Learning and Equilibrium Selection in a Monetary Overlapping Generations Model with Sticky Prices

We study adaptive learning in a monetary overlapping generations model with sticky prices and monopolistic competition for the case where learning agents observe current endogenous variables. Observability of current variables is essential for informational consistency of the learning setup with the model setup but generates multiple temporary equilibria when prices are flexible and prevents a straightforward construction of the learning dynamics. Sticky prices overcome this problem by avoiding simultaneity between prices and price expectations. Adaptive learning then robustly selects the determinate (monetary) steady state independent from the degree of imperfect competition. The indeterminate (non-monetary) steady state and non-stationary equilibria are never stable. Stability in a deterministic version of the model may differ because perfect foresight equilibria can be the limit of restricted perceptions equilibria of the stochastic economy with vanishing noise and thereby inherit different stability properties. This discontinuity at the zero variance of shocks suggests one should analyse learning in stochastic models.     

Agglomeration and tax competition

Tax competition may be different in ‘new economic geography settings’ compared to standard tax competition models. If the mobile factor is completely agglomerated in one region, it earns an agglomeration rent which can be taxed. Closer integration first results in a ‘race to the top’ in taxes before leading to a ‘race to the bottom’. We reexamine these issues in a model that produces stable equilibria with partial agglomeration in addition to the core-periphery equilibria. A bell-shaped tax differential also arises in our model. Therefore, the ‘race to the top’ result generalises to a framework with partial agglomeration.     

Entry, exit, and imperfect competition in the long run

An infinite-horizon, stochastic model of entry and exit with sunk costs and imperfect competition is constructed. A subgame perfect Nash equilibrium for the general dynamic stochastic game is shown to exist as a limit of finite-horizon equilibria. This equilibrium has a relatively simple structure characterized by two numbers per finite history. Under very general conditions, it tends to exhibit excessive entry and insufficient exit relative to a social optimum.     

Cooperation vs. competition in R&D: The role of stability of equilibrium

We consider a model in which firms first choose process R&D expenditures and then compete in an output market. We show the symmetric equilibrium under R&D competition is sometimes unstable, in which case two asymmetric equilibria must also exist. For the latter, we find, in contrast to the literature that total profits are sometimes higher with R&D competition than with research joint venture cartelization (due to the cost asymmetry of the resulting duopoly in the noncooperative case). Furthermore, these equilibria provide another instance of R&D-induced firm heterogeneity.     

Multiplicity of Cournot Equilibria and Involuntary Unemployment

In an overlapping generations model with Cournot competition on the goods market it is shown that a continuum of stationary states and perfect foresight trajectories exists with unemployment at arbitrary low wages. Decisive for this is the influence that different forecast functions have on the objective demand curve, even though they are consistent with perfect foresight. With an example it is shown that simple adaptive and constant memory forecast rules generate such unemployment equilibria. The corresponding temporary equilibrium dynamics may display stable unemployment and unstable full employment equilibria.Journal of Economic LiteratureClassification Numbers: D43, D51, E24     

Optimal random monetary policy with nominal rigidity

This paper studies a money-in-the-utility function model with imperfect competition and one-period ahead nominal price setting. Under standard assumptions on preferences, Friedman's rule—setting the money growth rate equal to the household time discount factor—generates an equilibrium that is optimal within the class of deterministic policies. We then provide conditions under which a random monetary policy increases ex ante expected welfare relative to Friedman's rule. The result obtains because random policy can reduce the distortion associated with imperfect competition. Our result exhibits original features relative to existing cases of welfare-improving random monetary policy, such as Polemarchakis and Weiss (J. Econom. Theory 15 (1977) 345).     

A multiple equilibrium model of indicative planning

This paper considers how indicative planning can improve outcomes in an imperfectly competitive economy. We adopt a model of multiple equilibria under imperfect competition based upon one presented by Diamond. We introduce exogenous uncertainty into this model and distinguish between the information provision and coordination roles of a planning agency.     

