Modeling Decentralized Price Fluctuations Through Agent-Based Recognition of Scarcity

Since the time of Leon Walras, general equilibrium theory and the hypothetical Walrasian auctioneer have dominated market economics. Prices of commodities are assumed to reach "true" equilibrium values based on the underlying supply and demand curves of an economy, which can be represented by equations. In contrast to classical methods, the model in this paper attempts to show the behavior of an economy based on the cumulative actions and interactions of individuals in the system. Agents each produce one of ten commodities and trade with each other to fulfill their consumption needs for those commodities. They are able to change their price expectations to respond to scarcity, and may change which commodity they produce to take advantage of increased prices. The total amount of each commodity consumed is the metric by which the efficiency of a parameter configuration of the model is determined. Empirical analysis confirms that the model’s prices and consumption behaved in a manner similar to how free markets are thought to operate. Introduction and related work The agent-based simulation presented in this paper models a simple economy in terms of the human agents that make it up. As Axtell recently demonstrated[2], the traditional Walrasian auctioneer is not scalable to the size of actual economies, which refutes its existence. Economists have long realized this was the case, of course. The traditional equation-based descriptions of market equilibria were created not because they were thought to reflect the actual dynamics of real trading, but because they were a simple and useful method of understanding and predicting future economic events. Recently, however, new computational tools have become available that greatly lower the time required to simulate individual market transactions in an agent-based manner, promising to achieve a more detailed understanding of the economy. According to Alfred Marshall[6], the total supply and demand for goods in an economy can be aggregated to form an equation to find what level of price and production will result in the optimal level of consumption. This rests on the idea that different agents want different amounts of goods and are willing to pay different amounts for them. The aggregate of the wants of the consumers and suppliers can be used to determine the socially optimal amount produced and the price at which it is to be sold. This traditional technique has very modest computational requirements, and has been useful for getting rough ideas of the behavior of an economy even though it was known all along that prices do not actually get established by a global auctioneer. The mantra “all models are wrong, but some are useful”[7] is certainly applicable here. It is intuitively appealing, however, to study the economy as the interactions of the individuals who make it up. The founder of the Austrian School of Economics, Carl Menger, came to the relatively apparent, but no less important conclusion that not all humans behave the same way. Specifically, the realization that not all people value the same item to the same degree meant that both parties could gain from a trade and there would be more utility in the system without a physical increase in output.[5] The classical school posits that the representative agent can be substituted for the whole in order to study the effects upon the macro economy. The weakness of this hypothesis is in believing that a normal population and a single agent who is the average of that population will behave in the same way. As Kirman stated in his critique of the representative individual, “there is no plausible formal justification for the assumption that the aggregate of individuals, even maximizers, acts itself like an individual maximizer.”[3] There is also no reason to assume that a change in the environment of the representative individual will have the same economic impact as the same change enacted upon an interacting collective. Also, a heterogeneous population (as every real society is) behaves very differently than a population composed of individuals who were all “average.” For a very blunt example, our world behaves very differently than if composed of individuals who, like the “average person,” each had one ovary and one testicle. Simply aggregating the attributes of the agents does not represent the interactions present in a system of heterogeneous agents. Kirman also states the converse: that, for these reasons, there is no reason to believe that, because a collective is observed to behave rationally, the individuals who make it up must be rational as well. It can follow that the appearance of rationality, which paradoxically provides the basis for the classical assumption that the macroeconomic behavior has similarly rational microeconomic underpinnings, may result from non-apparent results of interactions within a heterogeneous population. It has been observed that prices change in predictable ways with regard to scarcity in the real world. When there is a political crisis in the Middle East, the price of oil and gas rises because the supply is less than the demand. People compete for the good, with the result that those who want it more (have a greater willingness to pay) obtain it and those who want it less decide they can do without it. The relative scarcity is indicated by the price level. Axtell states in “The Complexity of Exchange” that “agents use past prices to form idiosyncratic forecasts of future prices, and trade accordingly. New prices are created. Over time forecasting rules evolve, unprofitable ones are replaced by speculative ones, and the population of agents co-evolves to one another.”[2] Distributed and uncoordinated determination of prices seems more like the real world than the metaphor of the Walrasian auctioneer. This, again, makes intuitive sense, but the exact method or methods of price determination are still waiting to be worked out. Albin and Foley demonstrated in their “Distributed Exchange Without an Auctioneer” that agents trading from a random beginning distribution can greatly reduce inequality of utility, but fall short of the level of equality possible with the auctioneer[1]. The utility was determined by a Cobb-Douglas function of two goods. Each agent was given a random endowment of each good which added to a total of 100. They proceeded to engage in bilateral bargaining and develop searching strategies based on the acquired information for a certain number of trades to see how equitable a distribution can be reached. The fact that agents can gather information and trade to approximate Walrasian maximum utility in a market given a finite amount of time is interesting and a necessary logical step to showing how a real economy operates. In time, however, past strategies and trades will affect future production and utility will need to be calculated again. Our model tries to see the behavior of price, production, and scarcity in a market over time and what patterns of these factors emerge over time based on consecutive attempts to maximize utility.