Auctions with endogenous participation

We study endogenous-participation auctions where bidders only know the number of potential participants. After seeing their values for the object, potential participants decide whether or not to enter the auction. They may not want to enter the auction since they have to pay participation costs. We characterize equilibrium bidding strategies and entry decisions for both first- and second-price sealed-bid auctions when participation is endogenous. We show that there is a pure strategy entry equilibrium where only bidders with values greater than a certain cut-off point actually bid. In this context, both types of auctions generate the same expected revenue. We also show that, contrary to the predictions of the fixed number of bidders literature, the seller's expected revenue may decrease when the number of potential participants increases. In addition, we show that it is optimal for the seller to charge an entry fee, which contrasts with results from the existing literature on auctions with entry. As in the fixed-n literature, we show that first-price auctions generate more expected revenue than second-price auctions when buyers are risk-averse. Finally, we characterize the optimal auction – the auction that maximizes the seller's expected revenue – by using a direct revelation mechanism. The optimal auction involves a reserve price larger than the optimal reserve price in the fixed-n literature. The winner's payment is the second highest bid less the participation cost and losers receive a subsidy equal to the participation cost. Received: 17 August 1998 / 21 September 1999     

Optimal procurement mechanisms for divisible goods with capacitated suppliers

Procurement auction literature typically assumes that the suppliers are uncapacitated [see, e.g. Dasgupta and Spulber in Inf Econ Policy 4:5–29, 1990 and Che in Rand J Econ 24(4):668–680, 1993]. Consequently, the auction mechanisms award the contract to a single supplier. We study mechanism design in a model where suppliers have limited production capacity, and both the marginal costs and the production capacities are private information. We provide a closed-form solution for the revenue maximizing direct mechanism when the distribution of the cost and production capacities satisfies a modified regularity condition [Myerson in Math Oper Res 6(1):58–73, 1981]. We also present a sealed low bid implementation of the optimal direct mechanism for the special case of identical suppliers. The results in this paper extend to other principle-agent mechanism design problems where the agents have a privately known upper bound on allocation. The authors would like to thank the anonymous referees for valuable suggestions and comments.     

Mechanisms that efficiently verify the optimality of a proposed action

The best known achievement of the literature on resource-allocating mechanisms and their message spaces is the first rigorous proof of the competitive mechanism's informational efficiency. In an exchange economy withN persons andK+1 commodities (including a numeraire), that mechanism announcesK prices as well as aK-compenent trade vector for each ofN−1 persons, making a total ofNK message variables. Trial messages are successively announced and after each announcement each personprivately determines, usingprivate information, whether she finds the proposed trades acceptable at the announced prices. When a message is reached with which all are content, then the trades specified in that message take place, and they satisfy Pareto optimality and individual rationality. The literature shows that no (suitably regular) mechanism can achieve the same thing with fewer thanNK message variables. In the classic proof, all the candidate mechanisms have the privacy property, and the proof uses that property in a crucial way. ‘Non-private’ mechanisms are, however, well-defined. We present a proof that forN>K,NK remains a lower bound even when we permit ‘non-private’ mechanisms. Our new proof does not use privacy at all. But in a non-private mechanism, minimality of the number of message variables can hardly be defended as the hallmark of informational efficiency, since a non-private mechanism requires some persons to know something about the private information of othersin addition to the information contained in the messages. The new proof of the lower boundNK invites a new interpretation of the competitive mechanism's informational efficiency. We provide a new concept of efficiency which the competitive mechanism exhibits and which does rest on privacy even whenN>K. To do so, we first define a class ofprojection mechanisms, wherein some of the message variables are proposed values of the action to be taken, and the rest are auxiliary variables. The competitive mechanism has the projection property, with a trade vector as its action and prices as the auxiliary variables. A projection mechanism proposes an action; for each proposal, the agents then use the auxiliary variables, together with their private information, to verify that the proposed action meets the mechanism's goal (Pareto optimality and individual rationality for the competitive mechanism) if, indeed, it does meet that goal. For a given goal, we seek projection mechanisms for which theverification effort (suitably measured) is not greater than that of any other projection mechanism that achieves the goal. We show the competitive mechanism to be verification-minimal within the class of private projection mechanisms that achieve Pareto optimality and individual rationality; that proofdoes use the privacy of the candidate mechanisms. We also show, under certain conditions, that a verification-minimal projection mechanism achieving a given goal has smallest ‘total communication effort’ (which is locally equivalent to the classic ‘message-space size’) among all private mechanisms that achieve the goal, whether or not they have the projection property.     

