Coalition-Proof Nash Equilibria II. Applications

In Bernheim, Peleg, and Whinston (“Coalition-Proof Equilibria. I. Concepts,” J. Econ. Theory 42 (1987), 1–12), we proposed the notion of Coalition-Proof Nash equilibrium and Perfectly Coalition-Proof Nash equilibrium as solution concepts for strategic environments in which players can freely discuss their strategies, but cannot make binding commitments. This paper undertakes applications to several economic problems, including the behavior of Cournot oligopolists, oligopolistic entry deterrence, cooperation in finite horizon games, and social choice rule implementation.     

Overlapping expectations and Hart's conditions for equilibrium in a securities model

Hart (J. Econ. Theory9 (1974), 293–311) gave conditions for equilibrium to exist in a securities model where each agent undertakes asset transactions to maximize expected utility of wealth. These conditions rule out agents wanting to undertake unbounded balanced transactions to reach a Pareto superior allocation given their expectations. With mild extra assumptions to make agents unwilling to risk incurring unbounded losses on their portfolios, Hart's conditions become equivalent to an assumption of “overlapping expectations,” which is comparable to a much weaker form of Green's “common expectations” (Econometrica41 (1973), 1103–1124).     

Monetary and fiscal policy interactions in the EMU when cyclical conditions are uncertain

This paper examines economic policy interactions in the Economic and Monetary Union when the assessment of cyclical conditions in real time is surrounded by uncertainty. On the basis of a simple stylised model it shows that with a Nash-type of interaction different views about the output gap on the side of the policy players—the Council of the European Union, the European Commission and the European Central Bank—can give rise to excessive activism with policy players pushing economic variables into opposite directions. It argues that the costs of such policy conflicts can be reduced by agreeing on a common assessment of the cycle, by constraining policy variables, and/or by increasing the weight of fiscally conservative institutions. An alternative option to sidestep policy conflicts ensuing from diverging views of the cycle is to take policy decisions sequentially, as is the case in a Stackelberg-type of interaction. The paper shows that for a given misperception of the cycle, the impact on the policy instruments and on output and inflation are generally smaller in the Stackelberg equilibrium as compared to a Nash outcome. Alternative allocations of roles—that is leader versus follower—are discussed and assessed.

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.     

p-Best response set and the robustness of equilibria to incomplete information

In this paper, we use p-best response sets—a set-valued extension of p-dominance—in order to provide a new sufficient condition for the robustness of equilibria to incomplete information: if there exists a set S which is a p-best response set with , and there exists a unique correlated equilibrium μ^* whose support is in S then μ^* is a robust Nash equilibrium.     

Some extensions of a claim of Aumann in an axiomatic model of knowledge

The paper begins by presenting an axiomatic model of simple and iterated knowledge. A formal definition of the intuitive notion of common knowledge is given and shown equivalent to previous characterizations. It is shown that agents have information partitions. The second part generalizes Aumann's (Ann. Statist.4 (1976), 1236–1239) well-known propositions about common knowledge between two rational agents of each other's probability assignments. It is shown that: common knowledge of decisions—if these are rational—implies a common decision for like-minded agents; and that a “dialogue” in decisions leads to a common decision. A “no-trade” theorem is given which includes trade under complete uncertainty.     

Aggregation and the existence of a social utility function

In a well-known paper Gorman (Econometrica21 (1953)) established that the necessary and sufficient condition for the existence of an aggregate, or social, utility function, independent of the distribution of income, is that all individuals' income consumption paths be parallel straight lines. Recently Chipman (J. Econ. Theory8 (1974)), building on the paper of Hurwicz and Uzawa (in “Preference Utility and Demand”) has shown that if the distribution of income is proportional and individual preferences are homothetic, aggregate consumption behavior obeys the necessary integrability conditions. It is shown here that the consistency of aggregate behavior can be derived from more general conditions than the ones used by Chipman and Gorman. Examples of demand systems from which aggregate behavior implies a social utility function are provided. It is then shown that if individual demand functions are linear in income—a form employed by both Gorman and Chipman—it is not necessary that the distribution of income be fixed.     

