This monograph presents my view on the essential workings of the modern economy -- the view that I have developed over almost two decades. The presentation here is formal, that is, axiomatic. Axiomatic treatment conveys ideas clearly, and avoids any influence on analysis of a particular interpretation of the model and a specific ideology. Using the axiomatic method, I hope I have expressed my economic view clearly here, both its scope and limits. I could not find any existing economic model that would provide a formal framework within which to express my view consistently, so I had to develop a new formal theory that would do the job.

My basic view is summarized as follows: A modern economy embodies two major resource allocation mechanisms. One is the market mechanism, sometimes called the price mechanism. The other is a mechanism instituted by an organization of people called a firm. To realize coexistence of two mechanisms is not new; it goes back at least as far as Max Weber early in this century. Since then, the development of the neoclassical paradigm has greatly clarified the workings of the market mechanism. The neoclassical paradigm has indeed played an essential role in shaping my own thinking. On the other hand, not much consensus has been obtained in regard to the nature of the firm-specific mechanism, nor have many attempts been made to formalize any view. My view in this respect is quite different from that of Max Weber, and also from that of several recent schools of the theory of the firm which have gained some popularity, such as the behavioral model approach to the firm (Herbert A. Simon), the new institutional economics (Oliver E. Williamson), and the principal-agent theory. I view a firm as an organization characterized by (1) diversity of (and most likely, conflict among) the interests of its members, and (2) in spite of such diversity, the members' acceptance of a coordinated choice of activities. A firm understood in this way is precisely a coalition which is formed when people play a cooperative game, and this descriptive cooperative game is the firm-specific resource allocation mechanism. (The definition of the term "cooperative game" differs even among the contemporary researchers in game theory. My definition is spelled out in Section 2.1 of this monograph; in short, I define a cooperative game according to a behavioral principle, that is, according to whether or not players coordinate their strategy choice, rather than according to a specific game-theoretical model.)

The formal general equilibrium framework I provide in this monograph embodies both the neoclassical market mechanism and the descriptive cooperative game. The theory I develop here may be considered a synthesis of the neoclassical paradigm and the classical descriptive cooperative game theory. When I started my research in the theory of the firm more than eighteen years ago, the formal analysis of cooperative behavior at an appropriate degree of generality for economic application was not readily available. I have developed the cooperative game theory to the extent that my results can be applied for this purpose. Among the basic results I have obtained in this general equilibrium setup are: definition of a new descriptive equilibrium concept that can be interpreted as an outcome of simultaneous workings of the two resource allocation mechanisms; existence results for this concept; Pareto non-optimality of the equilibrium; and a welfare comparison of the present-day capitalism and market-cooperative socialism.

My further results on the cooperative decision-making in a firm are: developing a normative mechanism theory to implement Pareto optimality in the presence of increasing returns to scale; and providing a partial equilibrium analysis, which characterizes the coalitionally stable hierarchical structures in a firm.

This monograph presents the aforementioned work in a systematic and readable way. Chapters 1 and 2 are expository. Chapters 3-6 constitute the main body of the work, and are based on my original articles, most of which were published in various journals or in edited books.

Chapter 1 reviews some of the basic elements discussed in the theory of the firm literature, and indicates that the neoclassical theory is too simple to treat them. Many criticisms of the existing literature presented here reflect my own view.

Chapter 2 reviews the elements of descriptive cooperative game theory that are related to my approach to the theory of the firm. The Appendix to Chapter 2 consists of several simple economic examples which illustrate some of the theorems of Sections 2.1-2.4. Many of these examples capture diverse aspects of the main models of Chapters 3-6.

Chapter 3 is the basic part of my work: It presents my general equilibrium model which embodies both the neoclassical market mechanism (for allocation of non-human resources) and the cooperative resource allocation mechanism within the firm (for allocation of human resources). The equilibrium concept I propose here is a hybrid of the neoclassical competitive equilibrium (a typical descriptive noncooperative solution concept) and the core (a typical descriptive cooperative solution concept). There are two specific versions of my model: (1) the modern capitalistic economy as observed by Adolf A. Berle, Jr. and Gardiner C. Means (1932), in which ownership (stockholding) and control (management) of a firm are separated, and (2) the post-war market-cooperative socialism as observed by Jan Vanek (1972), in which the market mechanism is introduced into the socialist regime. An equilibrium existence theorem is established for the general model, which clarifies conditions on the data under which the present general-equilibrium method is valid. I remark on the technical matter that this existence theorem includes as special cases: Kenneth J. Arrow and Gerard Debreu's (1954) neoclassical competitive equilibrium existence theorem; John F. Nash, Jr.'s (1951) noncooperative equilibrium existence theorem; Herbert E. Scarf's (1967a) theorem for nonemptiness of the core; and my own strong equilibrium existence theorem. These existence theorems are properly located in the fixed-point theorem literature.

Chapter 4 continues the study of the descriptive economic model of Chapter 3. It first reports the simple fact that the two fundamental theorems of welfare economics, which establish relationship between the neoclassical competitive equilibrium and the Pareto optimum, are no longer true for the equilibrium concept I introduced. It then addresses a different welfare problem. The macro versions of the capitalistic economy and the associated socialistic economy are defined, and in this macro context, the following theorem is established: If the socialistic economy can be decomposed into subeconomies, each satisfying increasing returns with respect to the firm size, then for each equilibrium of the capitalistic economy there exists an equilibrium of the socialistic economy such that the former is Pareto superior to the latter. It is also suggested that given the generality of the assumptions, this welfare implication is likely to be the only result one can hope for in comparing the performance of the two systems.

Chapter 5 reports the result of the work that Martine Quinzii and I did jointly (1983), in which a new normative resource allocation mechanism (a new constitution) for a production economy with increasing returns to scale is proposed, so that if the people follow this rule while pursuing their self-interests, then the Pareto optimum will be achieved in equilibrium.

Chapter 6 reports my results that characterize the class of all hierarchical structures within a firm that have a nonempty core regardless of the preference relation of each member.

For more developed philosophical and conceptual discussions of the work in this monograph, see Tatsuro Ichiishi, "The Cooperative Nature of the Firm: Narrative," Managerial and Decision Economics, Vol. 14 (1993), 383-407.