Anonymous sequential games: Existence and characterization of equilibria

Summary In this paper we consider Anonymous Sequential Games with Aggregate Uncertainty. We prove existence of equilibrium when there is a general state space representing aggregate uncertainty. When the economy is stationary and the underlying process governing aggregate uncertainty Markov, we provide Markov representations of the equilibria.Table of notation Agents' characteristics space ( ) - A Action space of each agent (aA) - Y Y = x A - Aggregate distribution on agents' characteristics - (X) Space of probability measures onX - C(X) Space of continuous functions onX - _X Family of Borel sets ofX - State space of aggregate uncertainty ( ) - x _t=1 aggregate uncertainty for the infinite game - = (₁,₂,...,_t,...) - ^{t t} (₁, ₂,..., _t) - L₁(^t,C ×A),v _t Normed space of measurable functions from ^t toC( x A) - 8o(^t,( x A)) Space of measurable functions from ^tto( x A) - X^t X^t= x _s=1 ^t X - _X ^t Borel field onX ^t - v Distribution on - v_t Marginal distribution of v on ^t - v(^t)((¦^t)) Conditional distribution on given ^t - v^t(^s)(v_t(¦^s)) Conditional distribution on ^t given ^s (wheres) - _t Periodt distributional strategy - Distributional strategy for all periods =(₁,₂,...,_t,...) - _t Transition process for agents' types - ( _t,^t,y)(P _t+1(, _t , ^t ,y)) Transition function associated with _t - u _t Utility function - V _t (, a, , ^t) Value function for each collection (, a, , ^t ) - W _t (, , ^t ) Value function given optimal action a - C() Consistency correspondence. Distributions consistent with and characteristics transition functions - B() Best response correspondence (which also satisfy consistency) - E Set of equilibrium distributional strategies - x _t=1 ( ^t , (x A)) - S Expanded state space for Markov construction - (, a, ) Value function for Markov construction - P( _t ^* , _t y)(P(, _t ^* , _t , _y )) Invariant characteristics transition function for Markov game We wish to acknowledge very helpful conversations with C. d'Aspremont, B. Lipman, A. McLennan and J-F. Mertens. The financial support of the SSHRCC and the ARC at Queen's University is gratefully acknowledged. This paper was begun while the first author visited CORE. The financial support of CORE and the excellent research environment is gratefully acknowledged. The usual disclaimer applies.     

Equilibria and Pareto optima of markets with adverse selection

Summary This paper examines the efficiency properties of competitive equilibrium in an economy with adverse selection. The agents (firms and households) in this economy exchange contracts, which specify all the relevant aspects of their interaction. Markets are assumed to be complete, in the sense that all possible contracts can, in principle, be traded. Since prices are specified as part of the contract, they cannot be used as free parameters to equate supply and demand in the market for the contract. Instead, equilibrium is achieved by adjusting the probability of trade. If the contract space is sufficiently rich, it can be shown that rationing will not be observed in equilibrium. A further refinement of equilibrium is proposed, restricting agents' beliefs about contracts that are not traded in equilibrium. Incentive-efficient and constrained incentive-efficient allocations are defined to be solutions to appropriately specified mechanism design problems. Constrained incentive efficiency is an artificial construction, obtained by adding the constraint that all contracts yield the same rate of return to firms. Using this notion, analogues of the fundamental theorems of welfare economics can be proved: all refined equilibria are constrained incentive-efficient and all constrained incentive-efficient allocations satisfying some additional conditions can be decentralized as refined equilibria. A constrained incentive-efficient equilibrium is typically not incentive-efficient, however. The source of the inefficiency is the equilibrium condition that forces all firms to earn the same rate of return on each contract.Notation ={ ₁,..., _k } set of outcomes - : ₊ generic contract or lottery - A = () ; - A_o A{, where denotes the null contract or no trade - S={1,...,¦S¦} set of seller types - L(s) number of type-s sellers - M number of buyers - u: × S seller's utility function, which can be extended toA× S by puttingu(, s) ; - v. × S buyer's utility function, which can be extended toA × S by puttingv(, s) ; - f:A ₀ ×S ₊ allocation of sellers - g:A ₀ ×S ₊ allocation of buyers - A ₊ sellers' trading function - :A ×S ₊ buyers' trading function This paper has had a long gestation period, during which I have been influenced by helpful conversations with many persons, by their work, or both. Among those who deserve special mention are Martin Hellwig, Roger Myerson, Edward Prescott, Robert Townsend and Yves Younés. Earlier versions were presented to the NBER/CEME Conference on Decentralization at the University of Toronto and the NBER Conference on General Equilibrium at Brown University. I would like to thank John Geanakoplos, Walter Heller, Andreu Mas Colell, Michael Peters, Michel Poitevin, Lloyd Shapley, John Wooders, Nicholas Yannelis and an anonymous referee for their helpful comments and especially Robert Rosenthal for his careful reading of two drafts. The financial support of the National Science Foundation under Grant No. 912202 is gratefully acknowledged.     

