Nash implementing non-monotonic social choice rules by awards

Summary. By a slight generalization of the definition of implementation (called implementation by awards), Maskin monotonicity is no more needed for Nash implementation. In fact, a weaker condition, to which we refer as almost monotonicity is both necessary and sufficient for social choice correspondences to be Nash implementable by awards. Hence our framework paves the way to the Nash implementation of social choice rules which otherwise fail to be Nash implementable. In particular, the Pareto social choice rule, the majority rule and the strong core are almost monotonic (hence Nash implementable by awards) while they are not Maskin monotonic (hence fail to be Nash implementable in the standard framework).Received: 12 April 2004, Revised: 18 March 2005, JEL Classification Numbers: D 79.I thank François Maniquet, Efe Ok and Ipek Ozkal-Sanver for their valuable contributions. The paper is part of a project on Electoral System Design supported by Bilgi University Research Fund.     

The Production Possibility Frontier as a Maximum Value Function: Concavity and Non-increasing Returns to Scale

This paper makes both a methodological as well as a substantive contribution to the literature on the concavity of the production possibility frontier (PPF). Rather than using the standard, calculus‐based techniques, the method here relies on the fact that the PPF is a maximum value function. The consequent simplification in analysis makes it possible to demonstrate that the conditions which are sufficient to guarantee global concavity of the PPF are considerably less stringent than those stated in the literature. Existing analyses have assumed that production functions are (a) concave and homothetic, or (b) display non‐increasing returns to scale (NIRS) and homogeneity. This paper shows that concavity without homotheticity, or NIRS and quasiconcavity without homogeneity (or even homotheticity) are sufficient, thus greatly increasing the generality of existing results. The analysis can be extended to include situations in which the input set includes industry‐specific factors.     

Economic globalization and the change of electoral rules

This paper takes up an argument from Ronald Rogowski about the “natural affinity” between trade and an electoral system with proportional representation. We draw on literature on the historical determinants of electoral system choice to advance the general argument that trade integration and PR are related because the adoption of PR helps to secure gains from trade. Our specific model of electoral rule changes in the age of globalization predicts that the likelihood of electoral rule change towards more proportionality increases with levels of trade integration in the world economy. The theoretical model draws on a micro model of the distributive effects of increased economic integration. Because more proportional systems are more credibly able to commit to compensate the losers of globalization processes, there will be increased demand to change the electoral system towards more proportionality under economic circumstances that increase the costs of maintaining a closed economy. In accordance with our model, our empirical tests find a positive association between (a) trade integration and the proportionality of the electoral system, (b) proportionality and social spending, and (c) global integration levels and the probability of electoral rules changes that render voting rules more proportional.     

On the existence of pure-strategy perfect equilibrium in discontinuous games

We provide sufficient conditions for a (possibly) discontinuous normal-form game to possess a pure-strategy trembling-hand perfect equilibrium. We first show that compactness, continuity, and quasiconcavity of a game are too weak to warrant the existence of a pure-strategy perfect equilibrium. We then identify two classes of games for which the existence of a pure-strategy perfect equilibrium can be established: (1) the class of compact, metric, concave games satisfying upper semicontinuity of the sum of payoffs and a strengthening of payoff security; and (2) the class of compact, metric games satisfying upper semicontinuity of the sum of payoffs, strengthenings of payoff security and quasiconcavity, and a notion of local concavity and boundedness of payoff differences on certain subdomains of a player's payoff function. Various economic games illustrate our results.     

The price normalization problem in imperfect competition and the objective of the firm

Summary. General equilibrium models of oligopolistic competition give rise to relative prices only without determining the price level. It is well known that the choice of a numéraire or, more generally, of a normalization rule converting relative prices into absolute prices entails drastic consequences for the resulting set of Nash equilibria when firms are assumed to maximize profits. This is due to the fact that changing the price normalization amounts to altering the objective functions of the firms. Clearly, the objective of a firm must not be based on price normalization rules void of any economic content. In this paper we propose a definition of the objective of a firm, called maximization of shareholders' real wealth, which takes shareholders' demand explicitly into account. This objective depends on relative prices only. Real wealth maxima are shown to exist under certain conditions. Moreover, we consider an oligopolistic market and prove the existence of a Nash equilibrium in which each firm maximizes the real wealth of its shareholders. Received: July 10, 1997; revised version: July 27, 1998     

The evolution of portfolio rules and the capital asset pricing model

The aim of this paper is to test the performance of capital asset pricing model (CAPM) in an evolutionary framework. We model an economy where a heterogeneous population of long-lived agents invest their wealth according to different portfolio rules, and prove that traders who either “believe” in CAPM and use it as a rule of thumb, or are endowed with genuine mean-variance preferences, under some very weak conditions, vanish in the long run.We show that a sufficient condition to drive CAPM or mean-variance traders’ wealth shares to zero is that an investor endowed with a logarithmic utility function enters the market.     

