Restricted houseswapping games

Restricted houseswapping games (RHGs) are a generalization of ‘one-sided matching games’, in which we specify a class II* of ‘allowable’ simple trading cycles. The cores of such games may be empty. Given II*, all possible closed RHGs have non-empty cores of II* is ‘strongly balanced’. Examples include the one-sided matching markets (^{Shapley and Scarf. Journal of Mathematical Economics 1974. 1. 23–37}. ^{Tijs et al., OR Spektrum 1984, 6, 119–123}; ^{Quinzii, International Journal of Game Theory 1984, 13, 41–60}) and the two-sided matching markets (^{Gale and Shapley. American Mathematical Monthly 1962. 69, 9–16}; ^{Shapley and Shubik, International Journal of Game Theory 1972, 1, 111–130}: and ^{Demange and Gale Econometrica 1985, 53, 873–888}).We then consider the subclass of RHGs in which there is no transferable resource. In this case, a weaker condition on II*, called ‘weak balancedness’, is sufficient to guarantee core non-emptiness. In addition, if II* is not weakly balanced, then there exists a preference profile such that the strict core of the resultant game is empty.Several other examples are given of II* that are (a) strongly balanced: (b) weakly balanced but not strongly balanced: and (c) not even weakly balanced.Finally, we discuss the issues of equilibrium definition, existence, and core-equilibrium allocation equivalence in RHGs.     

Solutions for cooperative games with r alternatives

We consider games with n players and r alternatives. In these games each player must choose one and only one alternative, reaching an ordered partition of the set of players. An extension of the Shapley value to this framework is studied. Received: 1 November 1997 / Accepted: 24 January 1999     

Consistency of assessments in infinite signaling games

In this paper we investigate possible ways to define consistency of assessments in infinite signaling games, i.e. signaling games in which the sets of types, messages and answers are complete, separable metric spaces. Roughly speaking, a consistency concept is called appropriate if it implies Bayesian consistency and copies the original idea of consistency in finite extensive form games as introduced by ^{Kreps and Wilson (Econometrica 1982, 50, 863–894)}. We present a particular appropriate consistency concept, which we call strong consistency and give a characterization of strongly consistent assessments. It turns out that all appropriate consistency concepts are refinements of strong consistency. Finally, we define and characterize structurally consistent assessments in infinite signaling games.     

Arbitrage, equilibrium, and gains from trade: A counterexample

We present a counterexample to a theorem due to Chichilnisky (Bulletin of the American Mathematical Society, 1993, 29, 189–207; American Economic Review, 1994, 84, 427–434). Chichilnisky's theorem states that her condition of limited arbitrage is necessary and sufficient for the existence of an equilibrium in an economy with unbounded short sales. Our counterexample shows that the condition defined by Chichilnisky is not sufficient for existence of equilibrium. We also discuss difficulties in Chichilnisky (Economic Theory, 1995, 5, 79–107).     

Sequential regularity in smooth production economies

In general equilibrium models where agents trade sequentially in multiple periods, the equilibria that endogenously occur in later periods can be robustly indeterminate if production sets are not everywhere differentiable (as. for example, with linear activities). The present paper proves that if technology is smooth, then equilibria are sequentially regular. That is. the equilibria of the endogenously generated economies occurring in later periods that confirm the unanimous expectations formed by agents in earlier periods are regular (and thus, for example, isolated from other equilibria). The paper also proves and utilizes the standard result that the overall intertemporal equilibria are regular.     

Volatility contagion: A range-based volatility approach

This article proposes a new approach to evaluate volatility contagion in financial markets. A time-varying logarithmic conditional autoregressive range model with the lognormal distribution (TVLCARR) is proposed to capture the possible smooth transition in the range process. Additionally, a smooth transition copula function is employed to detect the volatility contagion between financial markets. The approach proposed is applied to the stock markets of the G7 countries to investigate the volatility contagion due to the subprime mortgage crisis. Empirical evidence shows that volatility is contagious from the US market to several markets examined.     

The hybrid equilibria and core selection in exchange economies with externalities

This paper introduces a hybrid equilibrium concept that combines the elements of cooperative and non-cooperative behaviors in an exchange economy with externalities. For a fixed coalition structure (or a partition of traders), the hybrid equilibrium is a price and consumption bundle such that each coalition chooses a core solution from its budget set and the consumption bundles are feasible. It becomes the competitive equilibrium when the position is the finest, and it selects a core allocation when the partition is the coarsest. The paper provides sufficient conditions for the existence of a hybrid equilibrium for any coalition structure.     

A bootstrap algorithm for testing cointegration rank in VAR models in the presence of stationary variables

In this paper, a bootstrap algorithm for a reduced rank vector autoregressive (VAR) model which also includes stationary regressors, is analyzed. It is shown that the bootstrap distribution for estimating the rank converges to the distribution derived from the usual asymptotic framework. Because the asymptotic distribution will typically depend on unknown parameters, bootstrap distributions are of considerable interest in this context. The result of an application and some Monte Carlo experiments are also presented.     

