Showing papers in "Economic Theory in 1992"
TL;DR: In this paper, the authors explore the set of equilibria in a game-theoretic model in which players can jointly exploit a productive asset, and they find that under certain circumstances there may be efficient as well as inefficient equilibrium.
Abstract: In the present paper we explore the set of equilibria in a game-theoretic model in which players can jointly exploit a productive asset. As in repeated games, we find that under certain circumstances there may be efficient as well as inefficient equilibria. In the model we study, efficient trigger-strategy equilibria may exist from some starting states (stocks of assets) but not others. More precisely, there is a stock level, sayy′, such that an efficient trigger-strategy equilibrium exists from starting stocks greater than or equal toy′, but not from those strictly less thany′. (This statement is meant to include the cases in whichy′ is zero or infinite.) Under some circumstances, there may exist a new kind of equilibrium, which we call aswitching equilibrium. We show that, in our model, whenever y′ is positive (and finite), there is an open intervalI with upper endpoint y′ such that, from any starting stock inI there is an equilibrium of the dynamic game with the following structure: the players follow an inefficient but growing path until the stock reaches the levely′, and then follow an (efficient) trigger strategy after that. The use of a continuous-time model enables us to conveniently decouple the delay of information from the time interval between decisions.
152 citations
TL;DR: In this article, the existence of pure strategy Nash equilibria in large finite action games was proved. But the payoff depends on the player's action and the average response of others.
Abstract: In this note we provide a direct and simple proof of the existence of pure strategy Nash equilibria in large finite action games when the payoffs depend on own action and the average response of others The result is then extended to the case where the action set of each player is a compact subset of ℜn
146 citations
TL;DR: In this article, an extension of the finite housing market version due to Shapley and Shubik was formulated, and optimal solutions to such a model exist and have properties similar to those established for finite models, namely, an equivalence among the following: (i) optimal solution to the linear programming problem associated with the assignment model; (ii) the core of the associated market game; (iii) the Walrasian equilibria of a associated market economy.
Abstract: We formulate a model with a continuum of individuals to be assigned to a continuum of different positions which is an extension of the finite housing market version due to Shapley and Shubik. We show that optimal solutions to such a model exist and have properties similar to those established for finite models, namely, an equivalence among the following: (i) optimal solutions to the linear programming problem (and its dual) associated with the assignment model; (ii) the core of the associated market game; (iii) the Walrasian equilibria of the associated market economy.
139 citations
TL;DR: In this article, the authors developed a model which is consistent with this observation and showed that the lack of risk sharing results from the interplay of two factors: first, contingencies must be based on information produced by measurement systems, which may be manipulable, and when two parties to a contract meet, they often have incomplete information.
Abstract: Theory suggests that optimal contracts should include many contingencies to achieve optimal risk sharing. However, in practice, few contracts are as complex as theory suggests. This paper develops a model which is consistent with this observation. The lack of risk sharing results from the interplay of two factors. First, contingencies must be based on information produced by measurement systems, which may be manipulable. Second, when two parties to a contract meet, they often have incomplete information. The type of contract offered may reveal information about the party who proposes it. Different types of agents have different preferences over contingent contracts, because they have different abilities to manipulate the measurement system. These differences in preferences allow the parties to signal their types through the contracts they offer. Noncontingent contracts may be chosen in equilibrium because they are the only contracts which do not give any type an incentive to distort the measurement system and, hence, do not reveal information about the party proposing the contract.
107 citations
TL;DR: In this paper, the authors studied a general version of the neoclassical growth model under possible production uncertainty and established the existence of stationary Markov equilibria in pure strategies for the discounted game.