The Regulation of Private Schools Serving Low-Income Families in Andhra Pradesh,India

This paper sets out some findings of a research project carried out in private unaided schools in low-income areas of Hyderabad, India. The part of the research project documented here was designed to examine the question: Is the regulatory regime conducive to entrepreneurial action and market discovery with particular reference to the low-income schools in Hyderabad. This paper is narrowly focused, setting out the results of pattern matching empirical data with the Austrian economic concepts of entrepreneurship, rivalry, and market discovery. The research discovered that two regulatory regimes exist, one that is set out on paper in the Education Acts and associated rules, and another that operates in practice. That is, there is a combination of regulations on paper and regulations existing in an extra-legal sector. Generally it was found that the regulations in practice are consistent with market principles. Conversely the regulations set out on paper are not conducive to entrepreneurial innovation and market discovery. Recommendations for potential policy initiatives include the possibility of legitimising the extra-legal sector by introducing self-regulation possibly via self-evaluation systems for the private unaided schools.     

Biological Adaptation in Human Societies: a ‘Basic Needs’ Approach

The groundzero premise (so to speak) of the biological sciences is that survival and reproduction is the basic, continuing, inescapable problem for all living organisms; life is at bottom a survival enterprise. It follows that survival is the paradigmatic problem for human societies as well; it is a prerequisite for any other, more exalted objectives. Although the term adaptation is also familiar to social scientists, until recently it has been used only selectively, and often very imprecisely. Here a more rigorous and systematic approach to the concept of adaptation is proposed in terms of basic needs. The concept of basic human needs has a venerable history – tracing back at least to Plato and Aristotle. Yet the development of a formal theory of basic needs has lagged far behind. The reason is that the concept of objective, measurable needs is inconsistent with the theoretical assumptions that have dominated economic and social theory for most of this century, namely, valuerelativism and cultural determinism. Nevertheless, there have been a number of efforts over the past 30 years to develop more universalistic criteria for basic needs, both for use in monitoring social wellbeing (social indicators) and for public policy formulation. Here I will advance a strictly biological approach to perationalizing the concept of basic needs. It is argued that much of our economic and social life (and the motivations behind our revealed preferences and subjective utility assessments), not to mention the actions of modern governments, are either directly or indirectly related to the meeting of our basic survival needs. Furthermore, these needs can be specified to a first approximation and supported empirically to varying degrees, with the obvious caveat that there are major individual and contextual variations in their application. Equally important, complex human societies generate an array of instrumental needs which, as the term implies, serve as intermediaries between our primary needs and the specific economic, cultural and political contexts within which these needs must be satisfied. An explicit framework of Survival Indicators, including a profile of Personal Fitness and an aggregate index of Population Fitness, is briefly elucidated. Finally, it is suggested that a basic needs paradigm could provide an analytical tool (a biologic) for examining more closely the relationship between our social, economic and political behaviors and institutions and their survival consequences, as well as providing a predictive tool of some value.     

