Characterization of optimal plans for stochastic dynamic programs

This paper provides general techniques for the characterization of optimal plans resulting from stochastic dynamic programming. We show that under standard assumptions the optimal plans in both finite and infinite horizon problems can be obtained by an application of the Implicit Function Theorem to first order conditions. Further, we show that under certain checkable conditions, optimal plans and value functions are p-times differentiable for any integer p ? 0. Finally, we apply our technique to obtain a C^p plan and value function in a one sector infinite horizon growth problem under uncertainty.     

Ex ante contracting with endogenously determined communication plans

Summary. In this paper we introduce a new model of ex ante contracting for economies with asymmetric information to examine endogenously determined communication plans for information sharing in the interim stage. In contrast to the models used in previous research, in the present model agents negotiate not only on a contract of state contingent allocations but also on a communication plan, a set of rules describing how agents will reveal part of their private information at the interim stage to execute the trade contracts. We prove a result about the nested structure of the set of allocations implementable by various communication plans and establish the existence of core strategies for this cooperative game under various regularity conditions. Received: 4 March 1998; revised version: 17 September 1999     

Two Remarks on the Property-Rights Literature

We first point out that the recent property-rights literature is based on three assumptions: (1) that contracts are always subject to renegotiation; (2) that the exercise of a property right confers a private benefit and (3) that parties are risk-neutral. Building on Hart–Moore (1999), we provide conditions under which an optimal contract consists of nothing more than an assignment of property rights.
We also examine the robustness of some of the literature's standard predictions about asset ownership to the introduction of mechanisms for eliciting parties' ex post willingness to pay for the assets (such as options or financial markets). To illustrate the issue, we revisit the Hart–Moore (1990) proposition that joint ownership is suboptimal, and argue that ownership by a single party is dominated by joint ownership with put options.     

Portfolio delegation under short-selling constraints

Summary. In this paper we study delegated portfolio management when the manager’s ability to short-sell is restricted. Contrary to previous results, we show that under moral hazard, linear performance-adjusted contracts do provide portfolio managers with incentives to gather information. We find that the risk-averse manager’s effort is an increasing function of her share in the portfolio’s return. This result affects the risk-averse investor’s choice of contracts. Unlike previous results, the purely risk-sharing contract is now shown to be suboptimal. Using numerical methods we show that under the optimal linear contract, the manager’s share in the portfolio return is higher than what it is under a purely risk sharing contract. Additionally, this deviation is shown to be: (i) increasing in the manager’s risk aversion and (ii) larger for tighter short-selling restrictions. As the constraint is relaxed the deviation converges to zero.Received: 25 July 2002, Revised: 12 December 2004, JEL Classification Numbers: D81, D82, J33.Juan-Pedro Gómez: Correspondence toAn earlier version of the paper was circulated under the title “Providing Managerial Incentives: Do Benchmarks Matter?” We are grateful to an anonymous referee whose comments helped to improve the paper. We also thank comments by Viral Acharya, Alexei Goriaev, Ernst Maug, Kristian Rydqvist, Neil Stoughton, Rangarajan Sundaram, Fernando Zapatero and seminar participants at the 1999 SED meetings in Sardinia, the 1999 Workshop in Mutual Fund Performance at EIASM, Brussels, the 2000 EFA meetings in London, the Bank of Norway, the Stockholm Schools of Economics, the Norwegian School of Management and the 2001 WFA meetings in Tucson. Sharma gratefully acknowledges financial support from the Asociacion Mexicana de Cultura.     

Bertrand versus Cournot revisited

Summary. Bertrand criticized Cournot's analysis of the competitive process, arguing that firms should be seen as playing a strategy of setting price below competitors' prices (henceforth, the Bertrand strategy) instead of a strategy of accepting the price needed to sell an optimal quantity (the Cournot strategy). We characterize Nash equilibria in a generalized model in which firms choose among Cournot and Bertrand strategies. Best responses always exist in this model. For the duopoly case, we show that iterated best responses converge under mild assumptions on initial states either to Cournot equilibrium or to an equilibrium in which only one firm plays the Bertrand strategy with price equal to marginal cost and that firm has zero sales. Received: December 11, 1995; revised version October 2, 1996     