Stable matchings and the small core in Nash equilibrium in the college admissions problem

Both rematching proof and strong equilibrium outcomes are stable with respect to the true preferences in the marriage problem. We show that not all rematching proof or strong equilibrium outcomes are stable in the college admissions problem. But we show that both rematching proof and strong equilibrium outcomes in truncations at the match point are all stable in the college admissions problem. Further, all true stable matchings can be achieved in both rematching proof and strong equilibrium in truncations at the match point. We show that any Nash equilibrium in truncations admits one and only one matching, stable or not. Therefore, the core at a Nash equilibrium in truncations must be small. But examples exist such that the set of stable matchings with respect to a Nash equilibrium may contain more than one matching. Nevertheless, each Nash equilibrium can only admit at most one true stable matching. If, indeed, there is a true stable matching at a Nash equilibrium, then the only possible equilibrium outcome will be the true stable matching, no matter how different are players' equilibrium strategies from the true preferences and how many other unstable matchings are there at that Nash equilibrium. Thus, we show that a necessary and sufficient condition for the stable matching rule to be implemented in a subset of Nash equilibria by the direct revelation game induced by a stable mechanism is that every Nash equilibrium profile in that subset admits one and only one true stable matching. Received: 30 December 1998 / Accepted: 12 October 2001 This paper is a revision of the paper “Manipulation and Stability in a College Admissions Problem” circulated since 1994. I thank Rich McLean, Abraham Neyman, Mark Satterthwaite, Sang-Chul Suh, and Tetsuji Yamada for helpful discussions. I thank the associate editor and the two anonymous referees for their helpful comments that have greatly improved the paper. I am grateful to the Kellogg G.S.M. at the Northwestern University for the hospitality for my visit. Any errors are mine.     

A new necessary condition for Nash implementation

In this paper we formulate a family of conditions called `B_k-monotonicity' that are necessary for Nash implementation, where k is a natural number that indexes a particular condition, and where the condition only becomes more restrictive as k increases. B_k-monotonicity is in general a stricter condition than Maskin monotonicity, and can be used to show that certain social choice correspondences that satisfy Maskin monotonicity cannot be Nash implemented.     

A topological invariant for competitive markets

This paper summarizes the concepts of global cones and limited arbitrage introduced in Chichilnisky (Economic Theory, 1995, 5, 79–108), and the corresponding results establishing that limited arbitrage is necessary and sufficient for the existence of a competitive equilibrium and for the compactness of Pareto frontier (announced in Chichilnisky (American Economic Review, 1992, 84, 427–434, and Chichilnisky (Bulletin of the American Mathematical Society, 1993, 29, 189–207). Using the same global cones I extend my earlier results to encompass ‘mixed economies’ based on Chichilnisky (CORE Discussion Paper No. 9527, 1995). I introduce a topological invariant for competitive markets which deepens the concept of limited arbitrage. This invariant encodes exact information on the equilibria and on the social diversity of the economy and all its subeconomies, and predicts a failure of effective demand.     

Gender wage gap: A semi-parametric approach with sample selection correction

Sizeable gender differences in employment rates are observed in many countries. Sample selection into the workforce might therefore be a relevant issue when estimating gender wage gaps. We propose a semi-parametric estimator of densities in the presence of covariates which incorporates sample selection. We describe a simulation algorithm to implement counterfactual comparisons of densities. The proposed methodology is used to investigate the gender wage gap in Italy. We find that, when sample selection is taken into account, the gender wage gap widens, especially at the bottom of the wage distribution.     

A study of proportionality and robustness in economies with a commonly owned technology

Abstract. Studying one-input one-output economies, we say that an allocation is proportional if the input-output ratio is identical among agents and if each agent maximizes her welfare given this ratio. We propose three equity axioms based on this definition, and we use them to compare the main solutions to this simple equity problem. We also combine efficiency, robustness axioms and our proportionality axioms to characterize two solutions. Received: 11 June 1997 / Accepted: 26 May 2000     

Single-peakedness and coalition-proofness

We prove that multidimensional generalized median voter schemes are coalition-proof. Received: 16 July 1998 / Accepted 23 March 1999     

A sufficiency result for constrained economies

This paper presents a general sufficiency result for constrained economies. The result shows that, when an equilibrium allocation satisfies the first order necessary conditions for hybrid efficiency (a new type of constrained efficiency), there exists a marginal cost pricing equilibrium in an associated economy. If this equilibrium is Pareto efficient in the associated economy, then the original equilibrium allocation is hybrid efficient. Hence. the necessary conditions are also sufficient.