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.     

From “tax state” to “debt state”

The paper is motivated by Joseph A. Schumpeter's The Crisis of the Tax State. It inquires whether the buildup of government debt in peacetimeprosperity is a threat to the stability, existence or creation of viable tax states. The paper begins by setting out Schumpeter's conception of the tax state and the nature of recent political-economic events which have reinvigorated the concept. Next the paper sets out some simple debt dynamics and sketches a debt-induced business cycle arising from heavy reliance on debt finance in peacetimeprosperity. Finally, the paper assesses threats to the tax state in light of recent work on path dependence and positive feedback. An attempt is made to throw some light on whether the plethora of new, and often small, states spawned by the demise of communism can be viable tax states.Essay on Government, the Tax State and Economic Dynamics submitted to the Third Schumpeter Prize Competition.     

Economics as mechanism: The mind as machine in Hayek's sensory order

InThe Sensory Order, Friedrich A. Hayek describes the human mind as an apparatus of classification that evolves through experience and that reaches decisions by modeling the alternative courses of action that are available to it. Hayek's mechanistic conception of mind argues aginst the possibility of central planning and against the cogency of any rule that denigrates subjective decision making by employers or other economic agents. As implied by Gödel's proof, no brain, human or mechanical, can ever be sufficiently complex to explain itself. There will therefore always be certain knowledge and rules that cannot be articulated to the satisfaction of a central planner or tribunal.     

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.     

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.     

Spieltheorie: Ein neues Paradigma der Sozialwissenschaft

Ohne ZusammenfassungDeutsche Fassung des Artikels Game Theory: A New Paradigm of Social Science, erschienen in New Methods of Thought and Procedure (Berlin-Heidelberg-New York: Springer, 1967). — Diese Arbeit wurde teilweise über das Econometric Research Program der Princeton University durch das Office of Naval Research unterstützt.     

Alternative Modelle und Hypothesen der Konsum- und Sparentscheidung(1)

Summary For the analysis of the allocation of personal disposable income to the different consumption goods and savings, an indirect-addilog-expenditure-system (IAES) has been constructed. Compared to the linear-expenditure-system (LES) the IAES to far more flexible and is not based upon the idea of minimum-consumption- or minimum-saving-quotas. On the other hand, marginal income shares are not fixed parameters. The IAES allows the derivation of a systematic savings- and consumption-function and supplies consistent income elasticities. But it will be shown that consistent demand systems are only restrictively able to consider all major determinants of the decision-problem consumption or saving. The derived system does not only neglect the effects of wealth on consumption and savings but also the results of real income fluctuations due to the business cycle. Also phenomena like unemployment and uncertainties regarding estimates of the future or inflation are neglected. With the help of an adjustment-procedure a part of these disadvantages has been eliminated. The adjustment with regard to the entire private consumption and savings supplied income elasticities which lead to an almost constant consumption- and savings-share in the period under investigation.     

Risk Aversion, Intergenerational Equity and Climate Change

The paper investigates a climate-economy model with an iso-elastic welfare function in which one parameter measures relative risk-aversion and a distinct parameter measures resistance to intertemporal substitution.We show both theoretically and numerically that climate policy responds differently to variations in the two parameters. In particular, we show that higher but lower leads to increase emissions control. We also argue that climate-economy models based on intertemporal expected utility maximization, i.e. models where = , may misinterpret the sensitivity of the climate policy to risk-aversion.     

Auctions for Universal Service Subsidies

The Telecommunications Act of 1996 requires that telephone service be available in high-cost areas at rates that are affordable and reasonably comparable to those charged in low-cost areas. It also requires that carriers serving high-cost areas at below-cost rates be compensated with explicit and sufficient subsidies. This paper analyzes an auction mechanism for the allocation of such subsidies. It shows that in a wide range of circumstances auctions are more efficient than traditional subsidy schemes. It also shows, however, that auction designs aimed at stimulating competition among several subsidized carriers may be particularly vulnerable to collusion.     

On the Durability of King and Council: The Continuum Between Dictatorship and Democracy

In practice one rarely observes pure forms of dictatorship that lack a council, or pure forms of parliament that lack an executive. Generally government policies emerge from organizations that combine an executive branch of government, the king, with a cabinet or parliamentary branch, the council. This paper provides an explanation for this regularity, and also provides an evolutionary model of the emergence of democracy that does not require a revolution. The analysis demonstrates that the bipolar king and council constitutional template has a number of properties that gives it great practical efficiency as a method of information processing and as a very flexible institutional arrangement for making collective decisions.     