Abstract: We study a strategic version of the neoclassical growth model under possible production uncertainty. For a general specification of the problem, we establish (i) the existence of stationary Markov equilibria in pure strategies for the discounted game, and (ii) the convergence, under a boundedness condition, of discounted equilibrium strategies to a pure strategy stationary Markovian equilibrium of the undiscounted game as the discount factor tends to unity. The same techniques can be used to prove that such convergence also obtains in all finitestate, finite-action stochastic games satisfying a certain “full communicability” condition. These results are of special interest since there are well known examples in the literature in which the limit of discounted equilibria fails to be an equilibrium of the undiscounted game.
87 citations
TL;DR: In this paper, the authors characterize equilibria of general equilibrium models with externalities and taxes as solutions to optimization problems, similar to Negishi's characterization of equilibrium models without externalities or taxes.
Abstract: We characterize equilibria of general equilibrium models with externalities and taxes as solutions to optimization problems. This characterization is similar to Negishi's characterization of equilibria of economies without externalities or taxes as solutions to social planning problems. It is often useful for computing equilibria or deriving their properties. Frequently, however, finding the optimization problem that a particular equilibrium solves is difficult. This is especially true in economies with multiple equilibria. In a dynamic economy with externalities or taxes there may be a robust continuum of equilibria even if there is a representative consumer. This indeterminacy of equilibria is closely related to that in overlapping generations economies.
87 citations
TL;DR: In this article, it was shown that the Borda count maximizes the probability that a Condorcet candidate is ranked first in a group election and that a transitive, binary ranking of the candidates is preserved in the group election.
Abstract: We prove that in the class of weighted voting systems the Borda Count maximizes the probability that a Condorcet candidate is ranked first in a group election. A direct result is that the Borda Count maximizes the probability that a transitive, binary ranking of the candidates is preserved in a group election. A preliminary result, but one of independent interest, is that the Borda Count maximizes the probability that a majority outcome betweenany two candidates is reflected by the group election. All theorems are valid when there is a uniform probability distribution on the voter profiles and can be generalized to other “uniform-like” probability distributions. This work extends previous results of Fishburn and Gehrlein from three candidates to any number of candidates.
68 citations
TL;DR: In this article, the authors examined the effects of extrinsic uncertainty or sunspots on competitive equilibrium when financial markets are incomplete, and showed that sunspot states will generate D =S−I dimensions of consumption allocation or real (as well as spot price or nominal) indeterminacy.
Abstract: This paper examines the effects of extrinsic uncertainty or sunspots on competitive equilibrium when financial markets are incomplete. For the canonical two-period, pure-exchange model with bonds (or so-called “nominal assets”, yielding fixed overall returns specified in units of account, and including pure inside money), the following result is established: Generically in endowments, if there areS sunspot states in the second period, but only 0
63 citations
TL;DR: This article study the Kiyotaki-Wright model with fiat money and show that the use of a low storage cost fiat money may be necessary for specialization and trade, and there can be valued fiat money steady states which are indeterminate, there are no nontrivial steady states in which all trades consist of fiat money for goods, and two fiat monies with different storage costs may both be valued.
Abstract: We study versions of the Kiyotaki-Wright (1989) model with fiat money and show that: (1) The use of a low storage cost fiat money may be necessary for specialization and trade, (2) there can be valued fiat money steady states which are indeterminate, (3) there are no nontrivial steady-states in which all trades consist of fiat money for goods, (4) fiat money may be valued even if it is not the least costly-to-store object, and lastly, (5) two fiat monies with different storage costs may both be valued.
59 citations
TL;DR: In this paper, an overlapping generations model with spatial separation and transaction costs is developed that displays steady state equilibria in which both cash (fiat currency) and trade credit are used in exchange.
Abstract: An overlapping generations model with spatial separation and transaction costs is developed that displays steady state equilibria in which both cash (fiat currency) and trade credit are used in exchange. Equilibria in which trade credit is used are not Pareto optimal. The question of the optimal quantity of money is addressed. Deflation is found to be optimal, contrary to the result for standard overlapping generations environments.
