The bargaining set of a large economy with differential information

Summary. We study the Mas-Colell bargaining set of an exchange economy with differential information and a continuum of traders. We established the equivalence of the private bargaining set and the set of Radner competitive equilibrium allocations. As for the weak fine bargaining set, we show that it contains the set of competitive equilibrium allocations of an associated symmetric information economy in which each trader has the “joint information” of all the traders in the original economy, but unlike the weak fine core and the set of fine value allocations, it may also contain allocations which are not competitive in the associated economy. Received: February 15, 1999; revised version: August 9, 1999     

The ‘science-as-market’ analogy: a constitutional economics perspective

The ‘science-as-market’ analogy has been used in support of the notion that in science just as in markets competition works as an effective instrument for reconciling the self-interested ambitions of individual agents with the social function that science and markets are supposed to serve. This paper examines the analogy from a constitutional economics perspective, drawing attention to the role that the rules of the constitution of the ‘game of science’ as well as the ‘market game’ play in conditioning the ways in which competition works in the two realms.     

Darwinism in economics: from analogy to ontology

Several social scientists, including ‘evolutionary economists’, have expressed scepticism of ‘biological analogies’ and rejected the application of ‘Darwinism’ to socio-economic evolution. Among this group, some have argued that self-organisation is an alternative to biological analogies or Darwinism. Others have seen ‘artificial selection’ as an alternative to natural selection in the socio-economic sphere. Another objection is that Darwinism excludes human intentionality. It is shown that all these objections to ‘biological analogies’ and ‘Darwinism’ are ungrounded. Furthermore, Darwinism includes a broad theoretical framework for the analysis of the evolution of all open, complex systems, including socio-economic systems. Finally and crucially, Darwinism also involves a basic philosophical commitment to detailed, cumulative, causal explanations. For these reasons, Darwinism is fully relevant for economics and an adequate evolutionary economics must be Darwinian, at least in these fundamental senses. However, this does not undermine the need for auxiliary theories and explanations in the economic domain.     

A multi-agent bilateral bargaining model with endogenous protocol

People do bargain over how to bargain. We examine the role of individuals’ ability to pursue certain bargaining protocols in a multi-agent bilateral bargaining model. Bargaining protocols are not completely settled, but will emerge endogenously in equilibrium. We show that players’ ability to partially influence bargaining protocols plays a crucial role in determining equilibrium outcomes. When discounting is not too high, there are multiple subgame perfect equilibria, including inefficient ones. As the number of players increases, both the set of discount factors that support multiple equilibrium outcomes and the set of the first proposing player’s equilibrium payoffs expand. The maximum loss of efficiency increases with respect to the discount factor. We would like to thank Hongbin Cai, John Conlon, Andrew Daughety, Taiji Furusawa, Byoung Heon Jun, Akira Okada, Ping Wang, and two anonymous referees for their comments and suggestions. Both authors gratefully acknowledge financial support from the Social Sciences and Humanities Research Council of Canada.     

A bargaining model in general equilibrium

The goal of the paper is to present a simple model of rational endogenous household formation in a general equilibrium framework in which Pareto optimality at the economy level is not necessarily obtained. The simplest example of household formation is the case in which pairs of individuals engage themselves in a bargaining process on the division of some wealth: if an agreement on the distribution is (not) reached, we can say that the household is (not) formed. The vast majority of existing bargaining models predicts agreements on an efficient outcome. A seminal paper by Crawford (Econometrica 50:607–637, 1982) describes a very simple game with incomplete information in which, even with rational agents, disagreement causes welfare losses. We embed that model in a general equilibrium framework and present some results on equilibria both in the bargaining game and the associated exchange economy. Crawford’s results support Schelling’s intuition on the reasons of disagreement: it may arise if players’ commitments are reversible. Crawford shows that high probabilities of reversibility tend to favor the bargaining impasse, in fact with low probability. We prove that even if those probabilities are arbitrarily close to zero, disagreement is an equilibrium outcome, with high probability. That conclusion seems to be an even stronger support to Schelling’s original viewpoint. In the exchange economy model with that noncooperative bargaining game as a first stage, we present significant examples of economies for which equilibria exist. Because of disagreement, Pareto suboptimal exchange economy equilibria exist for all elements in the utility function and endowment spaces and they may coexist with Pareto optimal equilibria even at the same competitive prices.     