On the generic nonconvergence of Bayesian actions and beliefs

Summary SupposeY _n is a sequence of i.i.d. random variables taking values in Y, a complete, separable, non-finite metric space. The probability law indexed by, is unknown to a Bayesian statistician with prior, observing this process. Generalizing Freedman [8], we show that generically (i.e., for a residual family of (,) pairs) the posterior beliefs do not weakly converge to a point-mass at the true. Furthermore, for every open setG , generically, the Bayesian will attach probability arbitrarily close to one toG infinitely often. The above result is applied to a two-armed bandit problem with geometric discounting where armk yields an outcome in a complete, separable metric spaceY _k. If the infimum of the possible rewards from playing armk is less than the infimum from playing armk', then armk is (generically) chosen only finitely often. If the infimum of the rewards are equal, then both arms are played infinitely often.     

Information processing for a finite resource allocation mechanism

Summary deal with an organization havingm individual agents (the agents) and one central agent or agency (the coordinator), and the problem of allocating a fixed supply ofn commodities among the agents. The coordinator wishes to distribute the commodities in such a way as to maximize an objective function whose arguments are functions known (implicitly) to the individual agents, but not to the coordinator. The more information the coordinator obtains about the individual agents' functions, the better the allocation decision he or she can make; however, gaining such information is costly, so that the coordinator must balance the potential gain against the cost of acquiring additional information. We find a satisficing solution to this problem which is computable and which terminates in a finite number of steps.We would like to thank Leo Hurwicz, Ken Matheny, Shailendra Mehta, Bill Novshek, Roy Radner, Stan Reiter, Vernon Smith, Mark Walker, and, especially, John Ledyard and Tom Marschak, for helpful comments and suggestions. We must, of course, however reluctantly, accept responsibility for any remaining defects.     

Institutional Evolution through Purposeful Selection: The Constitutional Economics of John R. Commons

The paper relates John. R. Commons view on the roleof human design in institutional evolution to the views thathave been advanced on this matter by F. A. Hayek, in German ordo-liberalism,and in constitutional political economy. It is argued that Commonsconcept of purposeful selection points in the direction ofa theoretical perspective that consistently integrates the notionsof institutional evolution and constitutional design.     

Giffen goods and market making

Summary. This paper shows that information effects per se are not responsible for the Giffen goods anomaly affecting traders demands in multi asset noisy, rational expectations equilibrium markets. The role that information plays in traders strategies also matters. In a market with risk averse, uninformed traders, informed agents have a dual trading motive: speculation and market making. The former entails using prices to assess the effect of error terms; the latter requires employing them to disentangle noise traders demands within aggregate orders. In a correlated environment this complicates the signal extraction problem and may generate upward sloping demand curves. Assuming (i) that competitive, risk neutral market makers price the assets or that (ii) uninformed traders risk tolerance coefficient grows unboundedly, removes the market making component from informed traders demands rendering them well behaved in prices.Received: 30 April 2002, Revised: 3 December 2003, JEL Classification Numbers: G100, G120, G140.Support from the Barcelona Economics Program of CREA and the Ente per gli Studi Monetari e Finanziari Luigi Einaudi, are gratefully acknowledged. I thank Anat Admati, Jordi Caballé, Giacinta Cestone, and Xavier Vives for useful suggestions. The comments provided by the Associate Editor and an anonymous referee greatly improved the papers exposition.     

Changing monetary transmission mechanisms within the EU

The paper presents a comparative analysis of monetary transmission mechanisms and changes in them after the secondERM in March 1983. The empirical model investigates the determination of money, income, prices, and interest rates in Germany, Denmark, and Italy based on the cointegratedVAR model. It provides empirical results on the macroeconomic effects of joining theERM and financial deregulation.     

Are Uniform Solutions Focal? – The Case of International Environmental Agreements

The application of uniform solutions has several drawbacks, notably their lack of cost efficiency and their inability to guarantee individual rationality. A proper specification of uniform solutions, however, reveals that uniform solutions that satisfy individual rationality always exist. When all countries hold private information about their own reduction costs, there only exists one solution that always satisfies individually rationality without use of side payments and the requirement of dominant strategy implementation: The solution that selects the smallest individually preferred uniform reduction which also give a theoretical explanation of the lowest common denominator effect.     