The conservative equal costs rule, the serial cost sharing rule and the pivotal mechanism: asymptotic welfare loss comparisons for the case of an excludable public project

We examine the asymptotic behavior of two strategyproof mechanisms discussed by Moulin for public goods – the conservative equal costs rule (CER) and the serial cost sharing rule (SCSR) – and compare their performance to that of the pivotal mechanism (PM) from the Clarke–Groves family. Allowing the individuals’ valuations for an excludable public project to be random variables, we show under very general assumptions that expected welfare loss generated by the CER, as the size of the population increases, becomes arbitrarily large. However, all moments of the SCSR’s random welfare loss asymptotically converge to zero. The PM does better than the SCSR, with its welfare loss converging even more rapidly to zero.     

On the smoothness of optimal paths

Abstract The aim of this paper is to study the differentiability property of optimal paths in dynamic economic models. We address this problem from the point of view of the differential calculus in sequence spaces which are infinite-dimensional Banach spaces. We assume that the return or utility function is concave, and that optimal paths are interior and bounded. We study the C ^r differentiability of optimal paths vis-à-vis different parameters. These parameters are: the initial vector of capital stock, the discount rate and a parameter which lies in a Banach space (which could be the utility function itself). The method consists of applying an implicit function theorem on the Euler–Lagrange equation. In order to do this, we make use of classical conditions (i.e., the dominant diagonal block assumption) and we provide new ones. Mathematics Subject Classification (2000): 90A16, 49K40, 93C55 Journal of Economic Literature Classification: C161, D99, O41     

Bounds on expectations of small order statistics from decreasing density populations

For i > (n + 1)/2, Danielak (Statistics 37:305–324, 2003) established an optimal positive upper mean-variance bound on the expectation of ith order statistic based on the i.i.d. sample of size n from the decreasing density population. We show that the best bounds on the expected deviation of the ith order statistics from the population mean, i ≤ (n + 1)/2, expressed in more general scale units generated by pth absolute central moments with p > 1 amount to zero. We also determine the respective strictly negative bounds in the mean absolute deviation units.     

Application of optimal control in man power planning

Many techniques are met in the literature (see for instance Bartholomew and Forbes (Statistical Techniques for Manpower Planning. wiley, New York 1979); Gunz (Organiz. Stud. 9(4), 529–554, 1988); Becker and Huselid (Human Resour. Manage. 38, 287–301, 1999); Wagner et al. (J. Manage. Med. 14(5/6), 383–405, 2000); Harris and Ogbonna (J. Business Res. 51, 157–166, 2001); Rogg et al. (J. Manage. 27, 431–449, 2001), among others), for planning the manpower resources. However, we haven’t seen in the literature an empirical study regarding the proper application of optimal control, which considered to be the most efficient method for multi-objective programming. With this in mind, we analyse in this paper the way of applying optimal control for manpower planning. For this purpose, and in order to facilitate the presentation, we first adopted a comparatively simple dynamic system (plant), with analytical presentation of stocks and flows. Next we proceed to the formulation of an optimal control problem, aiming to achieve in the most satisfactory way some preassigned targets. These targets mainly refer to a desirable trajectory of the plant stocks over time, in order to fully satisfy the needs for human resources over the planning horizon. Finally we present a method of solution of the formulated control problem which is based on the use of the generalized inverse Lazaridis (Qual. Quan. 120, 297–306, 1986). We believe that it is very important for successful management, that the policy makers have to know the effect of their polices and to determine the optimal path of the state variables (i.e. the ones describing the system) before the realization of the plan, so as to be able to reform their strategies, reallocate the resources and arrange the infrastructure accordingly, if all these are necessary, as it can be depicted from the optimal control solution.     

Optimal mechanisms for siting noxious facilities

We study Bayesian mechanism design in the context of the siting of noxious facilities. Under incomplete information, we characterize optimal mechanisms facilitating the siting and cost sharing of the facility. These mechanisms are allocatively and Pareto efficient. However, it appears that transfers occur when the good is not provided. This result is due to the weakening of the incentive notion to Bayesian–Nash equilibrium and to the balanced budget condition. This phenomenon disappears if the setting is perfectly symmetric.      

