Equilibrium as compatibility of plans
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Equilibrium as compatibility of plans Marek Hudik1 Ó Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract This paper uses a game-theoretic framework to formalize the Hayekian notion of equilibrium as the compatibility of plans. To do so, it imposes more structure on the conventional model of strategic games. For each player, it introduces goals, goaloriented strategies, and the goals’ probabilities of success, from which players’ payoffs are derived. The differences between the compatibility of plans and Nash equilibrium are identified and discussed. Furthermore, it is shown that the notion of compatibility of plans, in general, differs from the notion of Pareto efficiency. Since the compatibility of plans across all players can rarely be achieved in reality, a measurement is introduced to determine various degrees of plan compatibility. Several possible extensions and applications of the model are discussed. Keywords Goals Plans Goal-oriented strategies Hayekian equilibrium Compatibility of plans Nash equilibrium Pareto efficiency
1 Introduction In a market economy, a large number of individuals independently make production and consumption plans. Even though these plans are interrelated in a complex way, they usually turn out to be successfully fulfilled. To account for this coordinating aspect of markets, Hayek (1937, 2007) defined equilibrium as ‘‘compatibility of plans.’’ The Hayekian view of markets has inspired various approaches, such as the theory of market process (e.g., Boettke and Prychitko 1994; Buchanan and Vanberg 1991; Ikeda 1990; Kirzner 1997; O’Driscoll Jr. and Rizzo 2002; Lachmann 1977; Langlois 1986), evolutionary economics (e.g., Loasby 2001; Potts 2000; Witt 2008), or computational economics (e.g., Arthur 2010; Bowles et al. 2017; Vriend 2002). Regrettably, very few of these works attempt to formalize Hayek’s specific notion & Marek Hudik [email protected] 1
Faculty of Business Administration, University of Economics, Prague, W. Churchill Sq. 4, 13067 Prague 3, Czech Republic
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M. Hudik
of equilibrium. Consequently, the differences between the Hayekian and conventional views have yet to be precisely identified. This paper attempts to fill this gap. While many Hayekians are skeptical regarding the usefulness of the equilibrium concept as such, Hayek himself, in his earlier writings, considered equilibrium a useful approximation of the market order (Hayek 2007). However, later he noted that the equilibrium concept is rather unfortunate to serve this particular purpose: for one thing, order is a matter of a degree, while equilibrium does not allow for degrees; for another, order, unlike equilibrium, can be preserved even during a process of change (Hayek 2002, 15). At the same time, Hayek developed his specific notion of equilibrium as the compatibility of plans, which appears to be different from the conventional notion. To illustrate his concept, a seller’s plan to ‘‘sell a loaf of bread for at least one dollar’
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