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.     

Technological change and institutional inertia: a game-theoretic approach

In this paper, we study a co-evolutionary model of economic change at two hierarchical levels. At the lower level, institutions are given and the focus is on how resources are allocated and innovation produced in response to the pay-off structure induced by prevailing institutions. At the higher level, it is the institutions themselves that change as the outcome of a process of social bargaining. The main objective of the paper is to study the interaction between these two levels of change, attempting to provide some insight on issues like technological/institutional divergence, technological dead-end, institutional inertia, etc.It appears that evolutionary economics must be the theory of a process of cultural growth as determined by the economic interest, a theory of a cumulative sequence of economic institutions stated in the terms of the process itself. Thorstein Veblen (1898, p. 393).This work was undertaken while the author was a Research Fellow at the Institute for Advanced Studies of the Hebrew University of Jerusalem.     

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.     

The greenhouse effect: Damages,costs and abatement

The buildup of so-called greenhouse gases in the atmosphere — CO₂ in particular-appears to be having an adverse impact on the global climate. This paper briefly reviews current expectations with regard to physical and biological effects, their potential costs to society, and likely costs of abatement. For a worst case scenario it is impossible to assess, in economic terms, the full range of possible non-linear synergistic effects. In the most favorable (although not necessarily likely) case (of slow-paced climate change), however, it seems likely that the impacts are within the affordable range, at least in the industrialized countries of the world. In the third world the notion of affordability is of doubtful relevance, making the problem of quantitative evaluation almost impossible. We tentatively assess the lower limit of quantifiable climate-induced damages at $30 to $35 per ton of CO₂ equivalent, worldwide, with the major damages being concentrated in regions most adversely affected by sea-level rise. The non-quantifiable environmental damages are also significant and should by no means be disregarded.The costs and benefits of (1) reducing CFC use and (2) reducing fossil fuel consumption, as a means of abatement, are considered in some detail. This strategy has remarkably high indirect benefits in terms of reduced air pollution damage and even direct cost savings to consumers. The indirect benefits of reduced air pollution and its associated health and environmental effects from fossil-fuel combustion in the industrialized countries range from $20 to $60 per ton of CO₂ eliminated. In addition, there is good evidence that modest (e.g. 25%) reductions in CO₂ emissions may be achievable by the U.S. (and, by implication, for other countries) by a combination of increased energy efficiency and restructuring that would permit simultaneous direct economic benefits (savings) to energy consumers of the order of $50 per ton of CO₂ saved. A higher level of overall emissions reduction — possibly approaching 50% — could probably be achieved, at little or not net cost, by taking advantage of these savings.We suggest the use of taxes on fossil fuel extraction (or a carbon tax) as a reasonable way of inducing the structural changes that would be required to achieve significant reduction in energy use and CO₂ emissions. To minimize the economic burden (and create a political constituency in support of the approach) we suggest the substitution of resource-based taxes in general for other types of taxes (on labor, income, real estate, or trade) that are now the main sources of government revenue. While it is conceded that it would be difficult to calculate the optimal tax on extractive resources, we do not think this is a necessary prerequisite to policy-making. In fact, we note that the existing tax system has never been optimized according to theoretical principles, and is far from optimal by any reasonable criteria.During the academic year 1989–90 Dr. Ayres was at the International Institute for Applied Systems Analysis (IIASA), Laxenburg, Austria.During the summer of 1989 Mr. Walter was a member of the Young Scientists' Summer Program at IIASA.     

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.     

Klassische Nationalökonomie gestern und heute

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

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.     

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.     

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.     

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.     

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.     

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.     

Land use, biodiversity, and sustainability

We focus on the effects of deforestation for agricultural purposes on biodiversity. This topic has been dealt with in the recent literature where forested land and biodiversity are treated as synonyms. In contrast to that, this paper distinguishes between forested land and forest itself, the latter being interpreted as a measure of biodiversity. The regenerative capacity of forests is modeled as a function of the own stock and of the habitat size. In particular, the threat of a given minimum viable population to be achieved in the course of the reduction of habitats is taken into account. The corresponding structure of a sustainability indicator is elaborated.     

Mutually Destructive Bidding: The FCC Auction Design Problem

In general, synergies across license valuations complicate the auction design process. Theory suggests that a simple (i.e., non-combinatorial) auction will have difficulty in assigning licenses efficiently in such an environment. This difficulty increases with increases in fitting complexity. In some environments, bidding may become mutually destructive. Experiments indicate that a properly designed combinatorial auction is superior to a simple auction in terms of economic efficiency and revenue generation in bidding environments with a low amount of fitting complexity. Concerns that a combinatorial auction will cause a threshold problem are not borne out when bidders for small packages can communicate.     

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.     

Exchange rates and perfect competition

The purpose of this note is to demonstrate that the commonly held belief that incomplete and perverse pass-through are incompatible with perfect competition is wrong! To this end, we consider two types of firms both operating in two countries. The demand sides of the markets of the two countries are separated and each type of firm produces its good in one of these countries. We study the effect of an exchange-rate change on the competitive equilibrium prices in each country. When producing for the foreign market causes the same costs as producing for the home market then the law of one price holds and an exchange-rate change is completely offset by price changes. Furthermore, when cost functions neither exhibit economies nor diseconomies of scope between producing for the home and producing for the foreign market then prices move in the right directions in response to an exchange-rate change. However, with general cost structures, even in this simple perfectly competitive model, perverse directions of price changes can result from an exchange-rate change.     

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.     

Strategy-proof and individually rational social choice functions for public good economies

Summary We consider the problem of choosing an allocation in an economy in which there are one private good and one public good. Our purpose is to identify the class of procedures of choosing an allocation which satisfy strategy-proofness, individual rationality, no exploitation and non-bossiness. Any such procedure is a scheme of semi-convex cost sharing determined by the minimum demand principle.I wish to thank Professors Salvador Barbera, Matthew Jackson, Herve Moulin and William Thomson for their helpful suggestions and two anonymous referees for their detailed comments. Conversations with Professors Hideo Konishi, Shinji Oseto Ken-ichi Shimomura and Stephen Ching were helpful. This work is supported by the Japan Economic Research Foundation and Research Grants PB89-0294 and PB89-0075 from the Direcion General de Investigacion Cientifica y Tecnica, Spanish Ministry of Education.     

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.