Stability of the demand for M1 and harmonized M3 in Finland

We derive a theoretical model for the demand for money using the adjustment cost augmented money-in-the-utility-function approach. The steady-state-utility function-parameters of the model of narrow money (M1) estimated with cointegration techniques are stable over the foreign exchange rate regime shift; whereas in the model of harmonized M3 (M3H) they arenot stable. The theoretical model fits the M1 data. The adjustment cost parameters of the M1 model describing the dynamics of the demand for money might indicate technological improvements in banking and payments during the sample period. These results suggest that from the Finnish point of view M1 would be a more appropriate intermediate target for monetary policy than harmonized M3.The views expressed are those of the author and not necessarily the views of the Bank of Finland. I thank Juha Tarkka, Jouko Vilmunen, Pekka Ilmakunnas, Erkki Koskela, Paolo Paruolo, Anders Rahbek, Pentti Saikkonen, Juha Seppälä, Matti Virén and the participants of ESEM96 meeting and Money Demand in Europe conference (October 1997, Berlin) for useful comments and discussions and two anonymous referees and the editors for profound and constructive comments. The usual disclaimer applies. The data may be obtained from the internet, http://wotan.wiwi.hu-berlin.de/oekonometrie/engl/data.html     

The measurement of entry rates: Recondiseration and resolution

This paper extends the recent analysis of Audretsch and Fritsch on entry rates, and suggests a resolution to the possible policy confusion which they discuss. British data also show very different results for the determinants of entry depending on whether the ecological or labour market entry rate is used. It is shown that, in addition to the static, size-distribution effect discussed by Audretsch and Fritsch, there are dynamic factors at work which may lead to this result. However, there need be no conflict in policy signals arising from this, because the labour market approach can be shown to be a superior measure of entry rates where spatial analysis is undertaken.     

Schumpeterian endogenous growth theory and evolutionary economics

In this paper, we aim to discuss whether Schumpeterian models of endogenous growth can accommodate Schumpeters vision of development through creative destruction. Taking a methodological approach, our focus is on individual decision-making, technology, general equilibrium and welfare, and steady state dynamics as the fundamental principles underlying endogenous growth theory. In particular, the Aghion-Howitt model of Schumpeterian growth in various extended versions is analyzed in the light of Schumpeters work. Therefore, we also try to root Schumpeters work in historical context. We find endogenous growth theory far from carrying Schumpeters idea of an evolutionary approach to change and development. Rather the emergence of numerous models of an evolutionary type can be observed to provide for the formal structure appropriate to keeping Schumpeters legacy alive.JEL Classification: B1, B2, B4, O3, O4Corespondence to: Thomas Kuhn     

Demographic variables in demand systems: The case for generality

This paper provides evidence in favour of greater generality in the demographic demand literature. We propose two demographic demand procedures. One extends the Gorman model by allowing non additive interaction between overheads and Barten scaling. The other extends Price Scaling, by allowing the equivalence scale to vary with utility, and offers a test of Equivalence Scale Exactness (ESE). The rejection of ESE is robust to the assumed demand functional forms (RNLPS, QAIDS), to items chosen, and the estimation method (MLE, GMM). The results show that published cell averages yield well determined estimates of the demographic generalisation parameters.This paper was written during my visit to the UBC in Vancouver, Canada in 1992/93. I am grateful to two anonymous referees for their helpful remarks on an earlier version. The disclaimer applies.     

The “Dorfman Steiner” rule

Conclusion When this research was started, it was guessed that the Dorfman-Steiner rule would lose its relevance in an intertemporal setting. This belief has turned out to be false: along the optimal paths ofp (t) ands (t), and must be equal. The only difference with the Dorfman-Steiner result is that they will be different from unity.The author is chargé de cours at the Faculté Universitaire Catholique de Mons (Belgium). He has greatyl benefited from comments by M. Beuthe and J. J. Lambin.     