56 citations
TL;DR: In this paper, the set of equilibria of two-period, sunspot economies withS purely extrinsic states of nature in the second period andI assets with linearly independent nominal payoffs is considered.
Abstract: This paper considers the set of equilibria of two-period, sunspot economies withS purely extrinsic states of nature in the second period andI assets with linearly independent nominal payoffs. The span of the payoff matrix contains the vector [1, ... , 1] (i.e., inside money). The set of economies is described in terms of (sunspot-invariant) utility functions. IfS>I> 0, there is an open, dense set of economies such that, given a vector of no arbitrage asset prices, the set of equilibrium allocations contains a smooth manifold of dimensionS—I. Such a manifold contains at least one nonsunspot equilibrium (and at most a finite number of such equilibria).
TL;DR: In this article, it was shown that there is at least one degree of real indeterminacy in a two-period sunspot economy with inside money and S possible realizations of the sunspot.
Abstract: In a two-period sunspot economy with inside money andS possible realizations of the sunspot, we prove that, genetically in the space of utility functions, there areS — 1 degrees of real indeterminacy. This result generalizes the previously known result for sunspot models that, generically in endowments, there is at least one degree of real indeterminacy. The proof involves showing that generically the equilibrium allocation is different across states for some household. This property allows us to perturb the utility function in a simple way and to apply standard transversality arguments to prove our main theorem.
TL;DR: In this article, the authors studied the problem of an incomplete information monopolist seeking to design a line of contracts so as to simultaneously screen consumers by type and resolve the moral hazard problems associated with contract performance.
Abstract: We study the problem faced by an incomplete information monopolist seeking to design a line of contracts so as to simultaneously screen consumers by type and resolve the moral hazard problems associated with contract performance. We formulate the monopolist's problem as a mechanism design problem in which the set of consumer types is taken to be a Polish space, and the contract space an arbitrary compact metric space. Allowing for risk aversion on the part of the monopolist and consumers, and taking as the feasible set of mechanisms the collection of all measurable functions defined on the space of consumer types with values in the space of contracts, we present a new characterization of incentive compatibility in an infinite dimensional setting which allows us to reformulate the monopolist's design problem as an unconstrained optimization problem (i.e., as a problem without the incentive compatibility contraints). Using simple techniques, we then demonstrate the existence of an optimal screening mechanism for the monopolist. We thus extend the existing analysis of the incomplete information monopoly problem to an infinite dimensional setting with moral hazard, and we provide an existence result not available in the existing literature.
TL;DR: In this article, the authors consider games in characteristic function form satisfying a mild boundedness condition where, when the games have many players, most players have many substitutes and show that these games satisfy inessentially of large groups if and only if they satisfy the approximate core property.
Abstract: Inessentiality of large groups or, in other words, effectiveness of small groups, means that almost all gains to group formation can be realized by partitions of the players into groups bounded in absolute size. The approximate core property is that all sufficiently large games have nonempty approximate cores. I consider these properties in a framework of games in characteristic function form satisfying a mild boundedness condition where, when the games have many players, most players have many substitutes. I show that large (finite) games satisfy inessentially of large groupsif and only if they satisfy the approximate core property.
TL;DR: In this paper, the results of four overlapping generations experiments performed at the California Institute of Technology were presented, in which each agent had a two-period life span, with the exception of the first period, there were eight agents trading in each period; four buyers and four sellers (two young and two old).
Abstract: The paper presents the results of four overlapping generations experiments performed at the California Institute of Technology. Overlapping generations markets were created in which each agent had a two period life span. With the exception of the first period, there were eight agents trading in each period; four buyers (two young and two old) and four sellers (two young and two old). Parameters were selected so that a “small” set of equilibria existed. The markets were open for twenty-nine periods with a demand shift occurring at the fifteenth and sixteenth periods.
TL;DR: A large body of search literature has been developed around the random search model, which has been routinely used with the assumption of random search.
