Zero-sum condition: A necessary and sufficient condition for a transitive voting system

A simple and quick way to ascertain whether or not any given majority voting system can always produce a transitive social preference orderings without imposing any restriction on the distribution of diverse individual preference orderings is to examine whether all individual voting (preference) vectors satisfy the Addition Rule or not. This conclusion was obtained by first reformulating the voting mechanism into that of a linear mapping from T^m defined by q = Σp_i. It was found that the subset P of T that can accommodate all possible individual preference ordering profiles and such that every sum vector q = Σ p_i of its member vectors p_i is contained in T can be expressed as P = {p: p∈ T, s(p) = 0}. It was also pointed out that this is equivalent to the requirement that all individual preference (voting) functions must satisfy the Addition Rule. Finally, Borda's Rule and Saposnik's Contributive Rule were shown to be examples of transitive voting rules which satisfy these necessary and sufficient conditions.     

Evolution in Games with Endogenous Mistake Probabilities

J. Bergin and B. Lipman (Econometrica64 (1996), 943-956) show that the selection effect from the random mutations in the adaptive population dynamics in M. Kandori, G. Mailath, and R. Rob (Econometrica61 (1993), 29-56) and P. Young (Econometrica61 (1993), 57-84) is due to restrictions on how these mutation rates vary across population states. We here model mutation rates as endogenously determined mistake probabilities, by assuming that players with some effort can control the probability of implementing the intended strategy. This is shown to corroborate the results in Kandori-Mailath-Rob (1993) and, under certain regularity conditions, those in Young (1993). Journal of Economic Literature Classification Number: C72.     

Liberty and national security in Adam Smith’s possible world

Thomas P. M. Barnett argues that globalization’s spread presents the United States and other liberal democracies with two unprecedented national-security problems, and proposes an ambitious military strategy for their solution. This work argues that a successful strategy to solve one of these problems must also include rational policy, public policy that makes Adam Smith’s simple system of natural liberty a reality. Thus, Barnett’s military strategy and rational policy become complementary elements of a more comprehensive strategy to solve this national-security problem. Knowledge that Smith’s simple system of natural liberty moves the world toward peace can create a need for rational policy among voters.

Generic 4 × 4 Two Person Games Have at Most 15 Nash Equilibria

The maximal generic number of Nash equilibria for two person games in which the two agents each have four pure strategies is shown to be 15. In contrast to Keiding (1997),Games Econ. Behav.21, 148–160, who arrives at this result by referring to the enumeration of Grünbaum and Sreedharan (1967),J. Combin. Theory2, 437–465, our argument is based on a collection of lemmas that constrain the set of equilibria. Several of these pertain to any common numberdof pure strategies for the two agents.Journal of Economic LiteratureClassification Number: C72.     

Core allocations and the dimension of the cone of efficiency price vectors

Let (R₁,…,R_k) be an arbitrary partition of the grand coalition in an atomless exchange economy with k “large enough.” We prove that an optimal allocation x belongs to the core if and only if x cannot be improved upon by any coalition that includes at least one of the R_i's. K is “large enough” if k ? r + 1, where r is the linear dimension of the cone P of the efficiency price vectors for x. Recall that it is always true that r ? n, when n is the number of commodities in the market, and that under differentiability and interiority r = 1; thus k can be chosen to be 2 (i.e., for any coalition R, an allocation x belongs to the core of the market if and only if x is not blocked by any coalition that either contains R or contains its complement).     

Bounds for Mixed Strategy Equilibria and the Spatial Model of Elections

We prove that the support of mixed strategy equilibria of two-player, symmetric, zero-sum games lies in the uncovered set, a concept originating in the theory of tournaments, and the spatial theory of politics. We allow for uncountably infinite strategy spaces, and as a special case, we obtain a long-standing claim to the same effect, due to R. McKelvey (Amer. J. Polit. Sci.30 (1986), 283-314), in the political science literature. Further, we prove the nonemptiness of the uncovered set under quite general assumptions, and we establish, under various assumptions, the coanalyticity and measurability of this set. In the concluding section, we indicate how the inclusion result may be extended to multiplayer, non-zero-sum games. Journal of Economic Literature Classification Numbers: C72, D72.     

