Agent-based Monetary Models

Economy is a complex adaptive system, and the interaction of microcosmic individual determines the macroeconomic dynamics, while the macroeconomic dynamics has influence on the behavior of microcosmic individual. In this paper, from the view of limited logos and evolving economy, we apply agent-based economic modeling ways to research the behavior of learning equilibrium and selecting equilibrium in monetary economy. Inspired by the evolutionism of Darwinian, Holland developed genetic algorithm in 1975. Genetic algorithm is a kind of social learning model, and individual of population evolve through copy, changing beliefs and trial. Genetic algorithm provides methodology with microcosmic foundation to research macroeconomics from the view of evolution. Classifier system is a kind of rule learning system, developed by Holland in 1986, and it guides the behaviors of system in outer environment through learning rules and combines simple logic rules with searching new rules by genetic algorithm. Classifier system is viewed as individual learning model, differing from genetic algorithm. We provide an overlapping generations model based on genetic algorithm to research on equilibrium selection issues in inflation economies. In an overlapping generations model, there are two monetary regimes to be selected for the government: (1)"constant real deficit"regime, that is, the government decides a constant real deficit and maintain that real deficit by adjusting the supply of money; (2) "fixed growth rate of money"regime, that is, the government decides a fixed growth rate of money and maintain it by adjusting seignorage. However, whichever monetary regime the government takes, there always are two inflation equilibriums in an overlapping generations model, and the selection of equilibrium becomes an important issues in the research of economic theories. This paper, from the view of learning expectation, uses genetic algorithm to simulate the evolving dynamics of inflation expectations under constant real deficit and fixed growth rate of money regimes in overlapping generations model, then research: (1) under the two monetary regimes, the process of initial convergence to the inflation equilibrium; (2) after the parameters of monetary regimes, the process of switching from initial equilibrium to new one; (3) whether the two monetary regimes will lead to different inflation mobility of this two regimes. The agents in economics apply genetic algorithm to learn correct forecast rules and make consumption decisions to resolve utility maximization problems according to expectations. We apply C++Builder program to realize this model. We use not only traditional operators, such as reproduction, crossover and mutation, but also special ones, election operator and weak election operator. The result from these experiments shows: (1) with the evolution of the agents'expectations in economics, both of models fluctuante converge to the Pareto superior rational expectations equilibrium. (2) the change of economic parameter leads to the change of the expectation of agent, and with the change of expectation, the inflation switches to the new Pareto superior rational expectations equilibrium. Due to study, in the switching process, the mobility of inflation is far less than initial one, and the switching velocity is faster the convergence velocity. (3) Under the two different monetary regimes, there is no much difference in the mobility of inflation, and the hypothesize of Friedman(1977) are not held. Therefore, the results capture the three features of human agent experiment, and describe the fluctuate and the convergence process. We also provide a Kiyotaki-Wright model of money based on classifier system to analyze the behavior of agent in equilibrium and the dynamic ofmoney being a media of exchange. The essence of the Kiyotaki-Wright model is "consistent demands"called by Jevons(1875). In this environment, individual can not trade his production for the good that can give him positive utility, so he must make trade decision among competitive goods. There are two trade strategies for the agent: fundamental strategy and speculative strategy. Fundamental strategy is the one to lower storage cost, while speculative strategy is the one that agent offers to trade for the good that will increase his storage cost in order to get the good he can consume easily. According to the two strategies, there are two equilibrium: fundamental and speculative. Furthermore, they introduce legal money into the model, and there is an equilibrium that legal money is used as the media of exchange. We model the behavior rules of artificial agent on the basis of the evidence of experiment with human agent. The focus of the experiment is on the role of token in this environment. Classifier system is used to simulate learning behavior of agent, and differing from the design of Marimon,McGrattan and Sargent(1990), we give every agent a classifier system in order to separate the direct and indirect communications of agents. Like Duffy and Ochs(2000), our findings suggest that there is some support for the theoretical predictions; in particular, we find that subjects nearly always offer to trade for the token object when such a trade lowers their storage costs. However, contrary to theory, we also find that subjects frequently refuse to offer to trade the token object for more costly-to-store goods when the theory predicts they should make such trades. The same as the theory, the acceptability of the token object, good 0, appears not to be sensitive to the supply of good 0, and the acceptability of the intrinsically valued good 1 decreases with increases in the supply of good 0. This result differs from the findings of Duffy and Ochs(2000), but it is near to the theory. The results also suggest that artificial agent-based modeling may be...