Abstract: Search theoretic models, which characterize the behavior of agents and market outcomes in imperfect information environments, have been of considerable interest in a variety of economic contexts. In labor economics, such models have been used to portray the job search behavior of workers, wage determination, and to analyze labor market equilibrium. In empirical studies, they have been useful in the structural interpretation of labor market histories. There is also a vast literature in the context of consumer price search.1 Optimal sequential search strategies have also been studied in the context of research, development and exploration projects, innovation and choice of substitutable technologies, etc.2 In the search literature, two basic types of search models may be identified: random search and systematic search. Random search is typified by a scenario wherein an agent sequentially samples from the same offer distribution (offers can be prices, rewards, wages, or in general, opportunities, depending on the context), and the search decision is to decide, after obtaining a sample, whether to stop the search process or continue further search. In systematic search models, the agent faces a number of alternatives (sources, options, or projects), each with its own (possibly different) reward distribution, and thus, the agent in determining the search strategy has the choice of which alternative to explore at a point in time.3 A large body of search literature has been developed around the random search model. This assumption of random search, which has been routinely used with
TL;DR: In this article, the authors provided sensitivity and duality results for continuous-time optimal capital accumulation models where preferences belong to a class of recursive objectives, and they combined the same topology with a controllability condition to demonstrate the sensitivity of the optimal path with respect to changes in the initial endowment of capital.
Abstract: Summary. This paper provides sensitivity and duality results for continuous-time optimal capital accumulation models where preferences belong to a class of recursive objectives. We combine the topology used by Becker, Boyd and Sung (1989) with a controllability condition to demonstrate that optimal paths are continuous with respect to changes in both the initial capital stock, and the rate of time preference. Under convexity and an interiority condition, we nd the value function is dierentiable, and derive a multiplier equation for the supporting prices. Finally, under some mild additional conditions, we show that supporting prices obeying the transversality and multiplier equations are both necessary and sucient for an optimum. This paper provides sensitivity and duality results for continuous-time optimal capital accumulation models where the planner’s preferences are represented by a recursive objective functional. Time preference is exible. A previous paper (Becker, Boyd and Sung, 1989) established the existence of optimal paths by choice of an appropriate topology. In this paper, we combine the same topology with a controllability condition to demonstrate the sensitivity of the optimal path with respect to changes in the initial endowment of capital, and changes in the planner’s rate of time preference. Under convexity and an interiority condition, we nd the value function is dierentiable, and derive a multiplier equation for the
TL;DR: The authors analyzes how different types of product market organization affect firms' R&D investments in a stochastic innovation framework and identifies restrictions on the research project success probability distribution that yield an invariance result for expenditure per research project.
Abstract: This paper analyzes how different types of product market organization affect firms' R&D investments in a stochastic innovation framework. Product market competition determines payoffs to successful and unsuccessful firms. Restrictions on the research project success probability distribution are identified that yield an invariance result for expenditure per R&D project. The impact of the number of firms (n) on the amount of market R&D is shown to be sensitive to product market organization. For a major process innovation, firms undertake more R&D projects under Cournot product market competition than under Bertrand competition, forn sufficiently large. A numerical example is used to illustrate welfare tradeoffs.
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TL;DR: In this article, a new proof of this result is given, based on the Gap Theorem, which requires the existence of utility functions that are continuous with respect to the order topology.
Abstract: Debreu's fundamental result on the existence of utility functions that are continuous with respect to the order topology requires his Gap Theorem. A new proof of this result is given.
TL;DR: In this paper, an alternative short proof for the linear utility representation theorem is presented, in particular a generalization of the theorem of Blackwell and Girshick (1954) and a special case of Herstein and Milnor (1953) are proved by exploiting the topological group structure of finite-dimensional Euclidean vector space.
