1.Introduction
Complexity has come from abundant subjects of thought and has reacted upon them, from mathematics to physics, from computer science to social sciences. Meanwhile, with the development of economics and the emergence of new way of trade, economics is no longer rife with linearity, continuity and a variety of phenomena that are easily predicted or understood. These phenomena have been labeled as complexity economics. The price system is a typical example of the application of complexity in economics. In this system, there are many similar and interacting parts (individual producers, agents), simple rules to obey (cost-benefit analysis) and aggregate patterns form from individual behavior (price). This report will first introduce the definition and ideas of complexity economics and come to illustrate the characteristics of neoclassical economics. And before moving to concrete examples, it will interpret a relative ideology — the evolution of Walrasian behavior in price system. Then it will demonstrate several examples as concrete applications about price system which embody the operation principle of complexity in it. After that, an overview and a conclusion based on the illustration above will be stated. This report is aimed to introduce a new model and ideology of price system, and then a new ideology about economics, by illustrating and analyzing several representative examples.
2. From neoclassical economics to complexity economics
2.1 Definition of complexity economics
According to Richard H. Day (1994), the definition of complexity in economics in terms of dynamic outcomes is: an economic system that is dynamically complex if its conclusive endogenous processes do not asymptotically lead it to a fixed point, a limit cycle or an explosion (as cited in Rosser, 1996). But this definition is in a broad sense so that some systems that others would argue should not be included are included. To define it in a narrow sense, more specific characteristics are needed and will be stated in the next paragraph.
2.2 A comparison between the two types
Complexity economics seems to be an inversion of neoclassical theory. Axel Leijonhufvud remarks that neoclassical economics “smart people in unbelievably simple situations,” whilst the real world involves “simple people with incredibly complex situations.”(as cited in Gintis,2006). According to Gintis (2006), there are five main aspects where the two types differ. The first one is dynamics: the neoclassical economics is static, linear and thermodynamically closed so that it can be interpreted by algebraic geometry; while the complexity economics is dynamic, nonlinear and thermodynamically open, which lead itself to be far from equilibrium in general. The second one is agents: in the former, agents have “perfect information” and can optimize the information and surplus naturally; while in the latter, agents have “limited information” and face an obstacle of high price in information processing. This characteristic can be associated with the third one. The third one is networks: in neoclassical economics, agents face impersonal price system structure respectively without interaction; however, in complexity economics, agents have to participate in complex overlapping networks so that they can avoid the disadvantages of limited information and high costs in information processing as much as possible. In this way, under some appropriate circumstance, agents economics can form non-optimal but high-efficient model for operating in complex environments. The forth one is emergence: in neoclassical economics, all the macro properties can be derived from its micro properties (for example, the fundamental theorems of welfare); but in complexity economics, macro patterns are emergent properties derived from micro interactions and behaviors, in the same sense that the chemical properties of a complex molecule, such as various carbon of simple substance, is an emergent property derived from its nuclear and electronic structure. In this case, we cannot analytically derive the macro-level properties from micro-level ones (its component parts). The last one is evolution: there is no conditions or necessity to create novelty or growth in complexity in neoclassical economics; while in the complexity economics, the evolution of differentiation, selection and amplification contributes to the novelty and the growth of complexity.
3 The Evolution of Walrasian Behavior in Price System
In neoclassical economics, Walrasian equilibrium is the main concept in price system, which determines the price in markets according to linear supply-demand relationship. It is undeniable that Walrasian theory still plays an irreplaceable part in nowadays economics. However, this theory builds upon a central hypothesis which excludes strategic behavior of manipulating prices directly or indirectly in agents’ own advantages. In Complexity and Artificial Markets (Schredelseker and Hauser, 2008), specific computations are made to illustrate the evolutionary model in price system. It shows the results of simulation experiments about an economy in which agents may have different behavioral rules on price determination.
