Andreu Mas-Colell

• PhD in Economics, University of Minnesota 1972
• Professor Emeritus at Pompeu Fabra University

Inspired by the existing work on correlated equilibria and regret-based dynamics in games, we carry out a first exploration of the links between equilibria and dynamics in (exchange) economies. The leading equilibrium concept is Walrasian equilibrium, and the dynamics (specifically, regret-matching dynamics) apply to trading games that fit the econ...

In this paper we view bargaining and cooperation as an interaction superimposed on a game in strategic form. A multistage bargaining procedure for N players, the "proposer commitment" procedure, is presented. It is inspired by Nash's two-player variable-threat model; a key feature is the commitment to "threats." We establish links to classical coop...

We test the hypothesis that universities are more productive when they are both more autonomous and face more competition. Using survey data, we construct indices of university autonomy and competition for both Europe and the United States. We show that there are strong positive correlations between these indices and multiple measures of university...

In this paper we view bargaining and cooperation as an interaction superimposed on a strategic form game. A multistage bargaining procedure for N players, the "proposer commitment" procedure, is presented. It is inspired by Nash's two-player variable-threat model; a key feature is the commitment to "threats." We establish links to classical coopera...

It is shown that in any affine space of payoff matrices the equilibrium payoffs of bimatrix games are generically finite.

Since the introduction of the Shanghai ranking of the worldâ??s universities it has been clear that European universities are underperforming. This blueprint discusses the potential explanations and points at different reform priorities for higher education in Europe.

Some of the present day applications run on computer platforms with large and inexpensive memories, which are also error-prone. Unfortunately, the appearance of even very few memory faults may jeopardize the correctness of the computational results. ...

Summary. Recently published international rankings indicate that the performance gap between European and American universities is large and, in particular, that the best European universities lag far behind the best American universities. The country performance index we construct using the Shanghai ranking confirms that, despite the good performa...

Based on a survey of European universities, this policy brief states that despite the good performance of some countries, Europe as a whole trails the US by a wide margin. The reason is two-fold. First, Europe invests too little in higher education. Second, European universities suffer from poor governance, insufficient autonomy and often perverse...

In this paper we consider dynamic processes, in repeated games, that are subject to the natural informational restriction of uncoupledness. We study the almost sure convergence of play (the period-by-period behavior as well as the long-run frequency) to Nash equilibria of the one-shot stage game, and present a number of possibility and impossibilit...

This lecture offers thoughts on some issues concerning the effective development of the European space of higher education currently being pushed by the twin forces of the Bologna process and the Lisbon declaration of the EU. It is pointed out that the USA example is a good reference point but cannot be imitated mechanically, given the more segment...

A general formalism on stochastic choice is presented. Tje Rationalizability and Recoverability (Identification) problems are discussed. For the identification issue parametric examples are analyzed by means of techniques of mathematical tomography (Random transforms).

In this paper we consider dynamic processes, in repeated games, that are subject to the natural informational restriction of uncoupledness. We study the almost sure convergence to Nash equilibria, and present a number of possibility and impossibility results. Basically, we show that if in addition to random moves some recall is introduced, then suc...

This lecture offers thoughts on some issues concerning the effective development of the European space of higher education currently being pushed by the twin forces of the Bologna process and the Lisbon declaration of the EU. It is pointed out that the USA example is a good reference point but cannot be imitated mechanically, given the more segment...

We call a dynamical system uncoupled if the dynamic for each player does not depend on the payoffs of the other players. We show that there are no uncoupled dynamics that are guaranteed to converge to Nash equilibrium, even when the Nash equilibrium is unique.

Regret-based dynamics have been introduced and studied in the context of discrete-time repeated play. Here we carry out the corresponding analysis in continuous time. We observe that, in contrast to (smooth) fictitious play or to evolutionary models, the appropriate state space for this analysis is the space of distributions on the product of the p...

The need for research permit me to put on the table the ideological viewpoint from which I address today's reflections to you. It is that of historical Catalanism, in its more international version, which in these times I would accept as the will and ambition not to be just another European country. We aspire to be what we are not yet: a first-line...

We develop and implement a collocation method to solve for an equilibrium in the dynamic legislative bargaining game of Duggan and Kalandrakis (2008). We formulate the collocation equations in a quasi-discrete version of the model, and we show that the collocation equations are locally Lipchitz continuous and directionally differentiable. In numeri...

We consider repeated games where at any period each player knows only his set of actions and the stream of payoffs that he has received in the past. He knows neither his own payoff function, nor the characteristics of the other players (how many there are, their strategies and payoffs). In this context, we present an adaptive procedure for play cal...