Abstract: The paper presents an alternative short proof for the linear utility representation theorem. In particular a generalization of the theorem of Blackwell and Girshick (1954) and a special case of the theorem of Herstein and Milnor (1953) are proved by exploiting the topological group structure of finite-dimensional Euclidean vector space.
TL;DR: In this paper, the authors extend the Sonnenschein-Mantel-Debreu theorem characterizing aggregate demand functions from the set of n≧2 commodities to all of the 2 n −(n+1) subsets of two or more commodities.
Abstract: Two theorems are given; the first extends the Sonnenschein-Mantel-Debreu theorem characterizing aggregate demand functions from the set ofn≧2 commodities to all of the 2 n −(n+1) subsets of two or more commodities. The second theorem concerns spatial voting models for k≧2 candidates over a space of n≧2 issues. The theorem characterizes the sincere elecion rankings of thek candidates over all of the 2 n −1 subsets of one or more issues. Both theorems have the same kind of conclusion; anything can happen. By demonstrating the mathematical reasons for these conclusions and by recalling related, recent results from statistics, voting, and economics, it is argued that this “anything can happen” conclusion is the type one must anticipate for aggregation procedures; particularly for the processes commonly used in economic models where the procedure is responsive to changes in agents' preferences, changes in data, etc.
TL;DR: In this article, the authors studied the problem of optimal mechanism design for incomplete information Stackelberg games with several followers in which each follower, guided by his own probability assessments concerning the characteristics of the other followers, behaves as a Bayesian in choosing a reporting strategy.
Abstract: We study the problem of optimal mechanism design for incomplete information Stackelberg games with several followers in which each follower, guided by his own probability assessments concerning the characteristics of the other followers, behaves as a Bayesian in choosing a reporting strategy. Allowing for uncountably many types and infinite dimensional type descriptions, we present a new, general existence result for Bayesian incentive compatible (BIC) mechanisms. Because the existence problem is infinite dimensional, novel existence arguments are required. Our existence proof is based on two results: one on the sequential closure of the subset of BIC mechanisms with respect toK-convergence, and the other, a new result on sequential compactness in spaces of vector-valued functions.
TL;DR: In this paper, the authors define a choice process over social outcomes in which agents choose the institutional rules or mechanisms themselves without outside interference, and define endogenous mechanism selection as an infinite regress problem where outcomes are chosen by games which are themselves chosen by game, ad infinitum.
Abstract: This paper defines a choice process over social outcomes in which agents choose the institutional rules ormechanisms themselves without outside interference. Truly “endogenizing” the mechanism selection process in this way, however, involves facing an infinite regress problem in which outcomes are chosen by games which are themselves chosen by games, ad infinitum. This paper allows the possibility of such an infinite regress which we callfully endogenous mechanism selection.
TL;DR: In this article, the performance of three pricing institutions in a decentralized matching model was compared, and it was shown that the equilibrium with ex ante pricing generates participation rates that tend toward the pareto efficient level.
Abstract: This paper compares the performance of three pricing institutions in a decentralized matching model in which random matching occurs. In the first, sellers make public ex ante commitments to trade at pre-specified prices before matching occurs. In the second, the buyer and seller engage in an alternating offer bargaining game once a match has occurred. In the final pricing institution, one party is chosen at random to make a take it or leave it price offer. The steady state equilibrium with ex ante pricing pareto dominates the steady state equilibrium with ex post take it or leave it offers, which in turn pareto dominates the steady state equilibrium with alternating offers. As the discount factor goes to one, the equilibrium with ex ante pricing generates participation rates that tend toward the pareto efficient level. The ex post pricing institutions generate participation rates that are bounded away from efficient levels. The surplus loss associated with switching from ex ante pricing to take it or leave it offers is small when the discount factor is close to one. Contrary to many models of decentralized trade, ex post pricing institutions encourage too much search by buyers.
TL;DR: In this article, the authors characterized Arrow Social Welfare Functions (ASWF) as having maximal hierarchies and characterized the rationalizability of Arrow social welfare functions by weighted majority rule.
