THE AUSTRALIAN NATIONAL UNIVERSITY WORKING PAPERS IN ECONOMICS AND ECONOMETRICS Network Externalities and Institutional Adaptation1 Nhat Le School of Economics Faculty of Economics and Commerce Working Paper No. 427 November 2002 ISBN: 086831 427 7 1 Faculty of Economics, Australian National University, Canberra, ACT 0200, Australia. [email protected], phone: (61 2) 6125 54442, fax: (61 2) 6125 3700. Earlier versions of this paper were distributed under the title: “Multiple Game Linkages in Evolutionary Framework.” I would like to thank Steven Tadelis for his guidance. I wish to thank Peyton Young for his critical comments on several drafts. Thanks are also due to Masahiko Aoki, Douglas Bernheim, Marcelo Clerci-Arias, Avner Grief, Jonathan Levin, John McMillan, Rod Tyers and the participants of the comparative institutional analysis seminar at Stanford University, the theory workshop at the Australian National University. Financial supports from ACLS and RSPAS are greatly acknowledged. Abstract This paper presents a dynamic framework that explains how a set of institutions emerges when players extrapolate across multiple games. It explores the existence of a fundamental circularity whereby the high convention in one game reinforces the high convention in others, and vice versa, such that one possible outcome is a socially advantageous regime combining the high conventions. Likewise, the low conventions also reinforce one another to form a socially disadvantageous regime. A convention in one game reinforces the corresponding convention in the other game by altering the payoff structure in favor of the latter. The payoff structures of the games explored here are driven by the competition between the two alternative regimes. In the long run, however, the regime that adapts better into its milieu, or equivalently, is more firmly rooted in past adaptation, will overcome the alternative. This dominant regime will determine the asymptotic outcome in all games. JEL Classification Numbers: C7, D7, D8, O0 Keywords: Adaptation, Complementary institutions, Coordination games, Risk dominant strategies, Selection of conventions, Stochastically stable states. 1 I. Introduction When inquiring into the causes, nature, and implications of institutional change historians and development economists have long sought to consider the economic system as a coherent whole. Yet the nature of institutional change in the presence of complementarities is still not fully understood by researchers and policy makers alike. When designing policies in response to changes in conditions, policy makers still lack theoretical models that deal with institutional complementarities. There are some exceptions however. Li (1999) point out that the economic system is a complex set, which has many layers. An ex ante comprehensive policy, which aims to alter every aspect of the existing system altogether, may lose its complementary ex post when some parts of that system respond to the policy much more slowly than the others. From their point of view, it is reasonable to accept the view of Ogburn (1950) that the actual institutions at any time represent adaptation in part to past conditions. This problem is reinforced by network externalities between different institutions (Arthur, 1989; David, 1993). Thus, from a short-term perspective, a key property of the system is its inertia; the expected waiting time until the system transiting from one regime to another may be enormous. In the corresponding literature on development, some related issues have also been discussed. Stigler (1951) and Jacobs (1969) indicate that many ad hoc measures to transplant new organizations, rules, or technologies into a place that lacks a network of auxiliary institutions often meet with failure. Echoing them, Ciccone and Matsuyama (1996) note that there is a fundamental circularity between the choice of technologies by firms and the variety of intermediate inputs available, which include legal support, accounting, and financial services. Their analysis highlights linkages in the selection of conventions across markets. But they did not address this issue formally. The objective of this paper is to provide such an analysis. The focus is on reciprocal relationships in the selection of convention across spheres of human 2 interactions; how a particular set of complementary institutions comes into being; and why some institutions persist even when they are no longer optimal. This exercise requires us to specify the concept of selection of institutions. In the economists’ view, an institution is an equilibrium outcome of a game, which has multiple equilibria (Sugdent, 1989; Hurwicz, 1996). The selection of an institution, therefore, boils down to the question why one particular equilibrium outcome of the coordination game is chosen over the others. The most widely accepted selection concept is that of perfect Baysian equilibrium (see, for example, Myerson, 1991; Fudenberg and Tirol, 1991). It suggests that the system of belief and rational behavior together pin down what equilibrium of the game can be selected as a convention. There are some criticisms, however. First, the system of beliefs is often given exogenously. For instance, in the history literature, individuals’ preference sometime is determined either by rule makers (North, 1990) or by cultural patterns (Weber, 1951; Grief, 1994). Second, like most models in neoclassical economics, in standard game theory, individuals or players are assumed to be highly rational. This is rather an extravagant description of human behavior (Young, Ch1., 1998). In reality, people often have very limited understanding about the world around them, including the preferences of their partners. The learning theory has filled this gap by making selection of equilibrium endogenous rather than exogenous. In essence, the system of beliefs is formed in an adaptive, low rationality environment. Perhaps, the most prominent step in this approach is “trembling – hand perfection” by Selten (1975), which assumes people to behave “less” rationally by introducing the possibility of mistakes. A convention then is expected to emerge in the long run only if it is robust to mistakes or errors. Interestingly, Selten’s notion of convention selection is closely related to what Hayek, Menger, and other members of Austrian school called “spontaneous order”. But this notion may also have contributed to the development of two important concepts: the “risk dominant strategy” of Harsanyi and Selten (1988) and “adaptive play” by Foster and Young, (1990). In essence, there are some strategies that are least risky in the view of players. In the terminology of Harsanyi and Selten, these are risk dominant strategies. 3 If learning has any implication on the formation of expectations, the game should converge to a risk dominant strategy (Fudenberg and Levin, Ch. 1, 1998). Young (1993, 1998) has formalized this idea. In his framework, a player forms her expectation about the opponents’ action by sampling from her memory of previous plays. She then takes the best reply to that belief. But with some small chance, she makes a mistake and chooses a strategy other than what is suggested by her belief. Such mutations or errors play a crucial role in promoting long-term change. In particular, the theory suggests that, in the presence of random shocks or mutations, some conventions are inherently more stable than others. Young called them “stochastically stable states”, which in fact correspond one to one with risk dominant strategies in a 2× 2 coordination game (Young, Ch. 4, 1998). Over the long run these institutions occur with higher frequency than others. A corollary is that the selection process is ergodic, not path dependent. Young’s adaptive play is very useful for the purpose of this paper. However, since players are not allowed to extrapolate across games, the selection process offers an idiosyncratic rather than a perspective with institutional complementarities. Further, given network externalities, the selection of conventions is influenced by past adaptations (Arrow, 1997). History, therefore, matters (North, 1973; Grief, 1994). This feature is then re-emphasized by Young himself (Young, Ch. 1, 1998). But because players interact only in a single game, the structure of institutional linkages is hidden or absent. Thus, one learns little about the effect of past adaptation on the subsequent trajectory of institutional development. In this paper, Young’s work is built upon by constructing a formal model to analyze the selection of a set of complementary institutions to coordinate individuals’ behavior. Since the focus is on reciprocal relationships in the selection of equilibrium outcome across games, a set of corresponding conventions is sought, each of which reinforces another to emerge simultaneously. It is assumed that the high equilibrium in one game reinforces the high equilibrium in the other game and vice versa, to form the “high regime”. The two low equilibriums reinforce one another to form the “low regime”. As suggested by Grief (1994) and North (1995), a convention in one game reinforces the corresponding convention in the other game by altering the payoff structure in favor of the latter. We then allow the payoff structures in both games to be driven by competition between the two alternative regimes. In the long run, however, the regime that adapts better 4 into its milieu, or equivalently, is more firmly rooted in past adaptations, will overcome the alternative. This