Weakest-link public goods: Giving in-kind or transferring money

This paper extends the analysis of weakest-link public goods, whose level equals the smallest of the agents’ provision levels, by permitting an agent either to increase one's own provision or else augment both one's own provision and that of the other agent(s). Nash equilibria may be either symmetric with agents matching one another's provision or else asymmetric with an in-kind transfer by one agent to another. An equilibrium with cash transfers, but no in-kind transfers, may be Pareto superior to one with only in-kind transfers. If agents differ in their efficiency, then in-kind transfers by the low-cost agent may dominate a cash transfer. The possibility of Pareto-improving transfers is enhanced as the number of agents increases.     

On the Coalition-Proofness of the Pareto Frontier of the Set of Nash Equilibria

This article shows that the Pareto efficient frontier of the Nash equilibrium set of games with strategic substitutes is coalition-proof under the following conditions: (1) the game has three players, or, alternatively, a player's payoff depends on her own strategy and on the sum (but not on the composition) of other players' strategies; (2) an increase in a player's strategy either raises all other players' payoffs monotonically or reduces them monotonically; and (3) each player's payoff is strictly concave in her own strategy. Under these conditions, the Pareto dominance refinement is equivalent to the coalition-proof Nash equilibrium refinement.Journal of Economic LiteratureClassification Number: C72.     

Optimal incentive contracts with multiple agents

A setting in which a single principal contracts with two agents who possess perfect private information about their own productivity is considered. With correlated productivities, each agent's private information also provides a signal about the other agent's productivity. In contrast to the setting in which there is only one agent, it is shown that such private information may be of no value to the agents. It is only if the agents are risk-averse that their private information may allow them to command rents. Moreover, when the agents are constrained only to reveal their private information truthfully as a Nash equilibrium, the Pareto optimal incentive scheme may induce the agents to adopt strategies other than truth-telling. This leads to the consideration of truth-telling equilibria that are not Pareto dominated in the subgame played by the agents. Among all such equilibria, the one preferred by the principal restricts one agent to tell the truth as a dominant strategy and the other as a Nash response to truth.     

Pension,possible phaseout,and endogenous fertility in general equilibrium

The rich literature on Pay-As-You-Go (PAYG)-type pensions provides a notion that when pension return is dominated by the market return, generally it is impossible to phase pension out without hurting any generation. We show that PAYG pensions can indeed be phased out in a much richer framework where fertility is endogenous and general equilibrium effects are present. Interestingly, the factor that helps us to phase the pension out in a Pareto way is hidden in the structure of PAYG pension itself. Individualistic agents fail to recognize the benefits of their fertility decision on these programs and, therefore, end up in an allocation that is strictly dominated by the allocations that internalize this externality. Exploiting this positive externality, competitive economy can improve its allocations and can reach the planner's steady-state in finite time where each generation secures as much utility as in the competitive equilibrium. Clearly, it is possible to transition in a Pareto way to an economy either with no pension or with pensions whose return is not dominated by market return.     

Monitoring and Motivation in Principal-Agent Relationships: Some Issues in the Case of Local Authority Services

This paper examines a number of issues concerning the effects of monitoring on principals and agents involved in the provision of local authority services subject to competition. It examines, and then extends, existing theoretical work indicating the potential for sub-optimal outcomes which result from the principal introducing monitoring schemes which focus upon the measurable aspects of the agent's performance. The paper then departs from the received principal-agent paradigm in order to consider whether monitoring and competitive regimes more generally have negative effects on the welfare and performance of principals and agents in both theory and practice.     

Chores

We analyze situations where the provision of each of c public goods must be voluntarily assumed by exactly one of n private agents in the absence of transfer schemes or binding contracts. We model this problem as a complete information, potentially infinite horizon game where n agents simultaneously wage c wars of attrition. Providing a public good commits an agent not to take on the provision of another public good for a fixed period. We explore the strategic trade-offs that this commitment ability and the multiplicity of tasks provide. Subgame perfect equilibria (SPEs) are characterized completely for games with two agents and two public goods. For games with two identical agents and c > 1 identical public goods, we establish that an equilibrium that yields a surplus-maximizing outcome always exists and we provide sufficient conditions under which it is the unique equilibrium outcome. We show that under mild conditions, the surplus-maximizing SPE is the unique symmetric SPE. Journal of Economic Literature Classification Number: H41, C72, D13.     

Cooperative Outcomes through Noncooperative Games

This paper shows the equivalence between the stable solution set of any cooperative game in characteristic form (G1) and the subgame perfect Nash equilibria in pure strategies of a certain noncooperative game (G2). Players of G1 are named "agents." G2 is played by different players ("principals") who compete in wages to attract agents. The equivalence result holds when there are enough principals (if the game is superadditive, two principals suffice). Finally, another related cooperative game (G3) is constructed with both principals and agents as players. For G2 and G3 the same result is then proven, for any number of principals. Journal of Economic Literature Classification Numbers: C71 and C72.     

