A game of timing and visibility

We consider the following abstraction of competing publications. There are n players in the game. Each player i chooses a point x_i in the interval [0,1], and a player's payoff is the distance from its point x_i to the next larger point, or to 1 if x_i is the largest. For this game, we give a complete characterization of the Nash equilibrium for the two-player game, and, more important, we give an efficient approximation algorithm to compute numerically the symmetric Nash equilibrium for the n-player game. The approximation is computed via a discrete version of the game. In both cases, we show that the (symmetric) equilibrium is unique. Our algorithmic approach to the n-player game is non-standard in that it does not involve solving a system of differential equations. We believe that our techniques can be useful in the analysis of other timing games.     

What is macroeconomic causality?

The paper aims to develop an adequate account of macroeconomic causality. It discusses the definition that is central to Woodward’s interventionist account and the definitions that can be extracted from Hoover’s remarks on privileged parameterization and from the potential outcome approach that Angrist and Kuersteiner have introduced into macroeconomics more recently. The definition to be defended can be regarded as the gist that is common to all three definitions when they are relieved of overly restrictive conditions. It says (roughly) that X causes Y if and only if there is a possible intervention on X that changes Y, where X and Y stand for macroeconomic aggregates, where an intervention is understood as a manipulation of an intervention variable I that satisfies conditions requiring that I be a cause of X, and that there be no confounders of X and Y, and where an intervention variable is either a variable or a parameter.     

A leximin characterization of strategy-proof and non-resolute social choice procedures

Summary. We characterize strategy-proof social choice procedures when choice sets need not be singletons. Sets are compared by leximin. For a strategy-proof rule g, there is a positive integer k such that either (i) the choice sets g(r) for all profiles r have the same cardinality k and there is an individual i such that g(r) is the set of alternatives that are the k highest ranking in i's preference ordering, or (ii) all sets of cardinality 1 to k are chosen and there is a coalition L of cardinality k such that g(r) is the union of the tops for the individuals in L. There do not exist any strategy-proof rules such that the choice sets are all of cardinality to k where . Received: November 8, 1999; revised version: September 18, 2001     

A class of multiattribute utility functions

A function u(z) is a utility function if u′(z) > 0. It is called risk averse if we also have u′′(z) < 0. Some authors, however, require that u ⁽ⁱ⁾(z) > 0 if i is odd and u ⁽ⁱ⁾(z) < 0 if i is even. The notion of a multiattribute utility function can be defined by requiring that it is increasing in each variable and concave as an s-variate function. A stronger condition, similar to the one in case of a univariate utility function, requires that, in addition, all partial derivatives of total order m should be positive if m is odd and negative if m is even. In this paper, we present a class of functions in analytic form such that each of them satisfies this stronger condition. We also give sharp lower and upper bounds for E[u(X ₁,... , X _s )] under moment information with respect to the joint probability distribution of the random variables X ₁,... , X _s assumed to be discrete and representing wealths. Partially supported by OTKA grants F-046309 and T-047340 in Hungary.     

Designer path independent choice functions

Summary. This paper provides an algorithm for the construction of all PICFs on a finite set of alternatives, V, designed by an a priori given set I of initial choices as well as the determination of whether the initial set I is consistent with path independence. The algorithm is based on a new characterization result for path independent choice functions (PICF) on finite domains and uses that characterization as the basis of the algorithm. The characterization result identifies two properties of a partition of the Boolean algebra as necessary and sufficient for a choice function C to be a PICF: (i): For every subset A of V the set is an interval in the Boolean algebra 2 ^V . (ii): If A/B is an interval in the Boolean algebra such that C(A) = C(B) and if M/N is an upper transpose of A/B then C(M) = C(N). The algorithm proceeds by expanding on the implications of these two properties.Received: 5 November 2003, Revised: 20 July 2004, JEL Classification Numbers: D00, D70.     

Endogenous leadership and sustainability of enhanced cooperation in a repeated interactions model of tax competition: Endogenous leadership in tax competition

In this study, the endogenous timing of moves is analyzed in an infinitely repeated game setting of capital tax competition between a subgroup (a tax union) of countries agreeing on partial tax harmonization and outside countries. It is shown that in a subgame perfect equilibrium of the infinitely repeated tax competition game, they simultaneously set capital taxes in every stage game when a tax union comprises similar countries with respect to productivity, whereas they may set capital taxes sequentially in every stage game when a tax union comprises dissimilar countries. This finding is significantly different from Ogawa (2013), although we also assume that capital is owned by the country's residents, as in Ogawa's model. This is because a disadvantaged member country of the tax union would suffer from larger losses when a tax union comprising dissimilar countries, and thus the tax union will choose the strategy of moving Late for the sake of sustaining tax harmonization to avoid such losses.     

