On Renegotiation-Proof Equilibria in Finitely Repeated Games

This paper studies renegotiation-proof equilibria of Beno?̂t and Krishna (1993) in finitely repeated games with more than two players. We provide a simple characterization of the set of average payoffs from renegotiation-proof equilibria: the limiting set of average equilibrium payoffs is either efficient or dimensionally small as the horizon of the repeated game goes to infinity. Two sufficient conditions for the former to occur are provided. An example shows that those conditions cannot be weakened.Journal of Economic LiteratureClassification Numbers: C72, C73.     

Strategic interaction between futures and spot markets

We study an oligopolistic industry where firms are able to sell in a futures market at infinitely many moments prior to the spot market. A kind of Folk-theorem is established: any outcome between perfect competition and Cournot can be sustained in equilibrium. We then find that the Cournot outcome can be sustained by a renegotiation-proof equilibrium. However, this is not true for the competitive outcome. Furthermore, only the monopolistic outcome is renegotiation-proof if firms can buy and sell in the futures market. These results suggest, contrary to existing literature, that the introduction of futures markets may have an anti-competitive effect.     

Renegotiation-Proof Climate Agreements with Full Participation: Conditions for Pareto-Efficiency

Recent contributions show that climate agreements with broad participation can be implemented as weakly renegotiation-proof equilibria in simple models of greenhouse gas abatement where each country has a binary choice between cooperating (i.e., abate emissions) or defecting (no abatement). Here we show that this result carries over to a model where countries have a continuum of emission choices. Indeed, a Pareto-efficient climate agreement can always be implemented as a weakly renegotiation-proof equilibrium, for a sufficiently high discount factor. This means that one need not trade-off a “narrow but deep” treaty with a “broad but shallow” treaty.     

An international agreement with full participation to tackle the stock of greenhouse gases

Greenhouse gas emissions build up an atmospheric stock which depreciates over time. We identify weakly renegotiation-proof equilibria with full participation in a game of international emission reduction. Treaties are easier to reach for long-lived than for short-lived gases.     

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.     

Efficiency and equilibrium when preferences are time-inconsistent

We consider an exchange economy with time-inconsistent consumers whose preferences are additively separable. If consumers have identical discount factors, then allocations that are Pareto efficient at the initial date are also renegotiation-proof. In an economy with a sequence of markets, competitive equilibria are Pareto efficient in this sense, and for generic endowments, only if preferences are locally homothetic.     

The Three-Legged Race: Cooperating to Compete

In the prisoners' dilemma contest several couples play the finitely repeated prisoners' dilemma. Each time a couple cooperates, it scores a point, and a small prize is awarded to the winners. An analogue of the “folk” theorem for repeated games is obtained with subgame perfect equilibrium (SPE). Next, allowing renegotiations within each team, we study a solution concept based on renegotiation-proof equilibrium (RPE). If couples are informed about the score, no equilibrium exists. If they are not, cooperation is the unique equilibrium outcome.Journal of Economic LiteratureClassification Number: C72.     

Optimality and renegotiation in dynamic contracting

We characterize the optimal renegotiation-proof contract in a dynamic principal–agent model in which the type of the agent may change stochastically over time. We show that, under general conditions, the optimal contract with commitment is renegotiation proof even when type realizations are serially correlated. When the renegotiation-proofness constraint is binding, it is always optimal to partially screen the types by offering a menu of choices to the agent; and the distortion induced by the renegotiation-proofness constraint is non-decreasing in the persistence of types.     