Capital as a commitment: Strategic investment to deter mobility

This paper analyzes how an early entrant in a market can exploit its head start by strategic investment. The analysis is based on Spence's paper, Investment strategy and growth in a new market, (Bell J. Econ., 10 (1979), 1–19). We frist study the investment game in the no-discounting case, which embodies the key features of mobility deterrence. We establish the existence of a set of perfect equilibria and suggest that one particular equilibrium is most reasonable. This equilibrium, also valid with discounting, involves the follower firm being forever deterred from investing to its steady-state reaction curve, in contrast to Spence's proposed solution.     

Stationary cardinal utility and optimal growth under uncertainty

In the literature on multiperiod planning under uncertainty, it is generally postulated that preferences may be represented by a von Neumann-Morgenstern utility index that is additive over time. This paper accomplishes two objectives: First, an axiomatic basis is provided for a more general class of non-additive utility indices defined over infinite consumption streams. Second, this class of utility functions is applied to extend existing results (J. Econ. Theory4 (1972), 479–513; J. Econ. Theory11 (1975), 329–339) on the nature of optimal growth under uncertainty. Of particular interest are the existence and stability of a stochastic steady state.     

On equilibrium in Hart's securities exchange model

In this paper, we use a no unbounded arbitrage condition to give a very direct proof of the existence of equilibrium in Hart's unbounded securities exchange model (J. Econ. Theory, 9 (1974), 293–311). We also examine the relationship between the no unbounded arbitrage condition and the sufficiency conditions of Hart, ibid. and Hammond (J, Econ. Theory, 31 (1983), 170–175). We present an example to show that if traders are not sufficiently risk averse, then Hammond's overlapping expectations condition is not, in general, equivalent to the no unbounded arbitrage condition or Hart's sufficiency conditions, and therefore, is not sufficient to guarantee the existence of equilibrium. We also present an example to show that it is possible for the no unbounded arbitrage condition to hold without overlapping expectations, and therefore, it is possible for equilibrium to exist without overlapping expectations.     

On the informational efficiency of the competitive resource allocation process

The purpose of this paper is to formalize the competitive process as a parametric process, and then prove the minimality of its message space among the message spaces for a broad class of parametric processes that includes the class of processes considered by Hurwicz (in “Studies in Resource Allocation Processes” (K. J. Arrow and L. Hurwicz, Eds.), pp. 413–423, Cambridge Univ. Press, Cambridge, 1977), Mount and Reiter (J. Econ. Theory6 (1974), 161–192), and Osana (J. Econ. Theory17 (1978), 66–78). The proof of this result turns crucially on the “asymmetry property” (which is stronger than the well-known “uniqueness property” of Hurwicz) and on an injectiveness lemma which is applicable to parametric processes.     

The Equivalence of Wage and Price Staggering in Monetary Business Cycle Models

This paper considers the persistence puzzle documented by V. Chari, P. Kehoe, and E. McGratten (2000, Econometrica68, 1151–1179). Specifically, it addresses a claim by T. Andersen (1998, European Economic Review42, 593–603) and K. Huang and Z. Liu (1999, “Staggered Contracts and Business Cycle, Persistence,” Federal Reserve Bank of Minneapolis Discussion Paper 127) that staggered-wage models are better able to generate persistent real responses to monetary shocks than are staggered-price models. The paper argues that this result hinges on the assumption of homogeneous factor markets and shows that by assuming firm-specific factor inputs the staggered-price model is as capable as the staggered-wage model is of generating persistent real responses to monetary shocks. Journal of Economic Literature Classification Numbers: E24, E31, E32     

On least squares estimation with a particular linear function of the dependent variable

We consider the standard linear regression model where the endogenous variable y is substituted by Ty, T being a symmetric, idempotent matrix. Comparing the mean square error (MSE) matrices we show that a ‘naive’ LS-procedure may work better than a competing estimator usually proposed in the literature and may even perform better than the LS-estimator based on untransformed data. We derive necessary and sufficient conditions for MSE-dominance and outline some ideas for testing.     

A Unifying Pair of Cournot-Nash Equilibrium Existence Results

For games with a measure space of players a tandem pair, consisting of a mixed and a pure Cournot-Nash equilibrium existence result, is presented. Their generality causes them to be completely mutually equivalent. This provides a unifying pair of Cournot-Nash existence results that goes considerably beyond the central result of E. J. Balder (1995, Int. J. Game Theory24, 79-94, Theorem 2.1). The versatility of this pair is demonstrated by the following new applications: (i) unification and generalization of the two equilibrium distribution existence results by K. P. Rath (1996, J. Math. Econ.26, 305-324) for anonymous games, (ii) generalization of the equilibrium existence result of T. Kim and N. C. Yannelis (1997, J. Econ. Theory77, 330-353) for Bayesian differential information games, (iii) inclusion of the Bayesian Nash equilibrium existence results of P. R. Milgrom and R. J. Weber (1985, Math. Oper. Res.10, 619-632) and E. J. Balder (1988, Math. Operations Res.13, 265-276) for games with private information in the sense of J. C. Harsanyi (1967, Manage. Sci.14, 159-182). Journal of Economic Literature Classification Number: C72.     