Method in Experiment: Rhetoric and Reality

The methodological ideal of experimentalists, E, is easily stated: derive a testable hypothesis, H, from a well-specified theory, T; implement experiments with a design; implicitly in the latter are auxiliary hypotheses, A, that surface in the review/discussion of completed research reports (payoffs are 'adequate,' Ss are 'relevant,' instructions, context are 'clear,' etc.). We want to be able to conclude, if statistical test outcomes support not-H, that T is 'falsified.' But this is not what we do; rather we ask if there is a flaw in the test, i.e. not-A is supported, and we do more experiments. This is good practice—much better than the statistical rhetoric of falsificationism. Undesigned social processes allow E to accumulate technical and instrumental knowledge that drive the reduction of experimental error and constitute a more coherent methodology than falsificationism.     

Resource-monotonic allocation when preferences are single-peaked

Summary. We consider the problem of allocating an infinitely divisible commodity among a group of agents with single-peaked preferences. Thomson (1994a), S?nmez (1994), and Moulin (1999) introduce three different resource-monotonicity conditions. In each characterization they derive, the axioms are independent. Under Pareto-optimality, the three resource-monotonicity conditions are equivalent. We investigate whether the interchange of these conditions still yields a valid characterization, and when the characterization still holds, whether it is a tight result or not. We strengthen each of the results, that is either the used resource-monotonicity condition can be replaced by a weaker one, or by using another resource-monotonicity condition, the result is not tight. Our main result is that when at least three agents are present, the class of fixed-path rationing methods is characterized by weak one-sided resource-monotonicity, strategy-proofness, and consistency. Received: April 24, 2000; revised version: April 10, 2001     

Uhljeb – a post-socialist homo croaticus: a personification of the economy of favours in Croatia?

Party patronage combined with a collectivist culture appears to present a very resistant socialist legacy in Croatia. In-group favouritism and an overly bureaucratised system provide a fertile soil for uhljebs. An uhljeb is a public sector employee whose main ‘competence’ is membership of a political party or a nepotistic relationship. They now already count in the thousands, and often contribute to the further multiplication of uhljebs, and to an increase in clientelist arrangements. The practice of employing uhljebs both undermines and underpins the existing system. That ambivalence is one of the characteristics of the Russian sistema, and that is one of the important links to compare blat users and uhljebs, in addition to the practice of ‘pulling strings’. As key protagonists, uhljebs and blat users illustrate their own and society’s modus operandi: an intense ‘economy of favours’. Recent studies increasingly show that cultural variables influence economic outcomes and this article presents an extension of the ‘economy of favours’ into Croatia’s paradigm. Based on primary sources and international benchmarks, it provides a comparison of the cultural contexts of Eastern and Western European countries, and portrays a rising informal practice that, despite its omnipresence, has been under-researched in the academic literature.     

The Borda rule,Condorcet consistency and Condorcet stability

Summary. The Borda rule is known to be the least vulnerable scoring rule to Condorcet inconsistency, Saari (2000). Such inconsistency occurs when the Condorcet winner (the alternative which is preferred to any other alternative by a simple majority) is not selected by the Borda rule. This note exposes the relationship between the Borda rule and the Condorcet q-majority principle as well as the Condorcet q-majority voting rule. The main result establishes that the Borda rule is Condorcet q-majority consistent when where k is the number of alternatives. The second result establishes that is the minimal degree of majority decisiveness corresponding to the Borda rule under sincere voting. The same majority is required to ensure decisiveness under the Borda rule and to ensure that a q-rule (the generalized q-majority Condorcet rule) is a voting rule. Received: April 8, 2002; revised version: July 17, 2002 Correspondence to:S. Nitzan     

No-envy in queueing problems

We explore the implications of no-envy(Foley 1967) in the context of queueing problems. We identify an easy way of checking whether a rule satisfies efficiencyand no-envy. The existence of such a rule can easily be established. Next, we ask whether there is a rule satisfying efficiency and no-envytogether with an additional solidarity requirement how agents should be affected as a consequence of changes in the waiting costs. However, there is no rule satisfying efficiency, noenvy, and either one of two cost monotonicity axioms. To remedy the situation, we propose modifications of no-envy, adjusted no-envyand backward/forward no-envy. Finally, we discuss whether three fairness requirements, no-envy, the identical preferences lower bound, and egalitarian equivalence, are compatible in this context.     

COHERENCY AND COMPLETENESS OF STRUCTURAL MODELS CONTAINING A DUMMY ENDOGENOUS VARIABLE*

Let y be a vector of endogenous variables and let w be a vector of covariates, parameters, and errors or unobservables that together are assumed to determine y. A structural model y=H(y, w) is complete and coherent if it has a well‐defined reduced form, meaning that for any value of w there exists a unique value for y. Coherence and completeness simplifies identification and is required for many estimators and many model applications. Incoherency or incompleteness can arise in models with multiple decision makers, such as games, or when the decision making of individuals is either incorrectly or incompletely specified. This article provides necessary and sufficient conditions for the coherence and completeness of simultaneous equation systems where one equation is a binomial response. Examples are dummy endogenous regressor models, regime switching regressions, treatment response models, sample selection models, endogenous choice systems, and determining if a pair of binary choices are substitutes or complements.     