Bargaining and the observability of contractual commitments via third parties

This paper analyzes a two-stage model of bilateral bargaining where one of the agents has the option to delegate. A first approach is to assume that the contract between the agent and his representative is perfectly observable and can be renegotiated. Commitment effects arise although renegotiation is possible. Then, perfect observability of the contract is weakened to observe it with certain probability. Commitment effects as pure-strategy equilibria exist if this probability is sufficiently close to 1, in contrast to Bagwell's [1995] findings that imperfect observability undermines commitment. Considering the realistic case of the actual agreement between two parties being private information, the commitment value as equilibrium outcome disappears since having closed a renegotiation-proof contract offers costless self-insurance against strategic misunderstandings. The author is grateful for helpful comments from Vasco Santos, participants at the International Atlantic Economic Conference, October 7–10, 1999, Montreal, Canada, an anonymous referee, and David M. Aadland.     

Renegotiation-Proof Tariff Agreements

The institutional features of the World Trade Organization motivate the use of renegotiation-proofness as an equilibrium concept in repeated tariff-setting games. This paper shows the existence of a renegotiation-proof equilibrium that reduces tariffs below the noncooperative level. It is found that the one-shot Nash equilibrium cannot be used as a punishment to support such treaties. Punishments are either Pareto-efficient or one country barely accepts them. If the punishing country is hurt by the punishment then punishments will be as short as possible. If the agreement tariff levels are not Pareto-efficient then one country barely goes along with the agreement.     

Downstream mode of competition with upstream market power

In a two-tier oligopoly, where the downstream firms are locked in pair-wise exclusive relationships with their upstream input suppliers, the equilibrium mode of competition in the downstream market is endogenously determined as a renegotiation-proof contract signed between each downstream firm and its exclusive upstream input supplier. We find that the upstream–downstream exclusive relationships credibly sustain the Cournot (Bertrand) mode of competition in the downstream market, when the goods are substitutes (complements). In contrast to previous studies, this result holds irrespectively of the degree of product differentiation and the distribution of bargaining power between the upstream and the downstream firm, over the pair-specific input price.     

Finite Horizon Bargaining and the Consistent Field

We explore the relationships between noncooperative bargaining games and the consistent value for nontransferable utility (NTU) cooperative games. A dynamic approach to the consistent value is introduced: the consistent vector field. The main contribution is to establish that theconsistent fieldis intimately related to the concept ofsubgame perfectionfor finite horizon noncooperative bargaining games, as the horizon goes to infinity and the cost of delay goes to zero. We then show that in the general NTU case—unlike the transferable utility and pure bargaining cases—the finite horizon subgame perfect equilibria need not approach the consistent value.Journal of Economic LiteratureClassification Numbers: C71, C72.     

How long to eat a cake of unknown size? Optimal time horizon under uncertainty

This paper is concerned with the determination of the optimal time horizon for the cake–eating problem under uncertainty. It is shown that if the uncertain exhaustible resource stock is a discrete random variable admitting at most a finite number of values, the optimal planning horizon is infinite (finite) according as the marginal utility of extraction–cum–consumption is infinite (a finite positive value) as the latter approaches zero, thereby extending the scope of the similar result under perfect certainty. Other results show that uncertainty will generally lengthen the planning horizon, implying a more conservative extraction policy under uncertainty, and that the extraction policy aimed at extracting an amount equal to the expected value of the uncertain resource stock takes longer than the expected value of the optimal planning horizon. JEL Classification: D81 and Q31 Combien de temps pour manger un gâteau de taille inconnue? L’horizon temporel optimal en régime d’incertitude. Ce mémoire s’attaque à la détermination de l’horizon temporel optimal dans le cas du problème du gâteau–à–manger en régime d’incertitude. On montre que si le stock incertain de la ressource épuisable est une variable aléatoire discontinue qui ne peut prendre qu’un nombre fini de valeurs, l’horizon temporel est infini (fini) selon que l’utilité marginale de l’extraction–cum–consommation est infinie (prend une value finie positive) quand celle–ci approche zéro, et ce faisant élargit la portée d’un résultat similaire obtenu en régime de certitude parfaite. D’autres résultats montrent que l’incertitude accroît généralement l’horizon temporel, ce qui suggère qu’une politique d’extraction plus conservatrice va prévaloir en régime d’incertitude, et que la politique d’extraction visant à extraire une quantitéégale à la valeur anticipée d’un stock de ressource incertain prend plus de temps que la valeur anticipée de l’horizon temporel optimal.     