We develop and implement a collocation method to solve for an equilibrium in the dynamic legislative bargaining game of Duggan and Kalandrakis (2008). We formulate the collocation equations in a quasi-discrete version of the model, and we show that the collocation equations are locally Lipchitz continuous and directionally differentiable. In numeri...

This paper analyzes the properties of aggregate excess demand functions for economies with an arbitrary finite set of N commodities where agents face trading restrictions of a general, abstract form: their budget set is defined by K-dimensional planes in K-N. It is shown that, if there are at least K agents in the economy, the only general property...

This paper analyzes the properties of aggregate excess demand functions for economies with an arbitrary finite set of N commodities where agents face trading restrictions of a general, abstract form: their budget set is defined by K-dimensional planes in RN. It is shown that, if there are at least K agents in the economy, the only general property...

We explore the relationships between noncooperative bargaining games and the consistent value for nontransferable utility (NTU) cooperative games. A dynamic approach to the consistent value is introduced: the consistent vector field. The main contribution is to establish that theconsistent fieldis intimately related to the concept ofsubgame perfect...

We exhibit and characterize an entire class of simple adaptive strategies, in the repeated play of a game, having the Hannan-consistency property: in the long-run, the player is guaranteed an average payoff as large as the best-reply payoff to the empirical distribution of play of the other players; i.e., there is no “regret.” Smooth fictitious pla...

This article considers the specificity of cultural goods, services, and artifacts in the context of international trade theory. The analysis discusses possible justifications for import or export restrictions on cultural goods. Copyright Kluwer Academic Publishers 1999

We develop and implement a collocation method to solve for an equilibrium in the dynamic legislative bargaining game of Duggan and Kalandrakis (2008). We formulate the collocation equations in a quasi-discrete version of the model, and we show that the collocation equations are locally Lipchitz continuous and directionally differentiable. In numeri...

The topic to be reviewed in this lecture is included in what Bob Aumann described in his lecture as the bridges between cooperative and noncooperative theory. If I had all the time in the world, I would begin by presenting the basics of noncooperative game theory, but I cannot possibly do this. I will therefore remain very elementary, and I will be...

Issues relating to the emergence, persistence, and stability of cooperation among social agents of every type are widely recognized to be of paramount importance. They are also analytically difficult and intellectually challenging. This book, arising from a NATO Advanced Study Institute held at SUNY in 1994, is an up-to-date presentation of the con...

It is shown that under a weak regularity, a two-period incomplete market economy with a finite number of assets and general (e.g. uncountable) state spaces has an equilibrium. General state spaces are important in applications. The proof proceeds by establishing the existence of self-fulfilling spot price expectations possessing a strong continuity...

We consider a pure exchange, general equilibrium model, with two periods and a finite number of states, goods, numeraire assets, and households. Participation on the asset market is restricted in a household specific manner, imposing upper bounds on the amounts of borrowing which can be obtained using assets. Those bounds are assumed to depend on a...

We present a general result on the convergence to an equilibrium of a class of dynamic adjustment procedures — which includes gradient systems and best reply dynamics as special cases — when there are two players and strategy sets are one dimensional. We also show that there are no restrictions on the form of the gradient or best reply dynamics, ev...

The authors present and analyze a model of noncooperative bargaining among n participants, applied to situations describable as games in coalitional form. This leads to a unified solution theory for such games that have as special cases the Shapley value in the transferable utility case, the Nash bargaining solution in the pure bargaining case, and...

We consider economies with many agents and compare the competitive equilibria and the value allocations of the resulting coalitional games. In particular, we provide a (smooth and robust) example where the “value principle” does not hold for the Harsanyi NTU-value: there is a unique competitive equilibrium, which however does not belong to the (non...

The paper by G. Debreu, ‘Economies with a Finite Set of Equilibria’, appeared in Econometrica in 1970. As is commonly known, the paper has had since then a great impact on the style and the substance of economic theorizing. If I had been more energetic I would have verified this impact in the Index of Citations. Yet, whatever the latter says, it is...

[For part I see the authors, ibid. 20, No. 4, 959-1002 (1995; Zbl 0846.90139).] This is the second of two papers devoted to the study of egalitarian solutions for nontransferable utility (NTU) games with a large number of players. This paper is concerned with the egalitarian solutions of finite games as the number of players increases. We show that...

This is the first of two papers devoted to the study of egalitarian solutions for nontransferable utility games with a large number of players. This paper is concerned with the construction of egalitarian solutions for the limit situation with a continuum of players. We build on the concept of the potential introduced and exploit partial differenti...

This textbook aims to provide a comprehensive overview of the essentials of microeconomics. It offers unprecedented depth of coverage, whilst allowing lecturers to 'tailor-make' their courses to suit personal priorities. Covering topics such as noncooperative game theory, information economics, mechanism design and general equilibrium under uncerta...