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Below is the terse and concise summary of the computations of Schredelseker and Hauser (2008). Assume a set of N firms by i = {1, 2,…,N} competing in a market. For every output supplied to the market, this demand function has a clearing price P(Q(t)) for market at which it is sold. Assume all firms are “ex-ante symmetric” with a typical cost function C(q)= c1q(i)c2, where q(i) is the production of each firm i={1,2,…,N}, and the parameters c1 and c2 are positive. The principle that profits induced by current output is P(Q(t))qi −C(qi), i ={1,2,… ,N}. When the profits are realized, firms can choose a better strategy in the long-run operation by comparison and iteration. In this way, the individual profit function can be presented:
And the relative profit is:
From the two functions, we can see the effect on prices that one firm changes its output (quantity) is completely offset by another firm as there is no externalities in the product. And the resulting equation, after maximization and without iteration, simply: P , which means that the price is equal to marginal cost in the Walrasian allocation. So a conclusion can be drawn that only if agents maximize relative profits with no imitation, the Walrasian equilibrium can be reached. Hence, in the real markets, agents imitating the most successful firm from the past round performance so that those strategies that do not perform as well as the average firm will be eliminated before coming to the next round. (Schredelseker and Hauser, 2008)
4 Prisoner’s Dilemma and Complexity
4.1 Introduction
Prisoner’s dilemma, which was framed by Merrill Flood and Melvin Dresher, is a non-zero-sum game in game theory, and also a canonical example of a game analyzed in game theory.
Here is the classical prisoner’s dilemma. “Two prisoners who are partners have been arrested and imprisoned by the police for a crime. They are placed in separate cells and offered an opportunity to confess. If neither confesses then they will both go free and will split their booty equally. However, if one confesses and the other does not then the person confessing will be set free an will get all of their swag. The other prisoner will then go to prison. The final option is for both prisoners to confess, wherein they will both go to prison but for a reduced term.”
4.2 Analysis
There are several concepts in the game theory, corresponding to the maximization of interest in different terms. Nash equilibrium is a condition that players gain nothing by changing only his own strategy. Pareto optimality is a condition that is impossible to make any individual better without making the others worse. The former and the latter focus on individual level and group level respectively.
What would we choose – to cooperate or to defect? Remaining silent seems the best choice for us to reach the Pareto optimality, but it is difficult for each prisoner to do this practically. In the beginning, the dilemma has one assumption. Everyone in the game is selfish. So, we only seek for the maximized interest without considering another, and the result of another is not a decisive factor for us. Reconsidering the dilemma, there are two situations for another – betrays or remains silent, betray another seems a dominant strategy for us. Betraying another seems a rational choice for each individual, but overall it is not a rational and number one choice.
However, the situation would change if we repeat countless time. Being fear of punishment in the following rounds, the prisoners would avoid betraying each other, and being confident to remain silent, therefore the probability of reaching Pareto optimality would be increase, and the result seems to be more rational for entirety.
4.3 Real-life Examples in Economics
There are some real-life examples of the prisoner’s dilemma. One is the price collision in supermarket industry. Two participants could be Wellcome and PARKnSHOP, which are the two biggest supermarket chains in Hong Kong. The action of cooperation increases the prices of particular goods, and the action of noncooperation is on the contrary. The other example is the tariff war between the countries. Two participants could be China and the United State. The action of cooperation decreases the tariff, and the action of noncooperation is on the contrary.
4.4 Complexity
Prisoner’s dilemma seems no relationship with complexity, but it is wrong in fact. If we increase the number of prisoners and repeat countless time, the dilemma would start to reflect the behavior of complexity.
Firstly, it involves some living creatures, which are having unpredictable and irrational behaviors sometimes, so each participant is able to make mistakes from time to time. Secondly, the block of the information flow and the fear of punishment from the other are generating a pattern of constantly changing distributions of the strategies. With the increase in the number of repetitions, the dilemma would reflect a evolve strategy, which means the result of each experience being close to the Pareto optimality, by considering other participants in the experience and obtain a most favorable result in overall situation.
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In the dilemma, individuals are independent, and being imprisoned separately, so one’s decision is not affected by outside information. Moreover, although there are only two choices for an individual – to operate or to defect, when we increase the number of prisoners, the experience will give rise to complex collective behavior that fights for the maximum interest of entirety, and evolving to the Pareto optimality.
5 Oil price
The price of oil affects many other goods and services like transportations because oil is used as a source of energy in these activities. No one would like to pay higher price, yet the global market of oil depends on many different factors. In this rapid globalizing world, price of oil is not only affected by simply market’s demand and supply. There are more factors that are unexpectedly affecting the oil price in the world.
Factor 1: OPEC
OPEC (The Organization of Petroleum Exporting Countries) is a consortium of petroleum exporting countries in the world, which is responsible for 40% of world’s oil production (LiveCharts, 2014). Its job is to balance the oil production of member countries and world consumption. Since 40% of oil production is under OPEC’s control, any word it says would impact the world oil price a lot. In 2007-2008, oil price in the world increased a lot because OPEC has reduced the oil production of member countries in 2006, leading to an insufficient supply and hence raised oil price in the world’s oil market (Clover Global Solutions, 2012).