Public input competition

Public investment in infrastructure may help create agglomeration economies, by attracting mobile factors such as skilled labour. Competition among regions in public investment can then be destructive. This paper analyzes the Nash equilibria to a simple model of public input competition. Even though the regions are assumed identical, the equilibrium may not be symmetric. The problem with non-cooperative behaviour is not (only) that regions invest too much, but that too many regions may choose to invest. Depending on the parameter values, the Nash equilibrium may be efficient, may be inefficient or may not exist (at least not in pure strategies). Better mobility among regions leads to more aggressive competition. The analysis suggests that rents from public investment may be dissipated by governments' competition to attract mobile factors.     

Stock market wealth effects in an estimated DSGE model for Hong Kong

This paper develops and estimates an open-economy dynamic stochastic general equilibrium (DSGE) model of the Hong Kong economy. The model features short-run price rigidities generated by monopolistic competition and staggered reoptimization. We devote special attention to asset prices and wealth effects, which we believe to be important. For this reason we adopt a perpetual-youth approach. Model parameters and unobserved components are estimated with a Bayesian maximum likelihood procedure, conditional on prior information concerning the values of parameters. The estimations identify substantial wealth effects and indicate that the nominal interest rate responds to unexpected movements in stock prices.     

Uncertainty and insurance in strategic market games

Summary. For perfectly competitive economies under uncertainty, there is a well-known equivalence between a formulation with contingent goods and one with state-specific securities followed by spot markets for goods. In this paper, I examine whether this equivalence carries over to a particular form of imperfect competition. Specifically, I look at three Shapley-Shubik strategic market games: one with contingent commodities, one with Arrow securities traded under imperfect competition and one with Arrow securities traded under perfect competition. First I compare the feasibility constraints of these three games. Then I compare their equilibrium sets. As in Peck and Shell (1989), the only common equilibria between the first and the second game are those which involve no transfer of income across states. However, if the securities markets are competitive, then the set of equilibria of the contingent commodities game and the securities game coincide. Received: June 16, 1997; revised version: April 30, 1998     

Multistage R&D competition and patent policy

In this paper a model of multistage R&D patent policy is investigated. We study the impact of the duration of patent protection for intermediate products on R&D races when the discovery of the final product requires the accomplishment of an intermediate step. Using a multistage model where firms choose their levels of research investment at each stage, we find all subgame-perfect equilibria of the game. We also determine how competition affects a firm's level of research investment at different stages of the R&D competition.     

Learning to Play Limited Forecast Equilibria

This paper provides a learning justification for limited forecast equilibria, i.e., strategy profiles such that (1) players choose their actions in order to maximize the discounted average payoff over their horizon of foresight as given by their forecasts and (2) forecasts are correct on and off the equilibrium path. The limited forecast equilibria appear to be the stochastically stable outcomes of a simple learning process involving (vanishing) trembles.Journal of Economic LiteratureClassification Numbers: C72, D83.     

Optimal monetary policy with the cost channel and monopolistically-competitive banks

This paper studies the optimal nominal policy interest rate in a model with the cost channel and imperfect competition in the banking sector. Due to this market power, the interest rate on deposits is relatively low; in particular it is lower than the policy interest rate. This, in turn, leads to a suboptimal level of deposits and, as a result, to a low level of intermediation. Deviations from the Friedman Rule are optimal in this setup regardless of the assumption about price rigidity; since households can hold their assets in the form of cash or deposits, taxing money, which is an imperfect substitute for deposits, is optimal in order to increase the level of deposits and encourage intermediation. The main results of the paper are robust to the introduction of market power in the loan market as well as stickiness in both the deposit and the loan markets.     

