Binary games with many players

Summary. We examine a problem with n players each facing the same binary choice. One choice is superior to the other. The simple assumption of competition - that an individual’s payoff falls with a rise in the number of players making the same choice, guarantees the existence of a unique symmetric equilibrium (involving mixed strategies). As n increases, there are two opposing effects. First, events in the middle of the distribution - where a player finds itself having made the same choice as many others - become more likely, but the payoffs in these events fall. In opposition, events in the tails of the distribution - where a player finds itself having made the same choice as few others - become less likely, but the payoffs in these events remain high. We provide a sufficient condition (strong competition) under which an increase in the number of players leads to a reduction in the equilibrium probability that the superior choice is made.Received: 24 July 2003, Revised: 24 January 2005, JEL Classification Numbers: C72, D02, D49, L19.Flavio M. Menezes: Correspondence toThis paper has benefitted from comments by an anonymous referee and seminar participants at the ANU, Boston University, Harvard University Law, Economics and Organization Seminar, University of Wisconsin and at the Econometrics Society Australasian Meetings, Auckland New Zealand. We also thank Lucian Bebchuk, Eddie Dekel, Oliver Hart, Luis Kaplov, Paulo Monteiro and John Quiggin for very useful comments. All errors are our own. Menezes acknowledges the financial support from ARC (grant no. 00000055) and the hospitality of EPGE/FGV and RSPAS/ANU.     

Su Una Estensione Bidimensionale del Teorema di Scomposizione di Peccati

Facendo ricorso all’introduzione di una opportuna condizione di sincronia fra due coppie di tassi (i, j), esterna, e (i*, j*), interna, si dimostra che condizione necessaria e sufficiente per la validità finanzíaria di una estensione hidimensionale del teorema di scomposizione di Peccati è che le due coppie (i, j) e (i*, j*) soddisfino tale proprietà di sincronia.

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A two-dimensional extension of peccati’s decomposition theorem

Summary This paper keeps as starting poing the Peccati’s decomposition of the d.c.f. of an enterpreneural project seen as a present value of single-period results, recently given by the author in an unidimensional framework. The goal of the paper is twofold: the first is to provide a bidimensional extension of the decomposition in order to keep account of mixed projects, that is projects that according to any internal couple (i*, j*) reveal alternance of investment and respectively collection periods. A straightforward extension is given on the basis of a simple analogic argument. But a more careful evaluation of the problem suggests that if we require that the decomposition be meaningful from a financial point of view. things are no more simple either in one or in two dimensions. To solve the problem we introduce a proper synchrony condition: precisely, the pair of couples (i, j) and (i*, j*) are said to satisfy the synchrony condition if and only if the sequences of the signs of the partial balancesM _t (i, j) andM _t (i*, j*) are the same. After that we are able to show that, with reference to a couple (i, j) of external rates, a bidimensional decomposition centered on an internal couple (i*, j*) is meaningful if and only if the pair (i, j) and (i*, j*) satisfy the synchrony condition. Formally, the result comes as a nice byproduct of a rule on the factorization of particular bivariate polynomials recently given by Stucchi. In particular going back to a one-dimensional world, it turns out that for pure investment (Soper) projects the synchrony condition works as a condition of applicability of the Peccati’s decomposition.

Il testo è frutto di una riflessione congiunta degli autori che ne condividono l’impostazione generale e i risultati. In dettaglio, la stesura dell’introduzione e delle conclusioni deriva da una claborazione comune, quella dei paragrafi 4, 5 e 7 è dovuta a Pressacco mentre quella dei rimanenti è dovuta a Stucchi. Il lavoro è stato svolto nell’ambito della ricerca nazionale “Modelli per la Finanza Matematica”.     