Hybrid Contests

This paper examines hybrid contests where participants commit two types of resources to improve their probability of winning the prize. The first type is forfeited ex ante, before the prize is allocated, by winners and losers alike, while the second is committed ex ante by all contenders but expended ex post, after the prize is allocated, and only by the contestant that wins the prize. The model yields a number of interesting results. Among them is the finding that, as the number of contestants increases, the ex ante expenditures of individual contestants decrease while the ex post expenditure increases. Even more interesting, the total of the ex ante and ex post expenditures by the contenders in a hybrid contest may decrease with the number of competitors. The study also finds that there is no rent overdissipation, and compares the total expenditures in the contest and “all‐pay” allocation mechanisms.     

A Note on the Probability of k Pure Nash Equilibria in Matrix Games

A formula is derived for the probability that a "randomly selected" n-person matrix game has exactly k pure strategy equilibria. It is shown that for all n ≥ 2, this probability converges to e⁻¹/k! as the sizes of the strategy sets of at least two players increase without bound. Thus the number of pure strategy equilibria in large random n-person matrix games is approximately Poisson distributed with mean one. The latter is a known result obtained by a new proof in this note. Journal of Economic Literature Classification Number: C72.     

Asymptotic expected number of Nash equilibria of two-player normal form games

The formula given by McLennan [The mean number of real roots of a multihomogeneous system of polynomial equations, Amer. J. Math. 124 (2002) 49–73] is applied to the mean number of Nash equilibria of random two-player normal form games in which the two players have M and N pure strategies respectively. Holding M fixed while N→∞, the expected number of Nash equilibria is approximately . Letting M=N→∞, the expected number of Nash equilibria is , where is a constant, and almost all equilibria have each player assigning positive probability to approximately 31.5915 percent of her pure strategies.     

Stability of the cooperative equilibrium in N-person prisoners' dilemma with sequential moves

Summary. Nishihara [3] showed that N-person prisoners' dilemma has a cooperative Nash equilibrium, if the players decide their actions sequentially in the order determined by Nature under a certain information structure, and if each player's payoffs satisfy a certain inequality. This paper examines the stability of this cooperative equilibrium against two matters: players' slight mistakes and deviations by coalitions. The main results are as follows: (i) if the inequality on each player's payoffs strictly holds, then the cooperative equilibrium is a strictly proper equilibrium; (ii) if N≤3, and if full cooperation is Pareto efficient in N-person prisoners' dilemma, then the cooperative equilibrium is a strong Nash equilibrium; (iii) the cooperative equilibrium is in general a coalition-proof Nash equilibrium. Received: June 23, 1997; revised version: December 2, 1997     

A computational analysis of core convergence in a multiple equilibria economy

We examine the structure of the core of a trading economy with three competitive equilibria as the number of traders (N) is varied. The core first splits into two pieces at N=5 and then splits a second time into three pieces at N=12. Both of these splits occur not at a point but as a contiguous gap. We find that the speed of convergence of the core toward the three competitive equilibria is not uniform but when N is large, the convergence rate is approximately of the order 1/N.     

Facilitating Consumer Learning in Insurance Markets: What Are the Welfare Effects?

We model a monopoly insurance market in which consumers can learn their accident risks at a cost c . We then examine the welfare effects of a policy that reduces c . If c is sufficiently small (c  < c ^*), the optimal contract is such that the consumer gathers information. For c  < c ^*, both the insurer and the consumer benefit from a policy that reduces c further. For c   >  c ^*, marginally reducing c hurts the insurer and weakly benefits the consumer. Finally, a reduction in c that is successful, meaning that the consumer gathers information after the reduction but not before it, can hurt both parties.     

Fixed versus variable supply in the public provision of goods

Using discriminatory price auctions with variable supply, we explore a situation in which a corruptible public employee is in charge of producing and allocating a finite number of goods among consumers with uniformly distributed valuations. The negative effects of corruption are lower when the employee‘s task is to “provide at least q₀ goods” than when the employee is required to “provide exactly q₀ goods”.     

WHO BENEFITS FROM CORRODING KEIRETSU?

Abstract. Observations on Japan's industrial distribution system reveal that many producers maintain both keiretsu and non‐keiretsu channels. An intriguing question then is: what economic rationale underlies such an ambivalent policy? This motivated us to present a model of an incomplete keiretsu system. We find that the collapse of a keiretsu is not necessarily a misfortune for the firms remaining therein: they can turn the situation to their advantage if a keiretsu collapses partially. We show why some firms leave their keiretsu while others remain with it, and determine who the winners are.