A New Variant of the Winner's Curse in a Coasian Contracting Game

We examine behavior in a Coasian contracting game with incomplete information. Experimental subjects propose contracts, while automaton property right holders or robot players with uncertain preferences respond to those proposals. The most common pattern of proposals observed in these games results in too many agreements and, in some games, payoffs that are stochastically dominated by those resulting from rational proposals (which imply fewer agreements). In this sense, we observe a winner's curse similar to that observed in bidding games under incomplete information, such as the common value auction (Kagel, J.H. and Levin, D. (1986) American Economic Review. 76, 894–920) and the takeover game (Samuelson, W. and Bazerman, M.H. (1985) In Research in Experimental Economics, Vol. 3. JAI Press, Greenwich, pp. 105–137; Ball, S.B., Bazerman, M.H., and Carroll, J.S. (1990) Organizational Behavior and Human Decision Processes. 48, 1–22; Holt, C. and Sherman, R. (1994) American Economic Review. 84, 642–652). While the naïve model of behavior nicely predicts the winner's curse in those previous bidding games, it does not do so here. Instead, an alternative model we call the guarantor model explains the anomalous behavior best. Hence, we suggest this is a new variant of the winner's curse.     

Shiftable Externalities: A Market Solution

In this paper we propose a regulatory scheme for what has become known as shiftable externalities (Not In My Backyard type garbage location problemswhere the externality is characterized by the absence of jointness in supply).The scheme facilitates the establishment of a market for the externality, and it isfeasible for a wider class of regulation problems and more information efficientthan the other regulatory schemes that have been proposed for this type ofexternality. Finally, we show that it is possible to decentralize the participationdecision so as to take account of verification costs.     

Corporate Lobbying, Regulatory Conduct and the Porter Hypothesis

Michael Porter, the influential Harvard management guru, has promoted the idea that compliance with stricter environmental regulations can afford secondary benefits to firms through improved product design, innovation, corporate morale and in other ways. Once these secondary benefits are factored, the net cost of compliance is argued to be lower than conventionally thought and may even be negative. Whilst environmental economists have rejected the Porter Hypothesis as being based on excessively optimistic expectations of the likely size of such secondary benefits the underlying ideas do enjoy significant credence in the business community. In the context of a lobbying model of regulatory policy-making we argue that the EPA should change the way it conducts regulatory policy to take account of Porter's views – even if it knows those views to be misguided. The model serves to illustrate the more general point that fashions in management thinking can be expected to impact the optimal conduct of regulatory policy.     

Augmented serial rules for an excludable public good

Summary. We present a new class of rules named augmented serial rules for the provision of an excludable public good. First, we characterize this class by the four axioms of strategy-proofness, envy-freeness, access independence, and nonbossiness. Second, we identify two important subclasses by imposing an additional axiom: (i) anonymous augmented serial rules by anonymity, and (ii) Moulins serial rule by individual rationality.Received: 31 December 2002, Revised: 9 June 2004, JEL Classification Numbers: D71, D82, H41.This paper is a substantial revision of Serial cost sharing with simple games. I would like to thank Hervé Moulin, Yoshikatsu Tatamitani, an associate editor, and three anonymous referees for helpful suggestions and detailed comments. This research was partially supported by the Ministry of Education, Culture, Sports, Science, and Technology in Japan (Grant-in-Aid for 21st Century COE Program Microstructure and Mechanism Design in Financial Markets).     

The distribution of money and prices in an equilibrium with lotteries

Summary. We construct a tractable fundamental model of money with equilibrium heterogeneity in money balances and prices. We do so by considering randomized monetary trades in a standard search-theoretic model of money where agents can hold multiple units of indivisible tokens and can offer lotteries on monetary transfers. By studying a simple trading pattern, we can analytically characterize the monetary distribution. Interestingly, such distributions match those observed in numerically simulated economies with fully divisible money and price heterogeneity.Received: 16 April 2003, Revised: 11 February 2004JEL Classification Numbers: D30, D83, E40.A. Berentsen, G. Camera, C. Waller: The paper has benefitted from insightful comments of two anonymous referees, whom we thank. We also thank participants at the conference Recent Developments in Money and Finance, held at Purdue University in May 2003, and the EPRI/University of Western Ontario Money Conference held in October 2003. Correrspondence to: G. Camera