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.     

Robust Institutions

I propose to show how to translate the economic analysis of institutions developed in the tradition of worst case political economy into the lingua franca of robust statistics. An institution will be defined as contingent upon a design theory and the difficulty we consider is the use of the institution by the designer.The technical bridge between institutional robustness and statistical robustness is the the possibility of exploratory data analysis [EDA] with respect to the design theory. In an institutional context with EDA comes the recognition that the model is not completely specified, that we do not fully understand the structure of world before studying it. In a statistical context with EDA comes a non-normal error distribution.The relationship between evolutionary institutions and robust institutions is discussed. A conjecture that rule utilitarianism can be thought of as robust utilitarianism is defended with the historical example of William Paley's discussion of the utility of murder.     

Klassische Nationalökonomie gestern und heute

Ohne ZusammenfassungDieser Artikel ist dieungekürzte Fassung des Beitrages Klassische Nationalökonomie des Verfassers zum Staatslexikon (Band IV).     

Convergence and approximation results for non-cooperative Bayesian games: Learning theorems

Summary LetT denote a continuous time horizon and {G ^t :tT} be a net (generalized sequence) of Bayesian games. We show that: (i) if {x ^t : tT} is a net of Bayesian Nash Equilibrium (BNE) strategies for G^t we can extract a subsequence which converges to a limit full information BNE strategy for a one shot limit full information Bayesian game, (ii) If {x ^t : tT} is a net of approximate or _t-BNE strategies for the game G^t we can still extract a subsequence which converges to the one shot limit full information equilibrium BNE strategy, (iii) Given a limit full information BNE strategy of a one shot limit full information Bayesian game, we can find a net of _t-BNE strategies {x ^t : tT} in {G ^t :tT} which converges to the limit full information BNE strategy of the one shot game.We wish to thank Larry Blume, Mark Feldman, Jim Jordan, Charlie Kahn, Stefan Krasa, Gregory Michalopoulos, Wayne Shafer, Bart Taub, and Anne Villamil for several useful discussions. The financial support of the University of Illinois at Urbana-Champaign Campus Research Board is gratefully acknowledged.     

Phillips-Kurve und Bargaining-Theorie

Ohne ZusammenfassungSymbole N Beschäftigung - F (N) Produktionsfunktion (F>0,F <0) - Substitutionselastizität - Arbeitsangebot=Arbeitskräftepotential - Reallohnsatz - w Nominallohnsatz - p Preisniveau - T Zykluslänge - s Kosten der Erhöhung vonv (gemessen in Einheiten der Lohnsumme/Periode) - I Investition (konstant) - s_p (s_w) Sparquote aus Profiten (Löhnen) - Nutzendiskontrate - q Schattenpreis der Erhöhung von     

Non-computable strategies and discounted repeated games

Summary A number of authors have used formal models of computation to capture the idea of bounded rationality in repeated games. Most of this literature has used computability by a finite automaton as the standard. A conceptual difficulty with this standard is that the decision problem is not closed. That is, for every strategy implementable by an automaton, there is some best response implementable by an automaton, but there may not exist any algorithm forfinding such a best response that can be implemented by an automaton. However, such algorithms can always be implemented by a Turing machine, the most powerful formal model of computation. In this paper, we investigate whether the decision problem can be closed by adopting Turing machines as the standard of computability. The answer we offer is negative. Indeed, for a large class of discounted repeated games (including the repeated Prisoner's Dilemma) there exist strategies implementable by a Turing machine for whichno best response is implementable by a Turing machine.The work was begun while Nachbar was a visitor at The Center for Mathematical studies in Economics and Management Science at Northwestern University; he is grateful for their hospitality. We are also grateful to Robert Anderson and Neil Gretsky and to seminar audiences at UCLA for useful comments, and to the National Science Foundation and the UCLA Academic Senate Committee on Research for financial support. This paper is an outgrowth of work reported in Learning and Computability in Discounted Supergames.     

Measuring the severity of unemployment

A social-welfare (illfare) function framework is applied to compare two demographic groups as to the severity of their unemployment experience. This is based on the assumption that for each individual the disutility of unemployment is an increasing and convex function of spell length. The very concept of spell length and its distribution, however, is not unambiguous. In contrast to previous literature which focuses exclusively on the interrupted spell length in a stock of unemployed, we stress the usefulness of the concept of complete spell length in a cohort of unemployed. We establish an equivalence relationship between second-degree dominance in the cohort and first-degree dominance in the stock. For specific illfare functions the disutilityU(x) when applied to the cohort and the disutilityU(x) when applied to the stock will produce the same value of aggregate welfare (illfare).     