Nachfragesysteme für österreich

Summary This paper gives an empirical reexamination of the Linear-Expenditure-hypothesis for Austria. It starts with a brief theoretical discussion of the principal properties and restrictions of the Linear-Expenditure-System (LES). To obtain empirical estimates of the parameters of the LES two different estimation procedures are applied, i.e. the original method used byStone and a simplified version of the Systems-Least-Squares-approach (following theMarquardt-algorithm). There are no essential differences between these estimates. They all seem plausible and satisfy the theoretical restrictions.Usually the stability (i.e. time-invariance) of the parameters is accepted without proof. Using the Moving-Window-Regression-technique, however, most of the estimates vary significantly in time. To obtain a direct proof of the time-dependence of the parameters the LES is reestimated now including trend-factors. Especially results considering time-dependent marginal-budget-shares are considerably better than the static-model results.The conclusion of this paper is that the static version of the LES does not explain the consumer behaviour in Austria and that much more effort should be spent on the estimation of dynamic demand systems.     

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.     

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.     

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).     

Klassische Nationalökonomie gestern und heute

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

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.     

Is Technological Progress Pareto-Improving for a World with Global Public Goods?

This paper investigates the welfare effects of unilateral or multilateral technological progress in a world with global public goods. We focus on the consumption relation between the private and the public good, and then show that technological progress may beself-centered (benefit oneself but harm others), self-sacrificing (harm oneself but benefit others), or self-defeating (harm all) if two goods are substitutable. In addition, any type of technological progress improves every countrys welfare if the private and the public good are close complements.     

Democracy and Opinion Falsification: Towards a New Austrian Political Economy

Hayek's view of democracy as a process of forming opinion is taken as a starting point for inquiring into issues largely neglected by Public Choice and Constitutional Economics. In an Austrian perspective, fallible individual knowledge, political entrepreneurs and dissenting minorities attain a distinctive role in the process of political competition. Based on the observation that political opinions consist of preferences and theories, the concept of opinion falsification is introduced. It is a spontaneous result of social interaction creating preference falsification - the disguise of true feelings, but also knowledge falsification – the discovery of false beliefs. Democratic constitutions can limit the scope of preference falsification and increase the potential for knowledge falsification, thus supporting Hayek's view that it is in its dynamic, rather than its static, aspects, that the value of democracy proves itself.     

Die fluktuation der Arbeitskräfte

Zusammenfassung Es konnten vier Typen der Fluktuation isoliert werden, die neben persönlichen Komponenten für die Fluktuation der Arbeitskräfte maßgebend sind. Ein Teil der Fluktuation geht auf das Ausprobieren des Arbeitsplatzes — angesichts der Unvollkommenheit der Information — zurück (Probe-Fluktuation). Die Wechselneigung ist daher bei Personen mit kurzer Betriebszugehörigkeitsdauer sowie jüngeren Arbeitskräften (20 bis 30 Jahre) relativ hoch.Eine weitere Form der Fluktuation ist die Reaktion der Arbeinehmer auf Unterschiede in den Nettovorteilen verschiedener Arbeitsplätze (Lohn-Fluktuation). Die Arbeitskräfte wandern per Saldo aus Niedrig- in Hochlohnbetriebe, aus Klein- in Großbetriebe und aus schrumpfenden in expandierende.Das Bestehen eines dualen Arbeitsmarktes impliziert, daß benachteiligte Arbeitskräfte (Ungeschulte mit geringem betriebsspezifischem Training) häufig kündigen, während begünstigte Arbeitskräfte (Geschulte) relativ selten wechseln (Hilfskräfte-Fluktuation). Tatsächlich ist die Wechselneigung von Ungeschulten und Arbeitern (vor allem im industriell-gewerblichen Sektor) weit überdurch-schnittlich. Die Zahl der Wechselfälle wird neben der Wechselneigung durch die alternativen Beschäftigungsmöglichkeiten bestimmt (Konjunktur-Fluktuation). Die Fluktuation schwankt so deutlich mit der Anspannung auf dem Arbeitsmarkt, daß sie als Anspannungsindikator angesehen werden kann.die Branchenunterschiede in verschiedenen Maßzahlen der Fluktuation lassen sich im wesentlichen auf die dargestellten vier Fluktuationstypen zurückführen. (Zur Messung des Arbeitsplatzwechsels empfiehlt es sich, Verbleibenswahrscheinlichkeiten der betrieblichen Zugänge und dienstalterspezifische Fluktuationsraten zu errechnen.)

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Summary There are four main features of labour turnover. A substantial part of turnover is due to job shopping in view of imperfect information. Therefore, workers with short job tenure and younger employees (20–30 years) reveal a high propensity to quit. Another type of quit behaviour is the reaction of workers to differences in the net advantages of various jobs. The employed move from the low wage to the high wage sector, from small to largescale enterprises and from shrinking to expanding firms. The existence of a dual labour market implies that disprivileged workers (with low general and specific training) quit frequently and privileged workers rarely change the job. In fact, the turnover rate of white-collar workers and persons with higher formal education is far below average. The actual level of labour turnover does not only depend on the propensity to quit but also on the alternative job opportunities. Voluntary quits are so closely related to the tightness of the labour market that they can be regarded as a labour market indicator. Regression analysis shows that the differences in various measures of turnover are essentially due to these four features of turnover. (For measurement of labour turnover it is recomended to use the probabilities of a batch of entrants to survive certain points in time. as well as job tenure-specific turnover rates.)

     

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).