Proper strong-Fibonacci games

We define proper strong-Fibonacci (PSF) games as the subset of proper homogeneous weighted majority games which admit a Fibonacci representation. This is a homogeneous, type-preserving representation whose ordered sequence of type weights and winning quota is the initial string of Fibonacci numbers of the one-step delayed Fibonacci sequence. We show that for a PSF game, the Fibonacci representation coincides with the natural representation of the game. A characterization of PSF games is given in terms of their profile. This opens the way up to a straightforward formula which gives the number \(\varPsi (t)\) of such games as a function of t, number of non-dummy players’ types. It turns out that the growth rate of \(\varPsi (t)\) is exponential. The main result of our paper is that, for two consecutive t values of the same parity, the ratio \(\varPsi (t+2)/\varPsi (t)\) converges toward the golden ratio \({\varPhi }\).     

Regulation and Access Pricing: Comparison of Regulated Regimes

The statutory duties of regulators of British utilities include both the encouragement of competition and protection of consumers (through price caps). Competition depends on the terms on which new entrants can gain access to the monopolist's network. Where the incumbent in the retail market also owns the network, the regulator may determine prices in the capped and access markets separately or may make the price cap explicitly dependent on entry in the uncapped market. Contrary to the received wisdom that access charges should be separately regulated we show that higher welfare can be obtained in some circumstances by allowing the incumbent to determine access charges. This is achieved by permitting the incumbent to choose from a menu of retail prices which the regulator makes conditional on the extent of entry in the retail market.     

Understanding Social Market Economy,Francesco Forte and His Interpretation

The social thought which emerges from Francesco Forte’s economic writings proves to be mainly inspired by methodological individualism, though interpreted through a peculiar “personalistic” key. We will analyze the peculiar traits of his thought and the specific contribution that Forte gave to the understanding of a specific economic theory based on the doctrine of “Ordoliberalism” or the “Freiburg School.” In our work, we will show how Forte proposes an interpretation of that doctrine, according to two of his main points of reference in economic and philosophical thought: Luigi Einaudi and Antonio Rosmini Serbati. Finally, we will present an important aspect of Forte’s work: his institutional analysis in the light of the particular civil philosophy expressed by Christian social teaching.     

A GENERAL CHARACTERIZATION OF MULTIPRODUCT COURNOT COMPETITION

The problem of oligopolistic competition between multiproduct firms is analysed using a general framework, where a given number of firms have access to the same technology, and play a Cournot game, by simultaneously choosing a quantity vector.
Conditions guaranteeing the symmetry of the Cournot equilibrium are sought. The results obtained are very general, and can be given a straightforward natural economic interpretation, essentially requiring convexity of the cost function and the ruling out of pathological demand functions.     

An Empirical Analysis of Competition in Brand Differentiated Oligopoly

The paper studies the behaviour of four oligopolistic firms in the Italian coffee market. We study whether their behaviour is better represented by Bertrand behaviour or by collusive pricing. We also investigate the role of advertising in product differentiation.     

Assessing dependence between financial market indexes using conditional time-varying copulas: applications to Value at Risk (VaR)

We analyse the dynamic dependence structure between broad stock market indexes from the United States (S&P500), Britain (FTSE100), Brazil (BOVESPA) and Mexico (PCMX). We employ Patton’s [Int. Econ. Rev., 2006, 2, 527–556] conditional copula setting and additionally observe the impact of different copula functions on Value at Risk (VaR) estimation. We conclude that the dependence between BOVESPA and the other indexes has intensified since the beginning of 2007. In our case the particular copula form is not crucial for VaR estimation. A goodness-of-fit test based on the parametric bootstrap is also applied. The best fits are obtained via time constant Student-t and time-varying Normal copulas.     

REVERSE DISCRIMINATION AND EFFICIENCY IN EDUCATION*

This article shows that reverse discrimination policies can find a justification purely on efficiency grounds. We study the optimal provision of education when households belong to different groups, differing in the distribution of the potential to benefit from education among individuals, which is private information. The main result is that high‐potential individuals from groups with relatively few high‐potential individuals should receive more education than otherwise identical individuals from groups with a more favorable distribution of these benefits.     

Poverty and the Atkinson BI/FRT model: A note

By endogenizing an income-oriented poverty line in Atkinson’s (1995) model, welfare maximizing conditions for a basic income/flat rate tax scheme in economies with income poverty are derived and briefly discussed. (JEL: I38)