Factor 2: Oil inventories
Oil inventory is a measure to keep demand and supply in a harmonious balance (Clover Global Solutions, 2012). When the market supply exceeds the market demand, it stores the excess supply. When consumption is more than production, oil inventories provide oil to the unsatisfied market. Oil inventories allow corrections to the oil market in either direction (LiveCharts, 2014). It adjusts the oil price by regulating the supply and demand, keeping the oil market in a balance. Without oil inventories, price level falls dramatically when supply exceeds demand, and vice versa.
Factor 3: Restrictive legislation
Legislation has great impacts on oil price. Some energy policies may affect demand of oil, hence affecting the price. Apart from energy policies, tax is also one of the examples (Caltex, 2014). If the tariff of importing oil is increased, market price of oil will certainly increase. Saudi Arabia is an obvious example of using policies to affect market price of oil. Saudi Arabia interfere the oil market in order to ensure the long-term use of crude oil as a major source of energy in the world, stabilize world’s oil markets in short run and ensure the importance of the country itself to the world. In 80s, the oil production of Saudi Arabia was restricted by the OPEC because of the official price system of oil the country is adhering. Yet some of the members of OPEC cheated on the production quota, leaving the whole burden of the adjustment to Saudi Arabia. To counteract, Saudi Arabia abandoned the official price system, switching to the market-based pricing system. Huge amount of oil supply are then pushed into the market, reducing the oil price from $28/barrel in 1985 to $14/barrel in 1986. Saudi Arabia uses its oil production as a weapon to establish discipline on OPEC, affecting world’s oil price (Country-data, 1992).
Factor 4: Financial market – oil trading contracts
An oil trading contract is a guarantee on future oil supply and demand. Once suppliers and consumers signed an oil trading contract, supplier needs to provide a specific amount of oil at a specific price in a specific period and consumer needs to buy the specific amount of oil during the period (Clover Global Solutions, 2012). Parties signed the oil trading contracts to avoid any price change in the future, or to ensure supply or demand (Investopedia, 2014). Number of oil trading contracts increases over the years (EIA, 2014). Once a contract is signed, oil available in the future to the market is decreased, and so is the demand, reducing variables to future oil price.
Factor 5: Speculative buying
People scalp everything in the world. Oil is not an exception. In some period, people may foresee the price of oil will rise in the future. In this case, speculator will buy in oil trading contracts and sell it when the price is high. In 2008, speculators who predicted a rise in oil price bade up the oil price to $140/barrel, creating an unsustainable price level. Yet, since the market demand cannot support the inflation of oil price level, oil price dropped to $30/barrel in 2009 (Clover Global Solutions, 2012).
There are many more other factors affecting the world oil price. The above-mentioned are only some major factors. Others like production cost, political unrest, exchange value of dollars, spot markets, local and global competitions and world crisis are the minor ones and would not be discussed deep here.
6 Overview on the change of price system
Price system nowadays has changed a lot from the past decades. Due to globalization, more and more elements are introduced into the price system like the above-mentioned political unrest, trading contracts and exchange value of dollars. We are impressed by the elements in the current price system. Before doing this study, we did not think of so many contributing factors to the price variation. The research we have done gave us a brand new view to the price system. In the economics lessons we have had before, we can only learn something like demand and supply, tariff and competition. When we go to a macro view to the price system, we discovered that there can be many other variables to a market. We look forward to the change of the price system in the future.
7 Conclusion
There are many examples in complexity economics. Previously, we illustrated the differences between neoclassical economics to complexity economics, evolution of walrasian behavior in price system, and overview on the change of price system. Moreover, we explained the relationship between complexity and two examples in economics – the prisoner’s dilemma, and oil prices.
After “the Wealth of Nations” was published in 1776, the academia in economics discussed the classical economics, and studied land, labor and capital by a simple and predictable model. But nowadays, the capitals in economics involve more in the group psychology of living creatures (prisoner’s dilemma), and other unpredictable factors, e.g. weather (oil prices), therefore some aspects of economics nowadays are growing into a new branch called complexity economics.
Although the complexity economics is more unpredictable than the classical economics, it is beneficial to the relationship between economics and other disciplines, e.g. meteorology, and it is similar to the interdisciplinarity of other science disciplines, leading economics to be a more macro and more interdisciplinary discipline, and not a specialized, and it is a better way for the development of economics also.
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