Existence of an equilibrium in first price auctions

Summary We study the first price auction game with an arbitrary number of bidders when the bidders' valuations are independent from each other. In technical words, we work within the independent private value model. We show that if the supports of the valuation probability distributions have the same minimum and if this minimum is not a mass point of any of these distributions, then a Nash equilibrium of the first price auction exists. We then modify the first price auction game by adding a closed interval of messages. Every bidder has to send a message with the bid he submits. These messages are used in the resolution of the ties. The winner of the auction is chosen randomly among the highest bidders with the highest value of the message among the highest bidders. In the general case, we prove the existence of a Nash equilibrium for this augmented first price auction.I wish to thank Mamoru Kaneko and a referee for their comments on an earlier draft.     

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.     

Public-Choice Analysis of a New International Organization: The International Sea-Bed Authority

The usefulness of the public-choice approach for a better understanding of international organizations can be demonstrated by applying it to the analysis of the structure and functions of a new international organization, the International Sea-Bed Authority, established in 1994, after two decades of negotiations under the auspices of the United Nations, with the aim to control the oceans' mineral resources beyond the limits of national jurisdictions (which have been proclaimed by the U.N. Assembly common heritage of mankind). First, the reasons for establishing this organization, whose basis is the common heritage of mankind nature of ocean resources, are examined under two aspects: 1) definition and protection of property rights; 2) environmental control of sea-bed mining activities. Secondly, the organization's decisionmaking system is presented, including such features as the assembly, council with chamber voting, finance committee with decision by consensus, features that balance the voting power of members and protect those countries that bear the financial responsibility for the budget. Finally, some comments are offered about more general aspects of the theory of international organizations: the bureaucracy (and diplomacy) of these organizations as well as the interdependence among international organizations, which opens the way to forms of international logrolling and makes it advisable for countries not to exit from these organizations, even when they have no primary interest in them.     

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.     

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.     

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.     

Economic and political competition in neoclassical and evolutionary perspective

Neoclassical welfare economics still looms large in the discipline of public choice. Particularly, by constructing analogies of political competition fundamental shortcomings of old neoclassical paradigms found their way into a new theory of political economy. Especially the failure to deal with the problem of limited knowledge and with the role of institutions obscured fundamental differences between political and economic systems of coordination and control. Hence, I propose a non-neoclassical perspective, using Hayekian concepts like competition as a discovery procedure or spontaneous order to develop an alternative agenda for many fields of public choice. I shall first outline a critique of neoclassical equilibrium settings in economics and in similarly constructed models of democracy. Then various properties of economic and political institutions, the competition of ideas and institutional competition among jurisdictions will be discussed in an evolutionary perspective. Not surprisingly, these applications reveal some similarities to central themes of constitutional political economy.     

Incentive compatibility and the quantity-setting competitive firm under demand uncertainty

This paper examines the tie between the popular black box neoclassical quantity-setting firm under demand uncertainty and a firm with a rudimentary but explicit employee relation organizational structure in which workers are offered fixed wages for following management directives. Surprisingly, the quantity-setting firm unambiguously mimics optimal employment relation hiring and work rules when the contract is incentive-compatible ex post. The attitude toward risk is shown to be the key determinant of whether or not the quantity-setting firm replicates the optimal employment relation contract when ex post incentive-compatibility is relaxed.     

Rational Buyer Meets Rational Seller: Reserves Market Equilibria under Alternative Auction Designs

We examine efficiency properties and incentive compatibility of alternative auction formats that an electricity network system operator may use for the procurement of ancillary services required for real-time operations. We model the procurement auction as a hierarchical multiproduct auction, and study several designs such as a uniform price auction minimizing revealed social cost, a uniform price auction minimizing the system operator's cost and a pay as bid auction minimizing revealed social cost. We take into account that rational bidders will respond to any market design so as to maximize their expected benefit from participating in that market. Under the assumptions of our model, we show that the uniform price auction minimizing revealed social cost is the only one that guarantees productive efficiency. We also find that expected revenue (payment in our case) equivalence between pay as bid and uniform price auctions does not extend to the hierarchical products case and the ranking of these auctions is ambiguous and depends on the data. For the procurement auction minimizing the system operator's cost, we show that misrepresentation of capability may result in capacity shortages if there are capacity constraints. For the case where only higher capability resources are constrained, this will result in random price spikes decreasing in frequency with the price cap (this is the amount paid to capacity in demand states with shortages). When lower type resources are capacity constrained as well, price spikes will be seen for both type of resources. Such artificial shortages result in reduced reliability in real-time operations.     

