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3 - On building theoretical models using game theory

Published online by Cambridge University Press:  05 October 2014

Lawrence A. Boland
Affiliation:
Simon Fraser University, British Columbia
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Summary

The last dozen years have seen a reformulation of general equilibrium theory in which ‘markets’ and ‘market behavior’ are pushed into the background while the acts of individual exchange are brought into sharper focus. This game-theoretic approach to microeconomics, whose progenitor was Edgeworth not Walras, is likewise important for the light it sheds on the microfoundations of macroeconomics. Although less well-developed than neo-Walrasian analysis, Edgeworthian models too can formulate at the disaggregated level a number of intrinsically macroeconomic concerns. …

Consider the concept of equilibrium. … In an Edgeworthian framework … we are concerned not with markets but with acts of individual exchange. As an equilibrium concept we need some logical rest-point of an exchange mechanism. If it is possible for two individuals to gain from trade, that pre-trade allocation ought not to be termed an equilibrium. Intuitively, equilibrium will occur when no traders can improve their positions by exchange.

E. Roy Weintraub [1979, pp. 128–9]

In his book Value and Capital, John Hicks noted [1939/46, p. 20]:

If an individual is to be in equilibrium with respect to a system of market prices, it is directly evident that his marginal rate of substitution between any two goods must equal the ratio of their prices. Otherwise he would clearly find an advantage in substituting some quantity of one for an equal value (at the market rate) of the other.

In other words, one can easily see the act of individual maximization as a state of personal equilibrium. After all, as in the case of consumer theory, this is the direct consequence of our assuming and using strictly convex-to-the-origin indifference curves when explaining the consumer’s choice of a bundle of goods while facing market prices. What consumers will see is that, if along their budget lines they move left or right from the maximizing bundle, they will experience a lower level of utility. Thus, they will move back toward the maximizing bundle. And Hicks’s point is simply that this self-correcting behaviour is exactly what constitutes equilibrium behaviour in a market. So, unlike the discussion of equilibrium behaviour of whole markets or even whole macro economies in Chapter 2, Hicks’s version gives us a tool to characterize individual behaviour that does not obviously involve the kind of criticism discussed in that chapter, such as that about using a representative agent to provide micro-foundations.

Type
Chapter
Information
Model Building in Economics
Its Purposes and Limitations
, pp. 67 - 77
Publisher: Cambridge University Press
Print publication year: 2014

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