We establish conditions which (in various settings) guarantee the existence of equilibria described by ergodic Markov processes with a Borel state space S. Let $\scr{P}(S)$ denote the probability measures on S, and let $s\mapsto G(s)\subset \scr{P}(S)$ be a (possibly empty-valued) correspondence with closed graph characterizing intertemporal consis...

We study a general implementation problem for exchange economies with a continuum of players and private information, and test the robustness of the results for sequences of approximating finite economies. Assuming that the designer knows the distribution of the characteristics in the economy we consider continuous and unique implementation in both...

One of the most successful cooperative solution concepts in game theory is that of value. Originally defined for n-person games with transferable utility (“TU”) by Shapley [1953b], it has been extended to general games with nontransferable utility (“NTU”) by Harsanyi [1959, 1963] and Shapley [1969] and applied to numerous models. These applications...

In the applications of equilibrium theory one occasionally encounters situations where consumption sets are naturally compact. Two examples are: (i) fix-price equilibria where consumption is restricted to a given budget set and the equilibrating variables are ration-coupons prices (as in Drèze and Muller, 1980); (ii) models where the choice variabl...

Preface (1991): This paper first appeared in May 1973 as Working Paper IP-183 of the Center for Research in Management Science of the University of California - Berkeley. In spite of the high regard that this author had for it, it remained unpublished. It is on a topic very close to Trout Rader’s interest and it belongs to a line of the literature...

This paper establishes the following result for exchange economies with l commodities and n agents: for a generic set of utility functions of the first consumer, the number of critical equilibria is at most ln at every endowment. This result has application to, for example, the theory of general equilibrium Cournot competition.

This paper investigates the implications of gross substitutability of excess demand functions for the equilibria of exchange economies with countably many goods and arbitrarily many consumers. We provide uniqueness theorems for general models. We also show that the equilibrium trajectories of dynamic, stationary overlapping generations economies sa...

How should the benefits of the commons, say a publicly owned fishing resource, be distributed? A first possibility is equal division among the population. A second option is to distribute them among the people who actually exploit the resource in proportion to their activity level: this is the ""land to the tiller"" view. A third approach is the nu...

Motivated by recent work of Huang and Kreps it is shown that the existence of a general equilibrium in an exchange economy whose commodity space is a vector lattice is guaranteed if (in addition to standard hypotheses) the price space is also a lattice. This is very weak in contrast with the usual requirement that the topology of the commodity spac...

It is shown that in a two-period economy with a continuum of states and real assets, the following holds: (1) if the asset structure is complete, then equilibria is finite; (2) if there are a finite number of real assets (this can approximate completeness arbitrarily close) then, for a non-empty open set of economies, there are a continuum of disti...

This is a reprint of Technical Report 274, IMMSSS, Stanford, 1978. Substantial parts of it have appeared in P. Dubey, A. Mas-Colell, and M. Shubik: “Efficiency Properties of Strategic Market Games: An Axiomatic Approach,” J. Econ. Theory 22, 1980, and in A. Mas-Colell: “On a Theorem of Schmeidler, ” J. Math. Econ., 1984. Needless to say, the author...

In this paper we propose a general mathematical approach to existence problems in economics based on the geometry of vector bundles and the methods of intersection theory. The existence problem is formulated as: Does an approximate vector bundle admit a non-zero continuous section? The motivation and major application comes from incomplete market t...

The H&R Shapley value defined by Hsiao and Raghavan for multi-choice cooperative game is redundant free. If the H&R Shapley value is used as the solution of a game, there won't be any objection to a player's taking redundant actions. Therefore, the spirit of the law on equal job opportunities is automatically fulfilled. Also, if the H&R Shapley val...

How should the benefits of the commons, say a publicly owned fishing resource, be distributed? A first possibility is equal division among the population. A second option is to distribute them among the people who actually exploit the resource in proportion to their activity level: this is the ""land to the tiller"" view. A third approach is the nu...

Let P be a real-valued function defined on the space of cooperative games with transferable utility, satisfying the following condition: In every game, the marginal contributions of all players (according to P) are efficient (i.e., add up to the worth of the grand coalition). It is proved that there exists just one such function P--called the poten...

In this paper we argue that indeterminacy of equilibrium is a possibility inherent in economies with a double infinity of agents and goods, large-square economies. We develop a framework that is quite different from the overlapping generations one and that is amenable to analysis by means of differential calculus in linear spaces. The commodity spa...

We introduce adaptive learning behavior into a general-equilibrium life-cycle economy with capital accumulation. Agents form forecasts of the rate of return to capital assets using least-squares autoregressions on past data. We show that, in contrast to the perfect-foresight dynamics, the dynamical system under learning possesses equilibria that ar...