Asymmetric Factor Substitutability and Indeterminacy

We consider a discrete-time two-sector CES economy with sector specific external effects in which factor substitutability differs across sectors. For this general model, we provide sufficient conditions on the elasticities of capital/labor substitution for local indeterminacy of equilibria.Acknowledgement We would like to thank two anonymous referees, the editor Dieter Bös and Tapan Mitra for comments on an earlier version of this paper, previously entitled Capital Depreciation, Factors Substitutability and Indeterminacy, which allowed us to improve considerably the results.     

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.     

Learning in a Laboratory Market with Random Supply and Demand

We propose a simple adaptive learning model to study behavior in the call market. The laboratory environment features buyers and sellers who receive a new random value or cost in each period, so they must learn a strategy that maps these random draws into bids or asks. We focus on buyers' adjustment of the mark-down ratio of bids relative to private value and sellers' adjustment of the corresponding mark-up ratio of asks relative to private cost. The learning model involves partial adjustment of these ratios towards the ex post optimum each period. The model explains a substantial proportion of the variation in traders' strategies. Parameter estimates indicate strong recency effects and negligible autonomous trend, but strongly asymmetric response to different kinds of ex post error. The asymmetry is only slightly attenuated in observational learning from other traders' ex post errors. Simulations show that the model can account for the main systematic deviations from equilibrium predictions observed in this market institution and environment.     

Firm-provided training and temporary contracts

This paper analyses the relationship between workers type of contract and the probability of receiving firm-provided training. In particular, we raise the following question: do workers with temporary contracts face the same probability of receiving training as workers with permanent contracts, once we account for the fact that both types of workers have different probabilities of being employed in a firm providing training? The results from our empirical analysis using data from the Spanish labour market suggest that workers with temporary contracts not only are less likely to be employed in training firms but, once they are in those firms, they also have a lower probability of being chosen to participate in firm-provided training activities.JEL Classification: J23, M53Authors gratefully acknowledge financial support from Universidad de Alcalá under research project La relación entre temporalidad y formación en la empresa: un análisis comparativo entre los países de la Unión Europea (award no. UAH2002/022) and from the Spanish Ministry of Science and Technology under research project Observatorio del mercado de trabajo (SEC2001-0061). We have also benefited from our participation in the research project Estudio sobre la situación actual de la contratación temporal e indefinida en España financed by the Spanish Employment Office (INEM). We are grateful to participants in the XXVII Simposio de Análisis Económico (Salamanca), V Jornadas de Economía Laboral (Reus-Tarragona), and a seminar in the Istituto de Ricerca Sociale (Milano), and to one anonymous referee. The usual disclaimer applies.     

On Political Competition: Democracy, Opinion and Responsibility

In this paper, I consider the influence of political competition on opinion. After reflecting on the notion opinion as a concept in the economic analysis of politics, I turn to Hayek's Constitution of Liberty and consider his argument for democracy on the grounds that it is the form of government which best promotes progress in opinion. Yet Hayek's claim that democratically formed opinion improves is unsubstantiated. I turn to accounts of expressive voting thereafter to show why opinions which are realised in the form of votes may be anything other than propitious to democratic culture. I then return to Hayek and consider what becomes of opinion in Law, Legislation and Liberty. His claim that opinion improves under democratic institutions is no longer of great significance to him. Indeed, his account of the rise of bargaining politics provides evidence against the claim that opinion improves. I conclude by asking how democracy can be shielded from opinion, that is, how opinion might be improved in ways which go beyond Hayek's model of political competition outlined in Constitution of Liberty. To this end, I look to accounts of deliberative democracy and expressive politics for support.     

Convention, Social Order, and the Two Coordinations

The word coordination has two meanings, and thesemeanings are often conflated. One meaning, associated with ThomasSchelling, is seen in situations like choosing whether to driveon the left or the right; the drivers must coordinate to eachother's behavior. The other meaning, associated with FriedrichHayek, means that a concatenation of activities is arranged soas to produce good results. Along with the Schelling sense ofcoordination comes the notion of convention, such as drivingon the right. Some conventions are consciously designed; othersemerge without design (or are emergent). Along with the Hayeksense of coordination comes the notion of social order. Somesocial orders, such as the skeleton of activities within thefirm or within the hypothetical socialist economy, are consciouslyplanned. Other social orders, such as the catallaxy of the freesociety, function without central planning (or are spontaneous).Distinguishing between the two coordinations (and, in parallelfashion, between convention and social order) clarifies thinkingand resolves some confusions that have arisen in discussionsof coordination and spontaneous order. The key distinctionsare discussed in the context of the thought of, on the one hand,Menger, Schelling, David Lewis, and the recent path-dependencetheorists, and, on the other hand, Smith, Hayek, Polanyi, Coase,and the modern Austrian economists. The paper concludes witha typology that encompasses the several distinctions.     

