# AM04 Duopolies

Varian start his intermediate micro text by stating the maximization and equilbrium are the core principles of micro. Krugman recently stated that I am a “maximization and equilibrium” kind of guy. The goal of this lecture is to show that these two principles fail completely to help us understand behavior is a very simple model of a duopoly.

In last lecture (AM03), we introduced a simple duopoly model. Two ice-cream vendors buy ice-cream wholesale and can sell at any chosen price in the park. If they have matching prices, they split customers. Under Perfect Competition assumptions, with Full Information and Zero Transaction Costs, if they have different prices, then all customers go to the lower price vendor. Straightforward analysis of this duopoly model leads to the following conclusions:

- There is a huge amount of genuine uncertainty – probability calculations required for expected utility cannot be made. We cannot know how many people will come to the park on any given day. We cannot forecast the weather conditions, which influence the demand for ice-cream, with any degree of reliability. This means that vendors will adopt rules-of-thumb to make decisions, rather than maximize anything. This leads to the use of evolutionary Agent Based Models as the preferred modeling technique.
- The strategic calculations we make in the lecture, required by neoclassical theory, are based on EXTREMELY over-simplifying assumptions. In particular, full information eliminates the uncertainty, which in real life, would make estimation of the demand function extremely difficult. Not knowing the demand function, and not knowing the strategy (for price and quantity) that the other vendor will choose, the first vendor cannot possibly calculate profits as a function of his actions. This means that there is no function to “maximize”. The lecture gets over this hurdle by making extremely unrealistic assumptions, to allow us to calculate the demand, so that we can operate in a neoclassical framework. Both sellers know exactly what the other one is doing and exactly how many customers each will get. Furthermore, we show that these are not good approximations, in that when we relax these assumptions, entirely different results emerge.
- The relation between my actions, and their consequences, is mediated by an uncertain environment (weather, number of people), and by a strategic reaction (what the other guy will do). Economists use a revealed preference argument (due to Savage, Ramsey, De-Finetti) that “uncertainty” (horse races) can be reduced to “risk” (dice rolls). This allows them to use subjective Expected utility theory to create target function to maximize in conditions of uncertainty. However, I have shown elsewhere that this reduction is not legitimate. The standard Dutch book argument use to reduce uncertainty to risk is wrong. This material is not covered in the lecture; see my paper on “Subjective Probability Does Not Exist”.
- By changing the parameters (the fixed costs, variable costs, demand) we can get NO equilibria, unstable equilibria, and multiple equilibria. Knowledge of equilibria does not tell us anything about what will happen in the real world. What is all important for understanding behavior of dynamic systems is the disequilibrium dynamics: how do the vendors behave when out of equilibrium. It is this behavior that determines what will happen – convergence to equilibrium, divergence away from equilibrium, or continuous cycling between multiple equilibrium.
- In particular, if we relax the assumptions of full information and zero transaction costs, we find multiple equilibria, including some at which the two vendors charge different prices. This violates the law of one price – the two sellers are identical and selling the identical good, but they charge different prices for it. This is based on the reasonable assumption that even if one vendor charges a higher price, not all customers will leave him to go find the cheaper seller. Either customers do not have information, or they incur transaction costs by walking to the next stall. This shows the extreme sensitivity of supposedly central conclusions of economic theory to the virtually impossible assumptions of full information and zero transaction costs.
- The typical configuration of costs and profits leads to a Prisoner’s Dilemma in the Duopoly – both parties can profit by cooperation, by agreeing to charge the high monopoly price. However, the individual incentive is to under-cut the price, which leads to complete capture of a smaller profit. If both parties under-cut, then they both share a smaller profit. This is a “social dilemma”, where pursuit of selfish individual incentives leads to loss to both players. This is exactly the opposite of the “Invisible Hand” where pursuit of selfish motives (supposedly) leads to social benefits. Conventional Textbooks mention social dilemmas, but do not point out the conflict with the glorious Invisible Hand, since that would go against the ideological theme of free and unregulated markets creating efficiency.

To summarize, even in very simple real world situations, “maximization” is not possible because there is genuine uncertainty, which cannot be reduced to risk (quantifiable uncertainty). We simply do not know, and cannot calculate, the consequences of our actions, because there are too many other variables which determine this outcome. In addition, as studies of dynamic systems reveal, behavior in such systems is governed by disequilibrium dynamics, and not by the equilibria. In complex systems, study of the equilibria will not reveal any interesting aspects of the behavior, showing the economists must study what happens out of equilibrium to understand how the economy will behave. Thus “maximization” and “equilibrium” are not useful tools to study the behavior of even very simple economic systems. Furthermore, the central teaching that if every is free to maximize, this leads to socially optimal outcomes is directly violated in Prisoner’s dilemma situations where pursuit of individual profits cause harm to society, and even to the individual selfishly pursuing his own profits. Thus the main rhetorical strategy of conventional textbooks is to HIGHLIGHT the polar extreme cases where theory of perfect competition holds, which supports their ideological stance. A vast range of cases which deviate, even slightly, from this PERFECTION, are completely neglected and ignored, because they lead to situations where free markets create bad outcomes. Overcoming market failure requires either government intervention, or utilization of social dimensions of human behavior – humans know how to cooperate, and to sacrifice individual/personal gains for welfare of society. Both of these ideas go against the core ideology of conventional textbooks and hence are not pointed out.

Link to Video-Lecture and a detailed 3500 word outline/summary is given below

This is marvelous, Asad. I am very much looking forward to each of your posts!