Resource egalitarianism with a dash of efficiency

We study the problem of defining inequality-averse social orderings over allocations of commodities when individuals have different preferences. We formulate a notion of egalitarianism based on the axiom that any dominance between consumption bundles should be reduced. This Dominance Aversion requirement is compatible with Consensus, a version of the Pareto principle saying that an allocation y is better than x whenever everybody finds that everyone?s bundle at y is better than at x. We characterize a family of multidimensional leximin orderings satisfying Dominance Aversion and Consensus.     

The Phillips Curve and Optimal Policy in a Structural Signal Extraction Model

We study a monetary economy subject to “signal extraction” problems, and investigate within that framework the positive and normative aspects of monetary policy. As in Lucas (1972, Journal of Economic Theory,4, 103–124; 1973, American Economic Review, 63, 326–334), imperfect signal perception generates macroeconomic correlations similar to those found in the “Phillips curve” literature. Moving to normative aspects, we find that, when aggregate shocks are present, traditional nonactivist policies do not permit reaching the first best, and that an intelligent activist policy always leads to better outcomes. The specific characteristics and effectiveness of this optimal policy also depend crucially on the problem of signal extraction. Journal of Economic Literature Classification Number: E5.     

What Prevents Firms from Advancing in their Environmental Strategy?

The aim of this paper is to analyze the determinants of the strategic environmental behavior of firms and, more specifically, the external and internal barriers that limit and sometimes even prevent the environmental adaptation. The analysis focuses on a sample of industrial firms that have at least three workers and that are located in Aragón, a region situated in the northeast of Spain. In order to achieve this objective, first the theoretical literature on the topic is reviewed. Subsequently, from the firms which were sampled, the existence of an underlying structure among the totality of barriers is studied. Finally, this structure is analyzed in order to determine if it has any influence on the degree of proactivity of the firm’s environmental strategy.

Job Matching and Coalition Formation with Utility or Disutility of Co-workers

This paper studies the job matching market in Kelso and Crawford (1982), Econometrica50, 1483–1504, with one exception, that co-workers may generate utility or disutility in the workplace. We provide a simple idea to show how a great number of sufficient conditions for a nonempty core in the literature can be extended to this labor market. A generalized competitive equilibrium with a tax/subsidy system is also discussed. Journal of Economic Literature Classification Number: D71.     

On the Existence of Undominated Nash Equilibria in Normal Form Games

In this paper the existence problem of undominated Nash equilibrium in normal form games is analyzed. It is shown that an undominated Nash equilibrium exists, if (a) strategy sets are convex polytopes inRⁿand (b) utility functions are affine with respect to each player's own strategy. It is shown by counterexamples that, first, it is not sufficient to have concave utility functions instead of affine under condition (b) even when condition (a) is satisfied, and, second, it is not sufficient to have just compact and convex strategy sets instead of polytopes in condition (a) even when condition (b) is satisfied.     

Essential aggregation procedures on restricted domains of preferences

The restricted domains of individuals' preferences that permit the construction of Arrow social welfare functions and nonmanipulable voting procedures in which each of n voters has some power are characterized. In this context a domain is the Cartesian product of n sets of strict preference orderings. Variants of this result are obtained under the additional requirement of neutrality and in the case when alternatives are vectors whose ith components affect only the ith voter. Kalai and Muller's analogous result (J. Econ. Theory16 (1977), 457–469) concerning nondictatorial procedures is discussed and proved as a corollary to the main theorem.     

Supportability and anonymous equity

W. W. Sharkey and L. G. Telser (J. Econom. Theory18 (1978), 23–37) feel that invulnerability of a natural monopoly to the threat of competitive entry is well reflected in the concept of supportability. G. R. Faulhaber and S. B. Levinson (Amer. Econom. Rev.71 (1981), 1083–1091) point out that supportability is necessary for the achievability of anonymous equity, i.e., absence of consumer subsidies in public enterprise pricing. This paper reconciles supportability with market clearance and shows that supportability is sufficient for the achievability of anonymous equity.