Nonconvergent Electoral Equilibria under Scoring Rules: Beyond Plurality

We use Hotelling's spatial model of competition to investigate the position‐taking behavior of political candidates under a class of electoral systems known as scoring rules, though the model also has a natural interpretation in the firm location context. Candidates choose ideological positions so as to maximize their support in society. Convergent Nash equilibria in which all candidates adopt the same policy were characterized by Cox (1987). Here, we investigate nonconvergent equilibria, where candidates adopt divergent policies. We identify a number of classes of scoring rules exhibiting a range of different equilibrium properties. For some of these, nonconvergent equilibria do not exist. For others, nonconvergent equilibria in which candidates cluster at positions spread across the issue space are observed. In particular, we prove that the class of convex rules does not have Nash equilibria (convergent or nonconvergent) with the exception of some derivatives of Borda rule. We also look at “two‐party” equilibria. Implications for the firm location model are discussed.     

Macroeconomic effects of an indirect tax substitution

We study an indirect tax reform in a general equilibrium model with imperfect competition for both the Cournot and the Free entry equilibria. We show that it is possible to attain a positive balanced budget multiplier by means of a substitution of specific by ad valorem taxation. Moreover, although any tax substitution causes higher prices and the flow up of firms in the long-run, the Free entry equilibrium output can increase with respect to that of the Cournot equilibrium. Finally, in contrast with the partial equilibrium, welfare decreasing tax reforms are likely to occur even when the balanced budget multiplier is positive.      

Pure strategy and no-externalities with multiple agents

Summary. This note considers two properties of common agency models - pure strategy equilibria with simple competition are robust and equilibria in mechanisms can be reproduced as equilibria with simple competition provided an appropriate no-externalities assumption holds. This note provides counter examples to both these theorems when there are multiple agents.Received: 30 April 2002, Revised: 7 January 2003, JEL Classification Numbers: D82.     

Price normalization under imperfect competition

In general equilibrium models of imperfect competition the equilibria depend on how prices are normalized. This note shows that a price normalization preserves convexity properties if and only if prices are measured in terms of a fixed commodity bundle. I am grateful to an anonymous referee for helpful comments, inspiring a simplification in the proof of the main result, and the argument in the Remark.     

Imperfect monitoring in communication networks

Individuals in many social networks imperfectly monitor other individuals’ network relationships. This paper shows that, in a model of a communication network, imperfect monitoring leads to the existence of many inefficient equilibria. Reasonable restrictions on actions or on beliefs about others’ actions can, however, eliminate many of these inefficient equilibria even with imperfect monitoring. Star networks, known to be efficient in many settings, are shown to have desirable monitoring characteristics. More generally, this paper provides a formal framework in which to study incorrect perceptions as an equilibrium phenomenon in social networks.     

Stakeholders’ relationships and product market competition

In this article, we study the relationships between main stakeholders (shareholders, consumers and employees) when firms are consumer oriented (CO) in the sense of caring about consumers’ interests in the objective function. We let these firms first bargain with labour union over their employees’ wages and then compete either in the quantity space (Cournot competition) or in the price space (Bertrand competition). Our model shows that taking care of the consumers’ interests when determining product market strategies may reverse the traditional ranking between Cournot and Bertrand equilibria. This implies that if shareholders in a CO firm can choose either a quantity or a price strategy, they will surprisingly choose the latter. Moreover, we show that the conflicting interests between main stakeholders are attenuated under Bertrand competition compared to Cournot competition.     

UNIQUENESS OF EQUILIBRIUM PAYOFFS IN FINITELY REPEATED GAMES WITH IMPERFECT MONITORING*

This paper examines when a finitely repeated game with imperfect monitoring has a unique equilibrium payoff vector. This problem is nontrivial under imperfect monitoring, because uniqueness of equilibrium (outcome) in the stage game does not extend to finitely repeated games. A (correlated) equilibrium is equilibrium minimaxing if any player's equilibrium payoff is her minimax value when the other players choose a correlated action profile from the actions played in the equilibrium. The uniqueness result holds if all stage game correlated equilibria are equilibrium minimaxing and have the same payoffs. The uniqueness result does not hold under weaker conditions.