Incomplete contracts and institutional complementarity
Another interesting, and quite unexplored, field of research for incomplete contracts is given by the analysis of institutional complementarities in an incomplete contract framework characterized by multiple equilibria in which initial conditions are destined to reinforce over time.
Standard theories on incomplete contracts seem to be very fruitful in explaining the efficiency of given governance structures but they fail to provide an explanation for their inefficiency, that is, for the selection of an inefficient equilibrium where multiple alternative equilibria are potentially available for economic agents. Under the framework already analysed, there is virtually no explanation for the persistence of an inefficient allocation of property rights over time. As Aoki (2001) pointed out, the notion of institutional complementarity may provide a useful tool to analyse how equilibria are selected in an incomplete contract framework characterized by multiple equilibria. The notion of institutional complementarity relies on the idea that, in a given institutional framework characterized by incomplete contracts, economic agents face different domains and do not strategically coordinate their choices across domain games. As a consequence, the institutional choices in one domain act as exogenous parameters in other domains and constitute the ‘institutional environment’ under which choices are being made. In this setting ‘one type of institution rather than another becomes viable in one domain, when a fitting institution is present in another domain and vice-versa’ (Aoki 2001). Assume two domains of choices X and Y and, respectively, two sets of choices {X1, X2} and {Y1, Y2}, with agents i choosing in X and agents j choosing in Y, according to their utilities (respectively, u for i and v for j). Standard conditions of institutional complementarity are defined by the two following circumstances (see Pagano, 2003):1.
for agent i, the additional benefit of having institution X1 instead of institution X2 in domain X is greater when institution Y1 (instead of institution Y2) is chosen in the domain Y: u(X1; Y1) - u(X2; Y1) ≥ u(X1; Y2) - u(X2; Y2);2. for agent j, the additional benefit of having institution Y2 instead of institution Y1 in some domain Y is greater when institution X2 (instead of institution X1) is chosen in the domain X: v(Y2; X2) - v(Y1; X2) ≥ v(Y2; X1) - v(Y1; X1).
The above conditions, considered by Aoki (2001), restate in terms of institutional choices the super-modularity conditions among strategies considered by Milgrom and Roberts (1990) and are concerned with the property of incremental pay-offs with respect to a change in parameter value. They do not exclude the possibility that the level of the pay-offs of one rule is strictly higher than that of the other for the agents of one domain or of both domains, regardless of the choice of rule in the other domain. In other words, there is the possibility of a unique equilibrium. However, under the super-modularity condition, there can be two pure Nash equilibria (institutional arrangements) for the system that comprises X and Y, that is (X1, Y1) and (X2, Y2). When such multiple equilibria are possible, we say that domains X and Y are institutional complements of each other and that: X1 and Y1 are institutional complements; and X2 and Y2 are institutional complements. Moreover, as Aoki (2001) points out, when multiple equilibria exist, it is possible that the overall institutional arrangement could result in a Pareto-inferior outcome. For instance, suppose that (X2, Y2) is such that u(X2; Y2) - u(X1; Y1) > 0 and v(X2; Y2) - v(X1; Y1) > 0.
However if initial conditions are such that X1 or Y1 is selected in one of the two domains so as to act as a parameter in the other one, this selection will induce the choice of the institutional complement, respectively, Y1 or X1. As a consequence, the equilibrium selected will be (X1, Y1) rather than (X2, Y2), that is, the Pareto-inferior outcome.The analysis of institutional complementarities in an incomplete contract framework has the following implications: (i) the interdependence among domains may generate multiple institutional arrangements; (ii) according to initial conditions affecting the available choices in one domain, some Pareto- inferior institutional arrangement may emerge; (iii) since institutional arrangements are pure Nash equilibria, they are self-enforcing in nature and destined to perpetuate over time (by path dependency and cumulative causation) unless some exogenous change affects one domain or the other so as to shift the choice to another institutional arrangement.
This approach has been employed to analyse, in an incomplete contract framework, the emergence of self-enforcing path-dependent equilibria in corporate governance between technological and financial domains, the variety of capitalistic systems, and the structuring of alternative capitalistic systems in the United States, Germany and Japan (for instance, see Aoki, 2001 and Nicita and Pagano, 2003, 2005).