Matching markets with price bargaining

The extant microeconomic literature on matching markets assumes ordinal preferences for matches, while bargaining within matches is mostly excluded. Central for this paper, however, is bargaining over joint profits from potential matches. We investigate, both theoretically and experimentally, a seemingly simple allocation task in a 2×2 market with repeated negotiations. When inefficiency is possible, about 1/3 of the complete matches are inefficient and, overall, more than 3/4 of the experimental allocations are unstable. These results strongly contradict existing bargaining theories requiring efficient matches. Even with regard to efficient matches, the tested theories perform poorly. Standard bargaining and behavioral concepts, such as Selten’s (1972) Equal Division Core, are outperformed by the simplistic ε-Equal Split, i.e., an equal split of the joint profit plus/minus ε.     

Subjective ambiguity, expected utility and Choquet expected utility

Summary. Using the Savage set up, this paper provides a simple axiomatization of the Choquet Expected Utility model where the capacity is an inner measure. Two attractive features of the model are its specificity and the transparency of its axioms. The key axiom states that the decision-maker uses unambiguous acts to approximate ambiguous ones. In addition, the notion of ‘ambiguity’ is subjective and derived from preferences. Received: March 23, 2000; revised version: April 24, 2001     

Foundations for contest success functions

In the literature, the outcome of contests is either interpreted as win probabilities or as shares of the prize. With this in mind, we examine two approaches to contest success functions (CSFs). In the first, we analyze the implications of contestants’ incomplete information concerning the ‘type’ of the contest administrator. While in the case of two contestants this approach can rationalize prominent CSFs, we show that it runs into difficulties when there are more agents. Our second approach interprets CSFs as sharing rules and establishes a connection to bargaining and claims problems which is independent of the number of contestants. Both approaches provide foundations for popular CSFs and guidelines for the definition of new ones.

“The strategic approach also seeks to combine axiomatic cooperative solutions and non-cooperative solutions. Roger Myerson recently named this task the ‘Nash program’.”(Rubinstein 1985, p. 1151)

     

General equilibrium in economies with adverse selection

We model economies of adverse selection as Arrow–Debreu economies. In the spirit of Prescott and Townsend (Econometrica 52(1), 21–45, 1984a), we identify the consumption set of the individuals with the set of lotteries over net transfers. Thus, prices are linear in lotteries, but they may be non linear in commodity bundles. First, we study a weak equilibrium notion by viewing the economy of adverse selection as a pure exchange economy. The weak equilibrium set is non empty, but some of the allocations may be inefficient, and the equilibria indeterminate. Second, following Prescott and Townsend (Econometrica 52(1), 21–45, 1984a), we introduce an intermediary (firm) supplying feasible and incentive compatible measures. Equilibria are constrained efficient, but the equilibrium set is empty for an open set of economies containing the Rothschild and Stiglitz insurance economies. The research of A. Rustichini was supported by the NSF grant NSF/SES-0136556.     

Union-oligopoly bargaining and entry deterrence: a reassessment of limit pricing

This paper introduces wage bargaining in the framework of Milgrom and Roberts (Econometrica 50(2):443–459, 1982) where the workers’ reservation wage is the private information parameter critical for entry. We show that entry threat significantly distorts the wage, which in some cases adversely affects the firm’s ability to signal through price. Consequently, the separating equilibrium (in price) does not always exist. If, however, wage agreements are made public, signalling occurs with or without distortions in wage depending on whether the union’s bargaining power is high or low. Pooling equilibrium also exists and it features similar distortions. We also examine which signal, wage or price, generates greater social welfare. We would like to thank two referees for their helpful comments and suggestions. This paper is partially based on a chapter of Pal’s PhD thesis done at Indira Gandhi Institute of Development Research (IGIDR), India. For remaining errors we are solely responsible.     

Predicting the pattern of international trade in the neoclassical model: a synthesis

I propose a framework that takes a set of conceivable outcomes as the primitive and a prediction is defined by identifying a subset on the set of conceivable outcomes. This notion of predictability serves as an organizing principle for characterizing pattern of trade predictions in single economy and integrated equilibrium formulations of the neoclassical trade model. I identify allocative efficiency as the unifying subset selection criterion for the different formulations of the neoclassical trade model, ranging from Ricardo’s (in Principles of Political Economy and Taxation, reprinted by J. M. Dent, London, in Everyman’s library, 1817) original comparative advantage formulation to the multi-cone Heckscher–Ohlin specification with multiple countries, goods and factors. I am grateful to comments from Jim Anderson, Chris Starmer, Catia Montagna, Peter Neary, two anonymous referees, as well as participants at the June 2007 GEP Conference on ‘New Directions in International Trade Theory’. I am grateful for financial support from NSF research grant SES-0452991 and from Leverhulme Trust Programme grant F114/BF.     