Optimal money supply rules under asymmetric objective criteria

This paper examines the derivation and properties of optimal money supply rules when such rules are chosen to minimize a loss function with asymmetric properties. Optimal money supply rules derived under symmetric and asymmetric objective criteria are compared under alternative expectations scenarios. When shocks have no impact on variables in the loss function, the optimal rule under a symmetric objective criterion is then also optimal under an asymmetric objective criterion. When shocks have some impact on variables in the loss function, the optimal policy rule will be different under the alternative criteria.Earlier versions of this paper were presented to the Seventh Analytic Economics Workshop, Australian National University, to the Australasian Meetings of the Econometrics Society, University of New England, and to seminars at the University of Waikato, the University of Canterbury at Christchurch, and the University of Guelph. The author is grateful to participants in those sessions for helpful comments. Particular thanks go to Louis Christofides, John Fender, Rod Maddock, Adrian Pagan, John Pitchford, and Larry Taylor for helpful discussions. The author is also grateful to the editor and two anonymous referees of this Journal for their constructive comments and criticisms. Of course, any remaining errors are the sole responsibility of the author.     

The most ordinally egalitarian of random voting rules

Aziz and Stursberg propose an “Egalitarian Simultaneous Reservation” rule (ESR), a generalization of Serial rule, one of the most discussed mechanisms in the random assignment problem, to the more general random social choice domain. This article provides an alternative definition, or characterization, of ESR as the unique most ordinally egalitarian one. Specifically, given a lottery p over alternatives, for each agent i the author considers the total probability share in p of objects from her first k indifference classes. ESR is shown to be the unique one which leximin maximizes the vector of all such shares (calculated for all i, k). Serial rule is known to be characterized by the same property. Thus, the author provides an alternative way to show that ESR, indeed, coincides with Serial rule on the assignment domain. Moreover, since both rules are defined as the unique most ordinally egalitarian ones, the result shows that ESR is “the right way” to think about generalizing Serial rule.     

Weak monotonicity and Bayes–Nash incentive compatibility

An allocation rule is called Bayes–Nash incentive compatible, if there exists a payment rule, such that truthful reports of agents' types form a Bayes–Nash equilibrium in the direct revelation mechanism consisting of the allocation rule and the payment rule. This paper provides a characterization of Bayes–Nash incentive compatible allocation rules in social choice settings where agents have multi-dimensional types, quasi-linear utility functions and interdependent valuations. The characterization is derived by constructing complete directed graphs on agents' type spaces with cost of manipulation as lengths of edges. Weak monotonicity of the allocation rule corresponds to the condition that all 2-cycles in these graphs have non-negative length. For the case that type spaces are convex and the valuation for each outcome is a linear function in the agent's type, we show that weak monotonicity of the allocation rule together with an integrability condition is a necessary and sufficient condition for Bayes–Nash incentive compatibility.     

An evolutionary approach to regional systems of innovation

This article examines how the birth and the development of regional systems of innovation are connected with economic selection and points to implications for regional-level policies. The research questions are explored using an evolutionary model, which emphasizes geographical spaces and production of intermediate goods. In particular, we are concerned with how cooperative behaviour of technology producers is affected by the need to protect technological secrecies and of being financially constrained by firms demanding innovative input. Based on the theoretical model, we provide an analysis using computer simulations. The primary findings are, first, that the model generates predictions suited for empirical research as to the way in which economic selection influences cooperative behavior of innovative actors. Second, we demonstrate how a region’s entrepreneurial activity and growth can be controlled in a decentralized way by regions.     

Weak monotonicity and Bayes–Nash incentive compatibility

An allocation rule is called Bayes–Nash incentive compatible, if there exists a payment rule, such that truthful reports of agents' types form a Bayes–Nash equilibrium in the direct revelation mechanism consisting of the allocation rule and the payment rule. This paper provides a characterization of Bayes–Nash incentive compatible allocation rules in social choice settings where agents have multi-dimensional types, quasi-linear utility functions and interdependent valuations. The characterization is derived by constructing complete directed graphs on agents' type spaces with cost of manipulation as lengths of edges. Weak monotonicity of the allocation rule corresponds to the condition that all 2-cycles in these graphs have non-negative length. For the case that type spaces are convex and the valuation for each outcome is a linear function in the agent's type, we show that weak monotonicity of the allocation rule together with an integrability condition is a necessary and sufficient condition for Bayes–Nash incentive compatibility.     