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.     

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.     

Sparen und Einkommensverteilung

Summary The wage and salary bill in Austrian manufacturing industry is divided into a fixed and a variable part on the assumption that wages of skilled labour and salaries can be regarded as fixed, wages of unskilled and semi-skilled workers as variable cost. The excess of value added (factor incomes) over the variable wage cost (gross profit) is shown to be more stable in the trade cycle than the excess of value added over the total wage cost (net profit); this accords with the idea of a relatively stable mark-up on variable cost.As a proportion of value added, gross profit and even more net profit in the above sense decline gradually over the period 1956 to 1972. This would indicate a declining degree of monopoly or increasing degree of competition which presumably applies mainly to the export markets. The hypothesis is advanced that more active competition has taken place in foreign markets which enabled Austrian manufacturing to increase its share in those markets. The reduction in profit margins was made possible by tax allowances i.e. by the quick write-off a considerable part of new investment. This tax allowances amounts to an interest free government loan to the investor, which in fact will not be repaid of the depreciation funds are reinvested immediately after the equipment is fully written off. The proportion of the industry's capital which is in this sense financed by the government increases over time as investment expands; a profit rate has to be earned only on the remaining capital stock, so that without reduction of the return on private capital the profit margins may be reduced. (The tax allowances thus amount to a virtual reduction of the capital coefficient which proceeds gradually over a long time.)The paper finally shows the relation between the share of savings and the share of corporate incomes in the total private income during the cycle. The share of saving moves with the cycle and this is made possible by a shift to corporate income.     

On economic disequilibrium and free lunch

There is a sharp disagreement between mainstream economists and advocates of energy efficiency as regards the potential for free lunches or no regrets policies to cut greenhouse gas emissions. From an economics perspective, the critical question is whether the economic system is — or is not — close to a Pareto-optimum equilibrium state. If so, it follows that most technological systems now in place are optimum, or nearly so, from an economic perspective. If not, there may be many sub-optimal technologies in place, with corresponding opportunities for very high returns on appropriate investments. This paper presents some of the evidence supporting the latter thesis.     

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.     

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).     

Makroökonomische Modelle für die österreichische Wirtschaft

Ohne ZusammenfassungVortrag, gehalten am 7. Juni 1957 in der Nationalökonomischen Gesellschaft in Wien.     

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.     

Endogenous Entry and Exit in Common Value Auctions

We develop and experimentally test a model of endogenous entry, exit, and bidding in common value auctions. The model and experimental design include an alternative profitable activity (a safe haven) that provides agentspecific opportunity costs of bidding in the auction. Each agent chooses whether to accept the safe haven income or forgo it in order to bid in the auction. Agents that enter the auction receive independently-drawn private signals that provide unbiased estimates of the common value. The auctioned item is allocated to the high bidder at a price that is equal to the high bid. Thus the market is a first-price sealed-bid common value auction with endogenous determination of market size.     

The Impact of Discounting on an Auction with a Buyout Option: a Theoretical Analysis Motivated by eBay’s Buy-It-Now Feature

An auction with a buyout option occurring over continuous time with rules similar to eBays buy it now option is analyzed. When auction participants make no distinction as to when a transaction occurs, the seller optimally chooses a buyout option price so high that bidders never exercise the option. However, time impatience on either side of the transaction can motivate the seller to offer an option price low enough so that the option is exercised with positive probability. Further, allowing a time impatient seller to offer such an option results in an ex ante Pareto improvement when bidders do not discount future transactions.     

The number and type of long-term equilibria

We consider a balanced-growth model with finitely many processes, a uniform rate of profits, and a given composition of final demand. Two types of equilibria are distinguished, black and white: the color of an equilibrium is defined by the relative sign of two determinants associated with the operated methods, and can be interpreted as a local property of a cross-dual dynamic process. Under standard economic assumptions, and flukes apart, the number of white equilibria exceeds that of black equilibria by one. In particular the total number of long-term equilibria is odd.