Arbitrage pricing theory and risk-neutral measures

Abstract We consider a market with countably many risky assets and finite factor structure, as in the “arbitrage pricing theory” of Ross (1976). We prove necessary and sufficient conditions in terms of parameters for the existence of an equivalent risk-neutral measure, i.e., a measure under which each asset return has zero expected value. We relate these conditions to a certain absence of arbitrage property of the model. Mathematics Subject Classification (2000): 91B24, 91B28 Journal of Economic Literature Classification: G10, G12     

Regulation in a political economy: explaining limited commitment and the ratchet effect

Abstract. This paper shows that in a political economy with repeated elections governments that possess full commitment behave as if their commitment is limited. Two different endogenous versions of the ratchet effect obtain: If contracts of previous governments tie newly elected governments, governments are unable to resist renegotiation. If previous contracts do not bind new governments and taxation has a crowding–out effect, a ratchet effect occurs that is similar, but not identical to the standard ratchet effect that is due to intertemporal non–commitment. Social welfare may be higher in the latter case, when the governing party is allowed to use bonds. Received: March 14, 2000     

Berlin transformations: another view

Books reviewed in this article: Hartmut Häußermann and Andreas Kapphan, Berlin: von der geteilten zur gespaltenen Stadt? Sozialräumlicher Wandel seit 1990 Stefan Krätke and Renate Borst, Berlin: Metropole zwischen Boom und Krise     

Berlin’s Transformations: Postmodern,Postfordist ... or Neoliberal?

Books reviewed in this article: Hartmut Häußermann and Andreas Kapphan, Berlin: von der geteilten zur gespaltenen Stadt? Sozialräumlicher Wandel seit 1990 Stefan Krätke and Renate Borst, Berlin: Metropole zwischen Boom und Krise     

Mixture sets on finite domains

Mixture sets were introduced by Herstein and Milnor (Econometrica 21:291–297, 1953) to prove a generalised expected utility theorem. Mixture sets provide an axiomatisation of convexity suitable for discrete, as well as continuous, environments (Mongin in Decis Econ Finance 24:59–69, 2001). However, the nature of mixture sets over finite domains has been little studied. In this paper, we provide a complete characterisation. More recently, another abstract convex structure for finite domains, the antimatroid, has appeared in the literature on decision theory and social choice. The relationship between mixture sets and antimatroids has not previously been explored. We show here that neither concept is a special case of the other.     

Applying jump-diffusion processes to liquidate and convert venture capital

This study attempts to apply real options and expand the model designed by Lin and Huang [Lin, T.T., Huang, Y.T.: J. Technol. Manage. 8(3), 59–78 (2003)], which helps venture capital (VC) companies to optimize project exit decisions. The expected discounted factor and a jump-diffusion process combine to assess the value of a start-up company, and determine the threshold of the exit timing of liquidation or convertibility for establishing the optimal disinvestment evaluation model for VC companies. When the project value is below V_L^*V_L^\ast, the VC company carries out liquidation, but when the project value exceeds V_C^*V_C^\ast, the VC company performs convertibility. The project value is ranging between (V_L ^*,V_C^*)\left({V_L ^\ast,V_C^\ast}\right), and the best choice is holding the decision and waiting to carry out the rights of liquidation and convertibility next time. Besides, this work attempts to identify the expected discounted time in terms of the investment time for VC companies.     

Testing measurement invariance using multigroup CFA: differences between educational groups in human values measurement

This article applies the testing procedures for measurement invariance using multigroup confirmatory factor analysis (MGCFA). It illustrates these procedures by investigating the factorial structure and invariance of the Portraits Value Questionnaire (PVQ, Schwartz et al.: J. Cross Cult. Psychol. 32(5), 519–542 (2001)) across three education groups in a population sample (N  =  1,677). The PVQ measures 10 basic values that Schwartz postulates to comprehensively describe the human values recognized in all societies (achievement, hedonism, self-direction, benevolence, conformity, security, stimulation, power, tradition and universalism). We also estimate and compare the latent means of the three education groups. The analyses show partial invariance for most of the 10 values and parameters. As expected, the latent means show that less educated respondents attribute more importance to security, tradition, and conformity values.     