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.     

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.     

Temporal risk and the nature of induced preferences

It has been known since the work of H. Markowitz (“Portfolio Selection: Efficient Diversification of Investments,” Yale Univ. Press, 1959) and J. Mossin (Amer. Econ. Rev.59 (1969), 172–174) that even an individual whose underlying preferences satisfy the von Neumann-Morgenstern axioms will not choose over delayed (i.e., “temporal”) risky prospects in a manner which can be modelled as expected utility maximizing. Since most economically important instances of risk taking (insurance, real investment, agriculture, career training) involve delayed as opposed to immediately resolved risk, the standard use of expected utility theory to model such decisions must be questioned. In this paper the technique of “generalized expected utility analysis” (M. J. Machina, Econometrica50 (1982), 277–323) and the theory of support functions (R. T. Rockafellar, “Convex Analysis,” Princeton Univ. Press, 1970) are applied to exactly model and hence determine the nature of preferences over temporal risky prospects.     

Non-Additive Beliefs and Strategic Equilibria

This paper studies n-player games where players' beliefs about their opponents' behaviour are modelled as non-additive probabilities. The concept of an “equilibrium under uncertainty” which is introduced in this paper extends the equilibrium notion of Dow and Werlang (1994, J. Econom. Theory64, 305–324) to n-player games in strategic form. Existence of such an equilibrium is demonstrated under usual conditions. For low degrees of ambiguity, equilibria under uncertainty approximate Nash equilibria. At the other extreme, with a low degree of confidence, maximin equilibria appear. Finally, robustness against a lack of confidence may be viewed as a refinement for Nash equilibria. Journal of Economic Literature Classification Numbers: C72, D81.     

Low information nash equilibria for oligopolistic markets

This paper deals with an infinite horizon n firm oligopoly in which firms are assumed to have incomplete information about one another's actions and profit functions. An equilibrium concept is defined that is similar to the Nash non-cooperative equilibrium, but is suitable for the information assumptions of the model. The equilibrium uses a type of bounded rationality which makes firms' computations relatively easy. This is due to an implicit assumption that computation is costly and a Bayesian approach is prohibitively costly. This low information Nash equilibrium is proved to exist, and, in addition, an adaptive expectations decision process is described which, if followed by all firms, leads to the low information Nash equilibrium.     

Economics of externalities and public policy

In this paper we study a particular case of “multiple” externalities associated to the production of a good/activity, whose external effects can change from positive to negative depending on the level of output (intersecting externalities). To analyze their impact on the public policy we propose a very simple two-agent partial equilibrium model in the technological context of externalities. In a static framework, the centralized solution always implies an optimal policy, which may consist of taxation or subsidization depending on the individual optimum and on the technology parameters. In a dynamic model with local knowledge of the efficiency function and instantaneous output adjustments, such an optimal policy can be structurally stable or unstable. In the latter case, under small changes of the parameters the policy may switch from low taxation/subsidization to high taxation/subsidization or vice versa, or even jump discontinuously from taxation to subsidization or vice versa. Furthermore, the decentralized solution based upon “tradable rights” can be economically equivalent to the centralized solution in the form of taxation policy but the two solutions may be not politically equivalent.

Evolutionary economics and the case for a constitutional libertarian paternalism—a comment on Martin Binder, “should evolutionary economists embrace libertarian paternalism?”

In his article “Should evolutionary economists embrace libertarian paternalism?”(Journal of Evolutionary Economics 24(3), 2014, 515–539) Martin Binder discusses the pros and cons of “libertarian paternalism” (LP) from an explicitly evolutionary viewpoint, concluding that as a general rule, evolutionary economists should be cautious regarding this new and highly influential policy approach. In this comment I argue that Binder starts from an incomplete model of the institutional status quo and neglects an obvious alternative to the standard variant of LP, namely, a constitutionally constrained LP. Most of Binder’s objections do not apply with equal force to such a refined variant of LP.     