The term ‘cooperative equilibria’ has been imported into economics from game theory. It refers to the equilibria of economic situations modelled by means of cooperative games and solved by appealing to an appropriate cooperative solution concept. The influence is not entirely one way, however. Many game theoretic notions (e.g. Cournot-Nash equilibr...

A first approximation to the study of the intertemporal aspects of resource allocation (capital theory from now on), consists of concentrating on the steady states (the rest points) of associated dynamical systems. Provided one does not lose sight from the fact that this is not an end in itself, there is much useful information to be gleaned from s...

Composed in honour of the sixty-fifth birthday of Lloyd Shapley, this volume makes accessible the large body of work that has grown out of Shapley's seminal 1953 paper. Each of the twenty essays concerns some aspect of the Shapley value. Three of the chapters are reprints of the 'ancestral' papers: Chapter 2 is Shapley's original 1953 paper definin...

For every range of admissible incomes, the authors characterize the class of Engel curves with the property that if an economy has, first, a price independent distribution of income and, second, preferences which are identical across consumers and generate Engel curves in the class, then the corresponding aggregate demand function satisfies the Wea...

The term ‘cooperative equilibria’ has been imported into economics from game theory. It refers to the equilibria of economic situations modelled by means of cooperative games and solved by appealing to an appropriate cooperative solution concept. The influence is not entirely one way, however. Many game theoretic notions (e.g. Cournot–Nash equilibr...

Since non-convexity is just the negation of convexity, it will be useful to begin by reviewing the justifications for the latter.

A price equilibrium existence theorem is proved for exchange economies whose consumption sets are the positive orthant of arbitrary topological vector lattices. The motivation comes from economic applications showing the need to bring within the scope of equilibrium theory commodity spaces whose positive orthant has empty interior, a typical situat...

In these notes we present an exposition of some modern versions of L. Wal ras’ tatonnement theory (see (1926)) with special emphasis on simultaneous price and quantity dynamics.

We provide an existence proof for Generalized Marginal Cost Pricing with given tax-subsidy rules. The novelty is that our approach allows for economic environments where all the generalized marginal cost pricing equilibria are inefficient in the aggregate. An example is recalled in order to suggest how non-pathological these environments are.

Andreu Mas-Colell has been doing pioneering work using differential topology in the analysis of general equilibrium. This work is regarded as outstanding and one of the major contributions to the development of rigorous economic theory in the last twenty years. The articles he has written have been difficult and technically demanding. In this book...

We aim at a succint presentation of the finite-dimensional mathematical theory associated with the so-called fundamental theorems of welfare economics. Very roughly these assert that, under some conditions, every price equilibrium is an optimum in the sense of Pareto and, conversely, under other (typically stronger) hypotheses, every optimum is a p...

Over a decade ago D. Schmeidler (1973) introduced a concept of non-cooperative equilibrium for games with a continuum of agents and, under a restriction on the payoff functions, established the existence of an equilibrium in pure strategies. The purpose of this note is to reformalize the model and the equilibrium notion of Schmeidler in terms of di...

It is shown that if there are three commodities or less, an excess demand function that fulfills the property of Gross Substitutability satisfies also the Weak Axiom of Revealed Preference.

Les démonstrations de l'existence des équilibres de prix au coût marginal nécessitent des hypothèses concernant la fonction de production agrégée qui permettent de conclure qu'il y a au moins un équilibre efficace au coût marginal. Dans ce papier nous présentons une économie à rendements croissants pour laquelle il n'y a pas d'équilibre efficace au...

This paper contributes empirically to our understanding of informed traders. It analyzes traders' characteristics in a foreign exchange electronic limit order market via anonymous trader identities. We use six indicators of informed trading in a cross-sectional multivariate approach to identify traders with high price impact. More information is co...

The first and fundamental paper of P. A. Samuelson on revealed preference theory (1937) is now almost forty-five years old. He must have been barely twenty when it was written. One feels, nevertheless, that revealed preference has not just been a youthful interest, but has remained very close to his heart. He has written on it repeatedly (e.g., 194...

The paper investigates the conditions under which an abstractly given market game will have the property that if there is a continuum of traders then every noncooperative equilibrium is Walrasian. In orther words, we look for a general axiomatization of Cournot's well-known result. Besides some convexity, continuity, and nondegeneracy hypotheses, t...

Some basic facts of public goods theory are presented in the primitive set-up of a collection of projects devoid of any linear structure. There is a single private good. Characterizations of Pareto optimal and core states in terms of valuation functions (i.e. supporting “prices”) are obtained. Voluntary financing schemes are discussed.

Modern Walrasian economics provides an overview of the decentralized economic coordination problem under the hypothesis that prices are publicly quoted and are viewed by economic agents as exogenously given. If this is regarded as the Hypothesis of Perfect Competition, then the modern Walrasian economics is a theory of perfect competition only in t...