Existence and optimality of oligopoly equilibria in linear exchange economies

Summary. We consider a linear exchange economy and its successive replicas. We study the notion of Cournot-Walras equilibrium in which the consumers use the quantities of commodities put on the market as strategic variables. We prove that, generically, if the number of replications is large enough but finite, the competitive behaviour is an oligopoly equilibrium. Then, under a mild condition, which may be interpreted in terms of market regulation and/or market activity, we show that any sequence of oligopoly equilibria of successive replica economies converges to the Walrasian outcome and furthermore that every oligopoly equilibrium of large, but finite, replica is Pareto optimal. Consequently, under the same assumptions on the fundamentals of the economy, one has an asymptotic result on the convergence of oligopoly equilibria to the Walras equilibrium together with a generic existence result for the Cournot-Walras. Received: June 20, 2002; revised version: November 20, 2002 RID="*" ID="*" Part of this paper was written while the second author was visiting the Universidad de Vigo. The support of the department of mathematics is gratefully acknowledged. Correspondence to: J.M. Bonnisseau     

Optimal fiscal and monetary policies in the face of rare disasters

This paper studies optimal fiscal and monetary policies in an economy exposed to large adverse shocks (rare disasters). We contrast optimal policies under commitment and discretion and identify several striking differences between these institutional environments. A government that can commit to its policy plans relies heavily on debt to smooth the adverse effects of large shocks over time. Lack of commitment seriously limits the government's ability to use debt as a shock absorber. Under discretion, an increase in debt leads to an increase in inflation expectations and therefore higher nominal interest rate distortions. Hence, the discretionary government keeps debt in close vicinity of its steady-state level, and the response of taxes, inflation, and interest rates to shocks is much more pronounced under discretion than under commitment. This is particularly relevant for large shocks and when the initial stock of government debt is already high at the time the shock occurs. We also argue that the adverse welfare effects of disasters are larger under discretion than under commitment, but these welfare differentials can be significantly reduced by making the discretionary government inflation averse.     

Nonparametric Analysis of Longitudinal Binary Data: An Application to the Intergroup Prisoner's Dilemma Game

The intergroup prisoner's dilemma game was suggested by Bornstein (1992, Journal of Personality and Social Psychology. 7, 597–606) for modelling intergroup conflicts over continuous public goods. We analyse data of an experiment in which the game was played for 150 rounds, under three matching conditions. The objective is to study differences in the investment patterns of players in the different groups. A repeated measures analysis was conducted by Goren and Bornstein (1999, Games and Human Behaviour: Essays in Honor of Amnon Rapoport, pp. 299–314), involving data aggregation and strong distributional assumptions. Here we introduce a nonparametric approach based on permutation tests. Two new measures, the cumulative investment and the normalised cumulative investment, provide additional insight into the differences between groups. The proposed tests are based on the area under the investment curves. They identify an overall difference between the groups as well as pairwise differences. A simultaneous confidence band for the mean difference curve is used to detect the games which account for any pairwise difference.     

Fiscal policy under loose commitment

Due to time-inconsistency or political turnover, policymakers' promises are not always fulfilled. We analyze an optimal fiscal policy problem where the plans made by the benevolent government are periodically revised. In this loose commitment setting, the properties of labor and capital income taxes are significantly different than under the full-commitment and no-commitment assumptions. Because of the occasional reoptimizations, the average capital income tax is positive even in the long-run. Also, the autocorrelation of taxes is lower, their volatility with respect to output increases and the correlation between capital income taxes and output changes sign. Our method can be used to analyze the plausibility and the importance of commitment in a wide-class of dynamic problems.     

PRIVATIZATION,EMPLOYEE SHARE OWNERSHIP AND GOVERNANCE: THE CASE OF EIRCOM

ABSTRACT: Sizeable employee share ownership plans (ESOPs) have been a unique feature of Ireland's privatization programme. Since the sale in 1999 of the national telecommunications operator, Eircom, the norm has been to allocate 14.9 per cent of equity to employees. We examine the role of the Eircom ESOP in the post‐privatization governance of the company. We find that the ESOP sought to maximize returns to employees as shareholders rather than behave in the interests of a wider set of stakeholders. This is explained in terms of the internal governance of the ESOP, namely its structure and rules, as well as the composition and motivations of the board of the ESOP Trustee.     

Randomization and simplification in dynamic decision-making

Randomization adds beneficial flexibility to the construction of optimal simple plans in dynamic environments. A decision-maker, restricted to the use of simple plans, may find a stochastic plan that strictly outperforms all deterministic ones. This is true even in noninteractive deterministic environments where the decision-maker's choices have no influence on his signals nor on the future evolution of the system. We describe a natural decomposition of simple plans into two components: an action selection rule and a behavior modification rule. In noninteractive environments optimal simple plans do not require randomization in the action selection rule. Only randomization in the behavior modification rule may be necessary.     

