Fairness plays a key role in explaining the emergence and maintenance of cooperation. Opponent-oriented social utility models were often proposed to explain the origins of fairness preferences in which agents take into account not only their own outcomes but are also concerned with the outcomes of their opponents. Here, we propose a payoff-oriented mechanism in which agents update their beliefs only based on the payoff signals of the previous ultimatum game, regardless of the behaviors and outcomes of the opponents themselves. Employing adaptive ultimatum game, we show that (1) fairness behaviors can emerge out even under such minimalist assumptions, provided that agents are capable of responding to their payoff signals, (2) the average game payoff per agent per round decreases with the increasing discrepancy rate between the average giving rate and the average asking rate, and (3) the belief update process will lead to 50%-50% fair split provided that there is no mutation in the evolutionary dynamics.

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Recently it was shown that financial time series are not completely random process but exhibit long-term or short-term dependences, which offer promises for predictability. However, we do not clearly understand the potential relationship between serial structure and predictability. This paper proposed a framework to magnify the correlations and regularities contained in financial time series through constructing accumulative return series. This method can help us distinguish the real world financial time series from random-walk process effectively by examining the change patterns of volatility, Hurst exponent, and approximate entropy. Furthermore, we have found that the predictable degree increases continually with the increasing length of accumulative return. Our results suggest that financial time series are predictable to some extent and approximate entropy is a good indicator to characterize the predictable degree of financial time series if we take the influence of their volatility into account.

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Structural information contained in financial time series can be magnified effectively by constructing the accumulative return. In order to make the magnification effects of different financial time series comparative, we first propose a standard method to characterize the strength of the accumulative magnification effect. Then, we employ decomposed-randomized technology to uncover the formation mechanism of the accumulative magnification effect. Our results show that (1) the standard deviation pattern is determined by volatility dependence, (2) the Hurst exponent pattern is induced by sign dependence, (3) an approximate entropy pattern is caused by the combined effect of sign dependence and volatility dependence.

Uncovering the evolutionary dynamics of economies is helpful for us to design economic policy. This paper develops an economic evolution model by examining the coupled dynamics of industry growth and interindustry structure. For each industry, its economic properties (mainly characterized by price and quantity) are incorporated into the model. The input-output relationships among different industries are described as input-output networks, in which nodes represent industries, and weights represent technological and economic constraints between pairing industries. By measuring the dynamic importance of each node, we find that all the nodes in the input-output networks have the same dynamic importance. On the basis of this empirical regularity and the rational expectation assumption, we show that the coupled dynamics of the economic properties of nodes and input-output networks can explain the evolutionary dynamics of national economies.

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