Abstract: In Armstrong [1985] I examined precisely dictatorial social welfare functions. These are those social welfare functions o with associated dictator k so that, for a profile / of preferences, the social preference a(f) agrees precisely with the preference /(/c) of the dictator rather than merely extending that preference. The characterization is that of relational monotonicity for g so that if a preference profile g was obtained by extending the preferences of individuals v in a society V from that of another profile /, (so that as subsets oflxl, where X is the alternative space, the weak order f(v) is contained in the weak order g(v) for all veV) then a(f) must also be extended by a{g). As mentioned in that paper Sarbadhikari had brought to my attention the fact that Arrow Social Welfare Functions (ASWF) other than the precisely dictatorial ones exist. The simplest example is where there is a secondary dictator whose preferences between alternatives are followed in case the primary dictator is indifferent between these alternatives. Indeed one could allow tertiary dictators or quaternary dictators etc. That is, one can conceive of a dictatorial pecking order, finite in extent for finite V, but possibly infinite in extent for infinite V. The purpose of this paper is to characterize which Arrow Social Welfare Functions have such a dictatorial hierarchy. This characterization is that the social welfare function satisfy, in addition, a certain Pareto condition which we call comonotonicity for its intimate connection with current non-linear expected utility literature. Precisely dictatorial ASWFS may be considered conservative or minimally decisive in expressing preference between as few alternatives as possible. We examine here maximally decisive ASWF and characterize them as having maximal hierarchies. At the conclusion we make some remarks as to the rationalizability of ASWFs by weighted majority rule.
TL;DR: In this paper, a general-equilibrium intertemporal model of a country engaged in international trade is developed, which can be used to address a wide variety of issues of interest under the assumption that prices of tradable commodities (consumer goods and capital goods) and interest rate are exogenous to the country.
Abstract: This paper develops a very general (general-equilibrium) intertemporal model of a country engaged in international trade which can be used to address a wide variety of issues of interest — in particular, econometric application — under the assumption that prices of tradable commodities (consumer goods and capital goods) and the interest rate are exogenous to the country. It allows for an arbitrarily large number of commodities which are distinguished into seven categories and for finite or infinite periods of time. This model can be used to draw various policy conclusions. We investigate how current net imports, the balance of payments on current account, current consumption expenditure, next-period bondholdings, current wealth, and current internal prices will react to exogenous changes in current external prices, the current interest rate, current taxes, current factor endowments, and current-period bondholdings. This paper also considers the integrability of net-import demand functions.
TL;DR: In this paper, the existence of equilibrium in behavior strategies for extensive form games when the game has infinite actions was proved under the assumption that the behavior strategies satisfy the bounded measurability condition, which implies that the behaviour strategies are restricted to those which can be viewed as continuous functions from the set of initial histories to the space of probability distributions over action spaces.
Abstract: We prove the existence of equilibrium in behavior strategies for extensive form games when the game has infinite actions. The result is derived under the assumption that the behavior strategies satisfy the bounded measurability condition. The condition implies that the behavior strategies are restricted to those which can be viewed as continuous functions from the set of initial histories to the space of probability distributions over action spaces which satisfy the Lipschitz bound.
TL;DR: In this article, the existence of a general equilibrium with differentiated commodities is proved for the classical case of a production set with constant returns, spanned by elementary activities without joint production, and with a finite set of primary factors.
Abstract: In this paper the existence of a general equilibrium with differentiated commodities is proved for the classical case of a production set with constant returns, spanned by elementary activities without joint production, and with a finite set of primary factors. This framework allows to proceed without strong assumptions concerning substitution possibilities, which are typical in general equilibrium theory with differentiated commodities, but which at least with respect to production are not adequate to the problem. Moreover, in our model general consumption sets are allowed. Thus true intermediate products are not excluded. Furthermore the possibility of survival without trade is not assumed.