Shanghai, 200433, China

1. Business-cycle-like and Entropy-like Phenomena in Human Game Experiments f’=1/(2Δ) Room 1 Δ=10 N agents Consumers M agents Suppliers Model Design The resources are determined by agents, M , differing from MDRAG Δ=6 X. H. Li, and J. P. Huang Department of Physics, Fudan University, Shanghai, 200433, China Room 2 M provide resources N choose resources Δ=3 For N, agents in Room 1 win For M, agents in Room 2 win Introduction Methods A. Hodrick-Prescott filter method {yt} is a time serial about economic developing, and it can be divided into two components, {gt} for the trend parts and {ct} for the cycle parts. Business cycle is always a problem for those economists, policy makers and enterprise leaders, because they want to find out the underlying principle to make decisions for their own sake. So far, researchers have tried a great many of ways to study this problem. Most are based on empirical analysis but few are convinced. Here we provide a bottom-up idea from the agent-based model, MDRAG, and try to reconstruct the business cycle. In the human experiments we set that agents, M, would change their strategies to choose every delta round and three delta values are used. We apply the method of H-P filter and principle of entropy (actually an entropy-like quantity) increase into analysis of the human experiments results. At last an extended model is proposed. Where λ indicates the smoothness of the trend parts If gtand ctare both i.i.d, then the parameter λ can be replaced by ratio of their variances For empirical data, λ = 1600 Human Experiment Results Fig. 1. Showing the human experiments results, N1/N2(M1/M2) changing with time. The blue line stands for the trend component when applied the H-P filter method and the red for the cycle component. Fig. 2. Using Fourier transform method to analyze the trend component (blue line in Fig. 1.) and trying to obtain something cyclical. Fig. 3. Showing the entropy-like quantity changing with time. Clearly, under each delta, the ELQ increases along with time and indicates that human players would take quite short rounds to reach an equilibrium state. On the other hand, this also explains that people have learning ability and adaptability when making choices. Extended Model For further study, we extend the game by giving suppliers (M agents) a threshold of changing the investment strategies under the help of computer modeling. So the frequency of changing M1/M2 will not be stable but depend on the given threshold value. We can see the ELQ now varies spontaneously. B. Entropy-like Quantity (ELQ) in multiple equilibrium game Here S is an entropy-like quantity. In a multiple equilibrium game, the system would reach a stable state along with time, which progress indicates the ELQ increases until stationary. Fig. 4. Up: Person and resource ratios Down: The entropy-like quantity Rather than the resource ratio remains unchanged in MDRAG, we build a game model by making it become unstable, which is determined by agents’ investment strategies. Through the use of method of H-P filter, we get cycles which correspond to deltas we set. Also we find a cyclical increase phenomenon of entropy-like quantity in the experiments. Conclusions W. Wang, Y. Chen, and J. P. Huang, Proc. Natl. Acad. Sci. USA 106, 8423 (2009); Corrections 106, 10872 (2009). R. J. Hodrick and E. C. Prescott, Carnegie Mellon University Discussion Paper, 1980:451