How to understand, and deal with dictatorship: an economist's view

This paper explains in simple English some of the main ideas about autocracy first developed elsewhere (e.g., in my book, The Political Economy of Dictatorship (Cambridge University Press, 1998). I use rational choice theory to explain the behavior of dictatorships and develop policy toward them. Issues discussed in this paper include: How do successful regimes stay in power? What determines the repressiveness of a regime? Which type of regime redistributes more, dictatorship or democracy? Can dictatorships be good for economic growth and efficiency? The starting point of my analysis is The Dictator's Dilemma-the insecurity every dictator necessarily experiences about how much support he really has. Because of this, the dictator finds that the tool of repression is not enough to maintain his regime, and successful dictators typically rule with the loyal support of at least some groups of subjects (while repressing others). The levels of repression and support and the nature of the groups that give their support (labor, business, ethnic group, etc.) determine the character of the dictatorship. Among other results discussed, I show that some types of dictators – tinpots and timocrats – respond to an improvement in economic performance by lowering repression, while others – totalitarians and tyrants – respond by raising it. Finally I discuss optimal policy by the democracies toward dictatorships and I show that a single standard-aid or trade with a progressively tightening human rights constraint- is desirable if aid or trade with dictatorships of any type is to lower, not raise, repression. Submitted: February 1999 / Accepted: 10 November 1999     

Optimal block designs for diallel crosses

Dey and Midha (Biometrika 83(2):484–489, 1996) constructed optimal block designs for complete diallel cross experiment using triangular partially balanced incomplete block designs with two associate classes. They listed optimal block designs for the lines in the range from 5 ≤ v ≤ 10. In this paper, we are also proposing additional optimal block designs for complete diallel cross experiment using two associate class partially balanced block designs for some additional values of v. Our method yields designs for proper and non-proper settings for complete diallel cross experiments. The proper and non proper designs are optimal in the sense of Kempthorne (Genetics 41:451–459, 1956) and non-proper designs are universally optimal in the sense of Kiefer (A survey of statistical design and linear models, North Holland, Amsterdam, 1975). The list of practically important designs is also given.     

On the Sub-optimality of Entry Fees in Auctions With Entry

We study a variation of Myerson’s (1981) model in which we allow for uncertainty about the number of bidders. In our set-up, an appropriate reserve price in a standard auction maximizes the auctioneer’s expected revenue. However, entry fees can be optimal only under some special conditions. Basically, there must be some homogeneity in bidders’ beliefs about the number of bidders and the auctioneer must know, to some extent, these beliefs.     

Extending design-optimality from an initial model to augmented models

We consider an initial linear model E(Y)=B a and an augmented model E(Y)=B a+C b. We show that, if a design is optimal for estimating K a in the initial model, then there exists a matrix L such that this design is also optimal for estimating K a+L b in the augmented model. Received: December 1998     

A view on Bhattacharyya bounds for inverse Gaussian distributions

Shanbhag (J Appl Probab 9:580–587, 1972; Theory Probab Appl 24:430–433, 1979) showed that the diagonality of the Bhattacharyya matrix characterizes the set of Normal, Poisson, Binomial, negative Binomial, Gamma or Meixner hypergeometric distributions. In this note, using Shanbhag (J Appl Probab 9:580–587, 1972; Theory Probab Appl 24:430–433, 1979) and Pommeret (J Multivar Anal 63:105–118, 1997) techniques, we evaluated the general form of the 5 × 5 Bhattacharyya matrix in the natural exponential family satisfying f(x|q)=\fracexp{xg(q)}b(g(q))y(x){f(x|\theta)=\frac{\exp\{xg(\theta)\}}{\beta(g(\theta))}\psi(x)} with cubic variance function (NEF-CVF) of θ. We see that the matrix is not diagonal like distribution with quadratic variance function and has off-diagonal elements. In addition, we calculate the 5 × 5 Bhattacharyya matrix for inverse Gaussian distribution and evaluated different Bhattacharyya bounds for the variance of estimator of the failure rate, coefficient of variation, mode and moment generating function due to inverse Gaussian distribution.