Renegotiation-Proof Dynamic Contracts with Private Information

This paper studies the issue of renegotiation in a model of dynamic moral hazard. I introduce the notion of a renegotiation-proof dynamic contract. I show that the constraint of renegotiation-proofness can have the effect of setting a higher lower bound to the set of attainable expected utilities of the agent. This result extends the notion of “credit rationing” from the static models of optimal contracting to a dynamic setting and is useful for thinking about competition for long-term contracts. This result also has implications for the long-run behavior of the expected utility of the agent under dynamic contracting. Journal of Economic Literature Classification Numbers: 026, 315.     

Renegotiation-proof relational contracts

We study infinitely repeated two-player games with perfect monitoring and assume that each period consists of two stages: one in which the players simultaneously choose an action and one in which they can transfer money to each other. In the first part of the paper, we derive simple conditions that allow a constructive characterization of all Pareto-optimal subgame perfect payoffs for all discount factors. In the second part, we examine different concepts of renegotiation-proofness and extend the characterization to renegotiation-proof payoffs.     

Double Bubbles in Assets Markets With Multiple Generations

We construct an asset market in a finite horizon overlapping-generations environment. Subjects are tested for comprehension of their fundamental value exchange environment and then reminded during each of 25 periods of the environment's declining new value. We observe price bubbles forming when new generations enter the market with additional liquidity and bursting as old generations exit the market and withdrawing cash. The entry and exit of traders in the market creates an M shaped double bubble price path over the life of the traded asset. This finding is significant in documenting that bubbles can reoccur within one extended trading horizon and, consistent with previous cross-subject comparisons, shows how fluctuations in market liquidity influence price paths. We also find that trading experience leads to price expectations that incorporate fundamental value.     

The permanent income hypothesis in an underdeveloped economy

After a concise but critical survey of several tests of the permanent income hypothesis (PIH), the authors advance their own test for India using annual data from 1919–1960. It employs Friedman's technique for calculating the permanent value of a variable. Two different specifications of the model are tested, using different values of the consumer's ‘horizon.’ In almost all cases it is found that the marginal propensity to consume out of transitory income is very similar to the marginal propensity to consume out of permanent income. The authors conclude that even a looser variant of the PIH is not valid for India. However, no valid generalization with respect to the appropriate planning horizon can be made, for the PIH was almost equally invalid with a horizon of one, two and two-and-a-half years. The authors briefly discuss the policy implications of their results for the savings efforts in underdeveloped countries.     

Risk Aversion and the Investment Horizon: A New Perspective on the Time Diversification Debate

Investment managers generally subscribe to the principle of time diversification. This implies that a larger portion of the portfolio should be devoted to risky assets as the investment horizon increases. In contrast, academics have shown that for investors with utility functions characterized by constant relative risk aversion, the optimal asset-allocation strategy is independent of the investment horizon. The relative risk aversion in these studies is assumed to be constant both with respect to wealth as well as investment horizon. We suggest a utility function that explicitly captures the notion that individuals are more risk tolerant when the investment horizon is long, thereby validating the intuitively appealing time diversification argument.     

On the coexistence of money and higher-return assets and its social role

This paper adopts mechanism design to investigate the coexistence of fiat money and higher-return assets. We consider an economy with pairwise meetings where fiat money and risk-free capital compete as means of payment, as in [28]. The trading mechanism in pairwise meetings is chosen among all individually rational, renegotiation-proof mechanisms to maximize society?s welfare. We show that in any stationary monetary equilibrium capital commands a higher rate of return than fiat money.     

A note on an intertemporal cost function for a class of dynamic problems

Some properties of an intertemporal cost function for isoperimetric problems are analyzed. It is demonstrated that the cost function will be strictly decreasing in the length of the horizon T, and under certain conditions, strictly convex in T.