The Sensory Order and other Adaptive Classifying Systems

Synopsis Hayek’s cognitive theory, which seeks to describe the operation of a particular order, in fact provides a paradigmatic account of knowledge-generating orders in general. We claim that this paradigm provides a fertile conceptual framework for exploring a variety of problems in economics and social theory. In particular, we shall show that Hayek’s conception of the ‘map’ and the ‘model’, which he uses to explain the operation of the complex adaptive classifying system called ‘mind’, are promising analytical devices with applications extending to social structures of various kinds and complexity. We use Hayek’s notion of the map and model to analyze how different social structures – regarded as classifying systems – work in terms of their input, processing, and output capabilities. The adaptive characteristics of such systems, via communicative routines, multi-level classification, and feedback, form central motifs for our discussion of markets, science, and other social structures. We show that by analyzing the knowledge-generating characteristics of such structures we are also able to gain insights about the circumstances affecting their adaptive properties.     

The Biodiversity Bargaining Problem

We employ cooperative bargaining theory and Nash’s ‘rational threats’ idea to cast light on the biodiversity bargaining problem. The problem of global environmental negotiations is argued to be of the nature of a bargaining problem, in which bargainers must agree on the distribution of cooperative surplus in order to move to the bargaining frontier. We discuss the importance of both efficiency (bargaining frontier) and fairness (recognition of characteristics of bargainers) in the choice of the appropriate contract. We show that the incremental cost contract, used to resolve the biodiversity bargaining problem, is of the form of an extreme point contract that fails to recognise the contributions of the South to the production of cooperative surplus. A rational response to such a contract is the use of threats of biodiversity destruction. Contracts must evince both efficiency and fairness in order to represent lasting solutions.     

The origins of meso economics

The paper starts from Schumpeter’s proposition that entrepreneurs carry out innovations (the micro level), that swarms of followers imitate them (meso) and that, as a consequence, ‘creative destruction’ leads to economic development ‘from within’ (macro). It is argued that Schumpeter’s approach can be developed into a new—more general—micro-meso-macro framework in economics. Center stage is meso. Its essential characteristic is bimodality, meaning that one idea (the generic rule) can be physically actualized by many agents (a population). Ideas can relate to others, and, in this way, meso constitutes a structure component of a ‘deep’ invisible macro structure. Equally, the rule actualization process unfolds over time—modelled in the paper as a meso trajectory with three phases of rule origination, selective adoption and retention—and here meso represents a process component of a visible ‘surface’ structure. The macro measure with a view to the appropriateness of meso components is generic correspondence. At the level of ideas, its measure is order; at that of actual relative adoption frequencies, it is generic equilibrium. Economic development occurs at the deep level as transition from one generic rule to another, inducing a change of order, and, at the surface level, as the new rule is adopted, destroying an old equilibrium and establishing a new one.     

Competitive and core allocations in large economies with differential information

Summary. We study the core and competitive allocations in exchange economies with a continuum of traders and differential information. We show that if the economy is “irreducible”, then a competitive equilibrium, in the sense of Radner (1968, 1982), exists. Moreover, the set of competitive equilibrium allocations coincides with the “private core” (Yannelis, 1991). We also show that the “weak fine core” of an economy coincides with the set of competitive allocations of an associated symmetric information economy in which the traders information is the joint information of all the traders in the original economy. Received March 22, 2000; revised version: May 1, 2000     

The process and a simple logic of ‘meso’. Emergence and the co-evolution of institutions and group size

‘Summing-up’ aggregation of micro decisions contrasts with structural emergence in complex systems and evolutionary processes. This paper deals with institutional emergence in the ‘evolution of cooperation’ framework and focuses on its size dimension. It is argued that some ‘meso’ (rather than ‘macro’) level is the proper level of cultural emergence and reproduction. Also Schumpeterian economists have discussed institutions as ‘meso’ phenomena recently, and Schelling, Axelrod, Arthur, Lindgren, and others have dealt with ‘critical masses’ of coordinated agents and emergent segregations. However, emergent group size has rarely been explicitly explored so far. In an evolutionary and game-theoretic frame, ‘meso’ is explained in terms of a sustainably cooperating group smaller than the whole population. Mechanisms such as some monitoring, memory, reputation, and active partner selection loosen the total connectivity of the static and deterministic ‘single-shot’ logic and thus allow for emergent ‘meso’ platforms, while expectations ‘to meet again’ remain sufficiently high. Applications of ‘meso-nomia’ include the deep structure of ‘general trust’ and macro-performance in ‘smaller’ and ‘well networked’ countries which helps to explain persistent ‘varieties of capitalism’.     