On choosing which game to play when ignorant of the rules

This paper suggests a theory of choice among strategic situations when the rules of play are not properly specified. We take the view that a “strategic situation” is adequately described by a TU game since it specifies what is feasible for each coalition but is silent on the procedures that are used to allocate the surplus. We model the choice problem facing a decision maker (DM) as having to choose from finitely many “actions”. The known “consequence” of the ith action is a coalition from game f _i over a fixed set of players \(N_i\cup\{d\}\) (where d stands for the DM). Axioms are imposed on her choice as the list of consequences (f ₁,..., f _m ) from the m actions varies. We characterize choice rules that are based on marginal contributions of the DM in general and on the Shapley Value in particular.     

Co-managing common-pool resources: Do formal rules have to be adapted to traditional ecological norms?

We examine the effectiveness of three democratically chosen rules that alleviate the coordination and cooperation problems inherent in collectively managed common-pool resources. In particular we investigate how rule effectiveness and rule compliance depend on the prevailing local norms and ecological values held by resource users. For this purpose, we employ a framed field experiment that is based on a rangeland model for semi-arid regions and carried out with communal farmers in Namibia and South Africa. Participants could vote for three ‘best practice’ management rules found in many places around the world that are discussed for implementation in the study area: (temporary) private property rights, rotational grazing or limitation of livestock numbers. All rules were designed in a way that facilitated cooperation or coordination of actions. The focus of this study lies on the interactions between these rules and prevalent ecological norms exhibited in the rounds prior to rule implementation. In contrast to previous lab experimental studies, we find that democratic voting of rules is not sufficient for high rule compliance and an overall enhancement in cooperation. Rules turned out to be inefficient if they were in conflict with the prevalent ecological norm.     

On Environmental Policy and Permitting

The literature on environmental policy under adverse selection usually assumes that firms' profit vary monotonically with a private information parameter. However, it is easy to demonstrate using standard production setups that regularity is not the rule. We show that policy requirements are very sensitive to this assumption. In particular, the optimal instrument resembles more an “adaptable” pollution standard than the economic instrument of an environmental tax. We also show that permitting, which results in some firms overinvesting in pollution‐control equipment, does not serve the objective of improving the environment but rather allows the agency to increase the proceeds of the policy.     

Growth,selection and appropriate contracts

We study a dynamic model where growth requires both long-term investment and the selection of talented managers. When ability is not ex-ante observable and contracts are incomplete, managerial selection imposes a cost, as managers facing the risk of being replaced choose a sub-optimally low level of long-term investment. This generates a trade-off between selection and investment that has implications for the choice of contractual relationships and institutions. Our analysis shows that rigid long-term contracts sacrificing managerial selection may prevail at early stages of economic development and when heterogeneity in ability is low. As the economy grows, however, knowledge accumulation increases the return to talent and makes it optimal to adopt flexible contractual relationships, where managerial selection is implemented even at the cost of lower investment. Measures of investor protection aimed at limiting the bargaining power of managers improve selection under short-term contracts. Given that knowledge accumulation raises the value of selection, the optimal level of investor protection increases with development.     

Welfare variations and the comparative statics of demand

By employing order-theoretic comparative statics, we provide necessary and sufficient conditions on the direct utility function (alternatively, on the indirect utility function) to guarantee that the compensating and equivalent variations are monotonically increasing in income. We also show that these conditions are sufficient to guarantee normal demand. Our results do not depend on the smoothness or strict quasiconcavity of the utility function, and can be extended to a setting with non-linear prices.     

The effectiveness of fiscal policy in a keynesian-monetarist model of Canada

This paper presents a simple macroeconomic model that includes all of the main channels of transmission for fiscal policy and that can generate either Keynesian or monetarist results for the impact of fiscal policy depending on the values assumed for particular parameters. The structure of this model, called KEMO for KEynesian-MOnetarist, was kept very simple and schematic. The objective of this paper is to examine through simulations of the model the degree of sensitivity of the fiscal multiplier to certain hypotheses concerning the way the economy functions and the value of certain parameters, as well as the dynamic process of adjustment of the economy to a fiscal shock.     

Stochastic evolutionary selection in finite populations

We primarily focus on a wide range of stochastic evolutionary game dynamics between two strategies which are characterized by a condition we call monotonicity: the sign of the difference between the probabilities of increasing and decreasing an A-individual completely depends on the difference of payoffs based on different strategies. When mutations are excluded, we provide sufficient conditions for selection to favor one strategy over the other and necessary conditions for selection to favor or oppose change, respectively. Moreover, we discuss which strategy will be favored in case of rare mutations and give a simple rule to determine evolutionary selection of strategies for large populations under some specific stochastic mutation–selection dynamics.     

A DEA model for resource allocation

This paper concerns inverse DEA. The aim is to estimate input/output levels of a given Decision Making Unit (DMU) when some or all of its input/output levels are changed, under preserving the efficiency index. We show that in the case of estimating increased required input vector when the output vector is increased, the current method which uses weakly efficient solution of the relevant multiple objective optimization problem may fail. We propose some sufficient conditions for input estimation.