Existence and efficiency of equilibrium in infinite economies with finite aggregate wealth

Summary. We prove the existence and efficiency of equilibrium in economies with infinitely many consumers in which there are finitely many agents who own a positive portion of the aggregate endowment. We prove existence for commodity spaces which are employed in the general equilibrium asset pricing models and use incomplete and intransitive preferences. We discuss the importance of existence of finitely many agents who own a positive portion of the aggregate endowment in obtaining efficient equilibrium. For general equilibrium asset pricing applications we require forward properness only at individually rational Pareto optimal allocations. We provide an Arrow-Debreu model for these economies. We also give an application of our approach and results by employing Stochastic Differential Utility as the utility of each consumer in an infinite horizon model.     

On optimality in intergenerational risk sharing

Summary. This paper defines and studies optimality in a dynamic stochastic economy with finitely lived agents, and investigates the optimality properties of an equilibrium with or without sequentially complete markets. Various Pareto optimality concepts are considered, including interim and ex ante optimality. We show that, at an equilibrium with a productive asset (land) and sequentially complete markets, the intervention of a government may be justified, but only to improve risk sharing between generations. If markets are incomplete, constrained interim optimality is investigated in two-period lived OLG economies. We extend the optimality properties of an equilibrium with land and give conditions under which introducing a pay-as-you-go system at an equilibrium would not lead to any Pareto improvement. Received: October 5, 1998; revised version: April 3, 2001     

Equilibrium Selection inn-Person Coordination Games

This paper investigates several approaches to equilibrium selection and the relationships between them. The class of games we study aren-person generalized coordination games with multiple Pareto rankable strict Nash equilibria. The main result is that all selection criteria select the same outcome (namely the risk dominant equilibrium) in two-person games, and that most equivalences break for games with more than two players. All criteria select the Pareto efficient equilibrium in voting games, of which pure coordination games are special cases.Journal of Economic LiteratureClassification Numbers: C70, C72, D82.     

The Castle on the Hill

A simple example of a stochastic game with irreversibility is studied and it is shown that the folk theorem fails in a robust way. In this game of Castle on the Hill, for a broad range of discount factors, including those close to one, equilibrium is unique. Moreover, the equilibrium for large discount factors is Pareto dominated by the equilibrium for low discount factors. A unique cyclic equilibrium is also possible for intermediate ranges of discount factors. Journal of Economic Literature Classification Numbers: C7, C6.     

Bayesian–Walrasian equilibria: beyond the rational expectations equilibrium

In general rational expectations equilibrium (REE), as introduced in Radner (Econometrica 47:655–678, 1978) in an Arrow–Debreu–McKenzie setting with uncertainty, does not exist. Moreover, it fails to be fully Pareto optimal and incentive compatible and is also not implementable as a perfect Bayesian equilibrium of an extensive form game (Glycopantis et al. in Econ Theory 26:765–791, 2005). The lack of all the above properties is mainly due to the fact that the agents are supposed to predict the equilibrium market clearing price (as agent’s expected maximized utility is conditioned on the information that equilibrium prices reveal), which leads inevitably to the presumption that agents know all the primitives in the economy, i.e., random initial endowments, random utility functions and private information sets. To get around this problematic equilibrium notion, we introduce a new concept called Bayesian–Walrasian equilibrium (BWE) which has Bayesian features. In particular, agents try to predict the market-clearing prices using Bayesian updating and evaluate their consumption in terms of Bayesian price estimates, which are different for each individual. In this framework agents maximize expected utility conditioned on their own private information about the state of nature, subject to a Bayesian estimated budget constraint. Market clearing is not an intrinsic part of the definition of BWE. However, both in the case of perfect foresight and in the case of symmetric information BWE leads to a statewise market clearing; it then becomes an ex post Walrasian equilibrium allocation. This new BWE exists under standard assumptions, in contrast to the REE. In particular, we show that our new BWE exists in the well-known example in Kreps (J Econ Theory 14:32–43, 1977), where REE fails to exist. This work was done in the Spring of 2005, when EJB was a visiting professor at the University of Illinois.     