The analytics of search with posted prices

Summary. This paper investigates the characteristics of the optimal posted price in the standard sequential search paradigm. Much of the intuition gleaned from the extensive sequential search literature in which the seller adopts a reservation price does not carry over to the posted price setting. For example, an increase in buyer valuations can lead to a reduction in the optimal posted price. We do, however, provide sufficient conditions on the hazard rate function h which ensure that an increase in demand induces an increase in the optimal posted price. As exhibited herein, the analysis of the posted price model depends critically upon analytical properties of h. Amongst the issues treated are the elasticity of demand, finite horizon, sale of multiple units, and competitive equilibrium. Received: October 21, 1999; revised version: March 7, 2000     

Existence and local indeterminacy of periodic equilibrium paths in infinite horizon models with external effects

Summary. It is expected that every periodic equilibrium path may exist even under standard assumptions such as low discounting and the concavity of utility functions in infinite horizon models with external effects. Nevertheless, until now no such example has been presented. In this note we will first construct a bounded growth model that has an external effect and every periodic equilibrium path under any discount factor. Next we will study the conditions under which periodic equilibrium paths have a local indeterminacy. Received: December 23, 1998; revised version: April 19, 1999     

Social Insurance and Redistribution with Moral Hazard and Adverse Selection*

Rochet (1991) showed that with distortionary income taxes, social insurance is a desirable redistributive device when risk and ability are negatively correlated. This finding is re‐examined when ex post moral hazard and adverse selection are included, and under different informational assumptions. Individuals can take actions influencing the size of the loss in the event of accident (or ill health). Social insurance can be supplemented by private insurance, but private insurance markets are affected by both adverse selection and moral hazard. We study how equity and efficiency considerations should be traded off in choosing the optimal coverage of social insurance when those features are introduced. The case for social insurance is strongest when the government is well informed about household productivity.     

Capacity constrained firms in (labor) markets with adverse selection

Summary. We discuss a competitive (labor) market where firms face capacity constraints and individuals differ according to their productivity. Firms offer two-dimensional contracts like wage and task level. Then workers choose firms and contracts. Workers might be rationed if the number of applicants exceeds the capacity of the firm. We show that under reasonable assumptions on the distribution of capacity an equilibrium in pure strategies (by the firms) exists. This result stands in contrast to the case of unlimited capacity. The utility level is uniquely determined in equilibrium. No rationing occurs in equilibrium, but it does off the equilibrium path. Received: December 29, 1999; revised version: November 30, 2000     

On optimal cycles in dynamic programming models with convex return function

Summary. In this paper we study the behavior of optimal paths in dynamic programming models with a strictly convex return function. Such a model has been investigated in Dawid and Kopel (1997) who assume that the growth of a renewable resource is governed by a piecewise linear function. We prove that in their model the optimal cycles undergo the following qualitative changes or bifurcations: a cycle of period n“bifurcates” into a cycle of period n+1 for increasing elasticity of the return function. We also show that under the assumption of a concave differentiable growth function the qualitative properties of the optimal policy remain valid: oscillating behavior is optimal. Furthermore, we demonstrate numerically that the period of a cyclic optimal path increases if the convexity of the return function (measured by the elasticity) increases. Received: January 22, 1997; revised version: October 13, 1997     

Regulating a Polluting Firm Under Asymmetric Information

This paper reinterprets the Laffont-Tirole model of regulation under asymmetric information to cover the case of pollution control. The asymmetry of information concerns the firm's cost of lowering its pollution. The regulator has three objectives: Ensuring an efficient abatement level, generating 'green taxes' and securing the survival of the firm. We show that when optimal abatement is important relative to tax generation, the regulator cannot use the policy of offering the firm a set of linear tax schemes from which to choose. By contrast, this policy is optimal in the Laffont-Tirole model under certain not very restrictive assumptions. We proceed to establish a simple rule for when to shut-down inefficient types. In an example with specific functional forms, we derive the optimal tax function both analytically and graphically. We show the effect on the optimal tax system of a change in a technological parameter.     

Scoring run-off paradoxes for variable electorates

   Summary. A no-show paradox occurs each time a single voter or a group of voters can manipulate the outcome by not participating to the election process. Among other voting procedures, the scoring run-off methods, which eliminate progressively the alternatives on the basis of scoring rules, suffer from this flaw. We here estimate how frequent this paradox is for three candidate elections under the classical Impartial Culture and Impartial Anonymous Culture assumptions, for different population sizes. The conditions under which this paradox occurs are also described, as well as the relationships with manipulations for a fixed number of voters. Received: October 21, 1999; revised version: January 12, 2000     

Private Value Allocations in Large Economies with Differential Information

We consider a Radner-type (e.g., Radner, 1968, Econometrica36, 31–58) pure exchange economy with differential information and a continuum of agents. We show that under appropriate assumptions the set of Aumann–Shapley private value allocations in such an economy coincides with the set of Radner competitive equilibrium allocations. Journal of Economic Literature Classification Numbers: C71, D51, D82.