Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

Over the past decade, the field of finite-dimensional variational inequality and complementarity problems has seen a rapid development in its theory of existence, uniqueness and sensitivity of solution(s), in the theory of algorithms, and in the application of these techniques to transportation planning, regional science, socio-economic analysis, energy modeling, and game theory. This paper provides a state-of-the-art review of these developments as well as a summary of some open research topics in this growing field.

Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications

Toward a Comparative Institutional Analysis

The northern California town of Mendocino, which was the shooting background for the film “East of Eden” starring James Dean, retains some of the air of its late nineteenth century role as a harbor to ship out lumber cut from the mountainsides. Ex-hippies-turned-farmers and artists live in the surrounding area. In the latter half of the 1990s, we rented a house facing the Pacific Ocean from an artist every summer. My wife and daughters went back and forth to Stanford for their activities, but I burrowed myself there for the summer with our dog Robin, brought back with us from Japan, and focused on writing my survey on comparative institutional analysis: Toward a Comparative Institutional Analysis (MIT Press, 2001). Mornings and evenings I took Robin for a walk on the cape where there was a greater than 180 ° view. In the morning, the horizon was veiled in fog, while in the evening the ocean was tinted red by the setting sun. It was the perfect place for rethinking problems and reorganizing chapters. Robin was a small mixed breed with some Shikoku-ken, but she was stubborn and at times got into fights with a large Coast Guard officer’s watch dog. My family enjoyed meals made from the organic produce we bought at the farmers’ market (so many varieties of tomatoes); we also went to the harbor to buy albacore tuna and fresh sea urchin still in its thorny shell.

The notion of bounded rationality was initiated in the 1950s by Herbert Simon; only recently has it influenced mainstream economics. In this book, Ariel Rubinstein defines models of bounded rationality as those in which elements of the process of choice are explicitly embedded. The book focuses on the challenges of modeling bounded rationality, rather than on substantial economic implications. In the first part of the book, the author considers the modeling of choice. After discussing some psychological findings, he proceeds to the modeling of procedural rationality, knowledge, memory, the choice of what to know, and group decisions. In the second part, he discusses the fundamental difficulties of modeling bounded rationality in games. He begins with the modeling of a game with procedural rational players and then surveys repeated games with complexity considerations. He ends with a discussion of computability constraints in games. The final chapter includes a critique by Herbert Simon of the author's methodology and the author's response.

Modeling Bounded Rationality

Super-modularity: Applications to convex games and to the greedy algorithm for LP☆

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Game theory for economic analysis

The purpose of this paper is to construct an abstract model of a society in which each member can cooperate with others by forming a coalition, but at the same time can be influenced by the members outside the coalition. A new concept of equilibrium, called here a social coalitional equilibrium, is proposed, and a sufficient condition for its existence provided. The social coalitional equilibrium may be considered a synthesis of the Nash equilibrium (a noncooperative solution concept) and the core (a cooperative solution concept). The paper provides a broadly applicable mathematical tool for proving existence of equilibrium for models of labor-managed market economies. THE PURPOSE OF THE PRESENT PAPER is to construct an abstract model of a society in which each member can cooperate with others by forming a coalition, but at the same time can be influenced by the members outside the coalition. A new concept of equilibrium, called here a social coalitional equilibrium, is proposed, and a sufficient condition for its existence provided. A coalition structure is endogenously determined in equilibrium. When the model is suitably specified, it describes noncooperative behavior of the members, and the social coalitional equilibrium is reduced to the Nash equilibrium. Given another extreme specification, the model is reduced to a cooperative game without sidepayments in characteristic function form, and the set of social coalitional equilibria corresponds precisely to the core. The need for study of the present model arose originally out of the author's recent investigation of labor-managed market economies, both the socialistic version and the capitalistic version, in [10, 11, 12]. Indeed, the model and the concept of social coalitional equilibrium were obtained by abstracting and generalizing the formal aspect of those studies. The socialistic labor-managed market economy has long been the object of study of various authors; see, e.g., Vanek [19]. The capitalistic labor-managed market economy seems to reflect the institutional aspect of the modern capitalistic society better than the economies formulated by other available general equilibrium models. It differs, for example, from the standard private ownership economy of Arrow and Debreu [1] (see also Debreu [6, Sec. 5.5]) in that (i) the ownership and control of a firm are separated; (ii) no particular firm is given a priori, but instead, the list of potential firms is given as a primitive datum; and (iii) the behavioral principle of the economic agents involves both noncooperative behavior and cooperative behavior. Because of the above feature (ii), any general equilibrium model of this economy has to formulate the economic mechanism that underlies the formation of firms in equilibrium. As

A social coalitional equilibrium existence lemma

Preface 1. Elements of the theory of the firm 2. Descriptive cooperative game theory 3. General equilibrium analysis of the nature of the firm 4. Welfare implications of the nature of the firm 5. Normative theory of production economy with increasing returns to scale 6. Stable hierarchical structures References Index.

Tatsuro Ichiishi

Papers

Super-modularity: Applications to convex games and to the greedy algorithm for LP☆

Game theory for economic analysis

A social coalitional equilibrium existence lemma

The cooperative nature of the firm

Coalition Structure in a Labor-Managed Market Economy