Transformation or Transmogrification? Ackerman, Hobbes (as in Calvin and Hobbes), and the Puzzle of Changing Constitutional Identity

In this article, I argue that Ackerman's approach to constitutional change is unable to distinguish between changes of degree and changes in kind, or between changes that transform and changes that transmogrify. As a consequence, the model Ackerman proposes fails at its most elemental purpose of illuminating questions of constitutional identity. Transformations fails to tell us who We the People really are or about what we are constituted.     

Non-manipulable domains for the Borda count

Summary. We characterize the preference domains on which the Borda count satisfies Arrows independence of irrelevant alternatives condition. Under a weak richness condition, these domains are obtained by fixing one preference ordering and including all its cyclic permutations (Condorcet cycles). We then ask on which domains the Borda count is non-manipulable. It turns out that it is non-manipulable on a broader class of domains when combined with appropriately chosen tie-breaking rules. On the other hand, we also prove that the rich domains on which the Borda count is non-manipulable for all possible tie-breaking rules are again the cyclic permutation domains.Received: 24 November 2003, Revised: 12 December 2004, JEL Classification Numbers: D71. Correspondence to: Clemens PuppeThe third author gratefully acknowledges the financial support from the Deutsche Forschungsgemeinschaft (DFG), Graduiertenkolleg 629 at the University of Bonn and from the Hungarian Scientific Research Fund (OTKA F 043496).     

Knowledge Questions: Hayek,Keynes and Beyond

This paper discusses the knowledge problem in terms of both the use and generation of knowledge. This is analyzed in the context of Hayek's failure to respond to the Keynes Challenge—the claim that markets fail to produce relevant knowledge—by suggesting that in the aftermath of The General Theory he was not well-positioned to address that problem. Ironically, his post-World War II work in cognitive psychology, The Sensory Order, offers a theory of the generation of knowledge which can provide a useful analogy for understanding the generation of market-level knowledge.     

Climate Policy without Tears CGE-Based Ancillary Benefits Estimates for Chile

This study examines a hithertoneglected set of benefits from climate policy,viz., the reduction in emissions of localair pollutants and the associated healthbenefits, in this case for residents ofSantiago de Chile. By using an economy-widemodel, we are able to compare these monetisedbenefits to the direct costs of carbonabatement, thereby determining the scope for no regrets CO₂ reductions. Sensitivityanalysis is performed in recognition of theuncertainty surrounding certain key parameterand exogenous variable values – notably,households' willingness to pay (WTP) forreduced mortality and morbidity risk, and thesubstitution elasticities among energy sourcesand between energy and other inputs. Ourresults suggest that, even with the mostconservative assumptions (low WTP, lowelasticities), Chile could reduce CO₂emissions by almost 20% from the 2010 baselinewith no net welfare loss, though a 10%reduction is closer to optimal. If insteadChile were to target a 20% reduction inparticulate concentrations, a particulate taxwould incur slightly lower costs than anequivalent carbon tax to achieve the samehealth benefits. While the latter is asecond-best method of addressing localpollution, the welfare loss of choosing thisinstrument could be fully compensated by carboncredit sales at a world market price of$20/tC.     

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.     

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.     

Vertical and Horizontal Trust Networks in Bureaucracies: Evidence from the Third Reich

In a seminal contribution to the literature on bureaucracy, Breton and Wintrobe (The Logic of Bureaucratic Conduct: An Economic Analysis of Competition, Exchange, and Efficiency in Private and Public Organization. New York, NY: Cambridge University Press, 1982) develop a model wherein subordinates and superiors in a bureaucratic structure trade with each other to advance the objectives of the superiors. The success of such an organizational arrangement (for superiors) is based upon the development of vertical trust networks in a way that facilitates the promise of informal payments by superiors in return for informal services provided by their subordinates. Breton and Wintrobe [Journal of Political Economy 94 (1986) 905] also provide a theoretical application of their model by describing the Nazi bureaucracy as a conglomeration of competing agencies that zealously carried out the Final Solution to the Jewish question. As an extension, this note develops two compelling empirical examples of vertical and horizontal trust networks within the Nazi regime: Einsatzgruppen As (Special Action Detachments) attempt to liquidate all Lithuanian Jews after the German invasion of the U.S.S.R. in 1941 and the 20 July 1944 attempt to assassinate Adolf Hitler.JEL Classification: D23, D73.