Consumption taxation, social status and indeterminacy in models of endogenous growth with elastic labor supply

In this paper, we examine the effects of consumption taxation on long-run growth in an infinitely lived representative-agent model of endogenous growth with endogenous labor supply in which the desire for social status induces private agents to care about others’ wealth or consumption levels. This analysis shows that the increase in consumption taxation raises (reduces) the long-run growth rate when the equilibrium path is locally indeterminate (determinate), provided the desire for social status is not too strong in the relative wealth model. By contrast, in the consumption externalities model, the same result holds, if the Frisch labor supply and labor demand curves have the ‘normal’ slopes at their intersection point, while the result is reversed if these two curves have the ‘wrong’ slopes.     

Non-cooperative bargaining and the incomplete informational core

In an exchange economy with incomplete information, the signaling core is defined by the set of state-contingent allocations to which no coalitions object under informational leakage through proposals by informed agents. An objection underlying the signaling core is supported by a sequential equilibrium of an ultimatum bargaining game with an informed proposer. We prove that a stationary sequential equilibrium allocation in a Rubinstein-type sequential bargaining game with a restart rule belongs to the signaling core if the belief of players satisfies a self-selection property.     

Large economies with differential information and without free disposal

We consider exchange economies with a continuum of agents and differential information about finitely many states of nature. It was proved in Einy et al. (Econ Theory 18, 321–332, 2001) that if we allow for free disposal in the market clearing (feasibility) constraints then an irreducible economy has a competitive (or Walrasian expectations) equilibrium, and moreover, the set of competitive equilibrium allocations coincides with the private core. However when feasibility is defined with free disposal, competitive equilibrium allocations may not be incentive compatible and contracts may not be enforceable (see e.g. Glycopantis et al. in Econ Theory 21, 495–526, 2002). This is the main motivation for considering equilibrium solutions with exact feasibility. We first prove that the results in Einy et al. (Econ Theory 18, 321–332, 2001) are still valid without free-disposal. Then, motivated by the issue of contracts’ execution, we adapt the incentive compatibility property introduced in Krasa and Yannelis (Econometrica 62, 881–900, 1994) and we prove that every Pareto optimal exact feasible allocation is incentive compatible, implying that contracts of competitive or core allocations are enforceable. We would like to thank two anonymous reviewers and the Associate Editor for their valuable suggestions and remarks. This work was partially done while V.F. Martins-da-Rocha was visiting the Dipartimento di Matematica e Informatica of the Università degli Studi di Perugia. We thank the audience of the First General Equilibrium Workshop at Rio. Section 6 dealing with contract enforcement and coalitional incentive compatibility has benefited from discussions with J. Correia-da-Silva, W. Daher, F. Forges, C. Hervès-Beloso, E. Moreno-García, K. Podczeck, Y. Vailakis and N.C. Yannelis.     

Alternative evolutionary theories: A historical survey

Our overview has the objective of making our study relevant to bioeconomists. The need for the ‘alternatives’ to the Synthetic Theory of Evolution in social-economic studies was substantiated, for example, by Colombatto (Journal of Bioeconomics, 5, 1–25, 2003), who maintains that the natural-selection theory is ‘ill suited’ to describing evolutionary processes in economics. He proposed an alternative ‘non-Darwinian’ approach by equating the ‘non-Darwinian’ approach with a definite version of neo-Lamarckism. Yet, as we will show, there is a palette of alternative approaches within and beyond the neo-Lamarckism. We hope to give bioeconomists more choice in their theoretical modeling and constructing of analogies between biology and economics. It will also be shown that in the light of suggested definitions the concept of ‘universal Darwinism’ recently discussed in bioeconomics makes little sense as a generalizing category. In addition, in the concluding part of the paper we demonstrate that the majority of alternative approaches are far from being pigeonholed as archaic and once and for all wiped off the theoretical landscape. On the contrary, in recent years one can observe some revival of interest in the theoretical ‘heresies’.