Implementation,Elimination of Weakly Dominated Strategies and Evolutionary Dynamics

This paper studies convergence and stability properties of T. Sjöström's (1994, Games Econom. Behav.6, 502–511) mechanism, under the assumption that boundedly rational players find their way to equilibrium using monotonic evolutionary dynamics and best-reply dynamics. This mechanism implements most social choice functions in economic environments using as a solution concept one round of deletion of weakly dominated strategies and one round of deletion of strictly dominated strategies. However, there are other sets of Nash equilibria, whose payoffs may be very different from those desired by the social choice function. With monotonic dynamics, all these sets of equilibria contain limit points of the evolutionary dynamics. Furthermore, even if the dynamics converge to the “right” set of equilibria (i.e., the one which contains the solution of the mechanism), it may converge to an equilibrium which is worse in welfare terms. In contrast with this result, any interior solution of the best-reply dynamics converges to the equilibrium whose outcome the planner desires. Journal of Economic Literature Classification Numbers: C72, D70, D78.     

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).     

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.     

Credible communication in dynastic government

This paper studies information disclosure in a model of dynastic government. When information about past policy choices comes exclusively from the reports of previous administrations, each administration has an incentive to choose its (suboptimal) one-shot expenditure policy, and then misrepresent its choice to its successor. Consequently, it has been suggested that “horizontal accountability,” i.e., a system of governance where auditing functions lie outside the executive branch, can ensure credible disclosure of a government's activities. This paper suggests a cautious approach to that view.The baseline model examines the reporting incentives of an external auditor who can independently verify the information each period. Even with auditing, credible disclosure is shown to be problematic. Various extensions to this baseline model are examined. In one extension, “liberal” (i.e., those prefering larger government expenditures) and “conservative” (those prefering smaller expenditures) regimes and auditors evolve over time. It is shown that “conservative” (“liberal”) auditors are not credible when the current regime is also “conservative” (“liberal”). Moreover, because information transmission stops when the auditor's and the regime's biases coincide, effective deterrents even in the “good” periods (when the auditor's and the administration's biases differ) are difficult to construct. In all periods the equilibrium requirement of auditor neutrality constrains the dynamic incentives for efficient policy choices. These constraints are shown to bind away from optimal policies in standard constructions of equilibrium. Various ways in which auditing protocols can overcome these problems are discussed.     

Political system and economic efficiency: The east European context

Sections 1 and 2 reexamine the proposition about democratization of socialism as a factor of economic efficiency—in the light of the challenge contained in the article by Stanislaw Gomutka, “Economic Factors in the Democratization of Socialism and the Socialization of Capitalism” (J. Comp. Econ., Dec. 1977, 1, 4:389–406). The author takes issue with Gomulka's conclusions, which view democracy as of little relevance for economic efficiency under socialism. Dissident views on the link between democracy and efficiency are discussed. Section 3 goes beyond this controversy in an attempt to analyze the prospects and efficiency aspects of a limited change within the existing Soviet-type political system (“Kadarism”).     

Estate taxation with warm-glow altruism

This article examines the properties of the optimal fiscal policy in an economy with warm-glow altruism (utility interdependence) and heterogeneous individuals. We propose a new efficiency concept, D-efficiency, that considers an implicit constraint in the act of giving: Donors cannot bequeath to donees more than their existing resources. Considering this constraint, we show that the market equilibrium is not socially efficient. The efficient level of bequest transfers can be implemented by the market with estate and labor-income subsidies and a capital-income tax. In the absence of lump-sum taxation, the government faces a trade-off between minimizing distortions and eliminating external effects. The implied tax policy differs from Pigovian taxation since the government’s ability to correct the external effects is limited. Finally, we show that the efficiency-equity trade-off does not affect the qualitative features of the optimal distortionary fiscal policy.