Contracts and externalities: How things fall apart

A single principal interacts with several agents, offering them contracts. The crucial assumption of this paper is that the outside-option payoffs of the agents depend positively on how many uncontracted or “free” agents there are. We study how such a principal, unwelcome though he may be, approaches the problem of contract provision to agents when coordination failure among the latter group is explicitly ruled out. Two variants are considered. When the principal cannot re-approach agents, there is a unique equilibrium, in which contract provision is split up into two phases. In phase 1, simultaneous offers at good (though varying) terms are made to a number of agents. In phase 2, offers must be made sequentially, and their values are “discontinuously” lower: they are close to the very lowest of all the outside options. When the principal can repeatedly approach the same agent, there is a multiplicity of equilibria. In some of these, the agents have the power to force delay. They can hold off the principal's overtures temporarily, but they must succumb in finite time. In both models, despite being able to coordinate their actions, agents cannot resist an “invasion” by the principal and hold to their best payoff. It is in this sense that “things [eventually] fall apart”.     

Bargaining Through Agents: An Experimental Study of Delegation and Commitment

While face-to-face bargaining has proven itself to be extremely efficient in the laboratory, it appears to break down often in the real world. This discrepancy, we assert, is explained by the fact that in the real world face-to-face bargaining is usually conducted not between principals but between the agents of principals. We find a substantial increase in inefficiency when bargaining is conducted through agents rather than through principals and offer an explanation for this rise in inefficiency. As such, this paper helps to shed light on the growing literature on delegation, commitment, and preference distortion games. Journal of Economic Literature Classification Numbers: C78, C92.     

The Important Thing Is Not (Always) Winning but Taking Part: Funding Public Goods with Contests

This paper considers a public good game with heterogeneous endowments and incomplete information affected by extreme free riding. I overcome this problem through the implementation of a deterministic contest in which several prizes may be awarded. I identify a monotone equilibrium, in which the contribution is strictly increasing in the endowment. I prove that it is optimal for the social planner to set the last prize equal to zero, but otherwise total expected contribution is invariant to the prize structure. Finally, I show that private provision via a contest Pareto‐dominates public provision and is higher than the total contribution raised through a lottery.     

Does and Should a Commodity Medium of Exchange Have Relatively Low Storage Costs?

I provide new existence and welfare results for a version of the Kiyotaki-Wright model. I construct an equilibrium where all agents use mixed strategies. Consequently, an object with a higher storage cost must have a higher acceptability. Therefore, the endogenous transaction pattern corresponds to the observation that money is dominated in rate of return by other assets (e.g., bonds), something that is a central issue in monetary economics. Furthermore, at least in a neighborhood of equal storage costs, the equilibrium that I construct Pareto dominates alternative equilibria in which better objects are widely accepted.     

Externality Policy Reform: A General Equilibrium Analysis

We characterize Pareto‐improving and equilibrium‐preserving policy reforms in a second‐best (Diamond/Mirrlees) world with a consumption externality. A counterintuitive finding is that, starting from an initial equilibrium with no direct quantity control on the externality, it is possible that all Pareto‐improving and equilibrium‐preserving directions of change require an increase in a negative externality. We provide intuition for these results by establishing a nexus between Guesnerie's approach to designing (tax) policy reforms and the standard Kuhn–Tucker technique for identifying the manifold of feasible Pareto‐optimal states, given the instruments available to the policy maker.     

Sunspots,indeterminacy and Pareto inefficiency in economies with incomplete markets

Summary. We consider two periods economies with both intrinsic and extrinsic uncertainty. Asset markets are incomplete in the certainty economy. If assets are nominal, there are enough commodities and the number of agents is greater than two and smaller than the total number of states of nature tomorrow (minus one), then a sunspot-invariant equilibrium is generically Pareto dominated by some sunspot equilibria. When assets are real, and there are enough commodities, if there are sunspot equilibria, there are sunspot equilibria Pareto dominating sunspot-invariant equilibria under the same restriction on the number of agents (and stronger restrictions on the number of commodities).Received: 20 October 2003, Revised: 1 April 2004, JEL Classification Numbers: D52.I wish to thank Paolo Siconolfi for helpful suggestions and comments. I aknowledge the financial support of M.I.U.R. and the kind hospitality of C.C.D.R. in Summer 2003.     

THE SECOND‐PRICE AUCTION SOLVES KING SOLOMON'S DILEMMA*

The planner wants to give k identical, indivisible objects to the top k valuation agents at zero costs. Each agent knows her own valuation of the object and whether it is among the top k. Modify the (k+ 1)st‐price sealed‐bid auction by introducing a small participation fee and the option not to participate in it. This simple mechanism implements the desired outcome in iteratively undominated strategies. Moreover, no pair of agents can profitably deviate from the equilibrium by coordinating their strategies or bribing each other.     

Cournot-Nash and Lindahl equilibria in pure public “bad” economies

Summary. Using a general equilibrium framework, this paper analyzes the equilibrium provision of a pure public bad commodity (for example pollution). Considering a finite economy with one desired private good and one pure public “bad” we explicitly introduce the concept of Lindahl equilibrium and the Lindahl prices into a pure public bad economy. Then, the Lindahl provision is analyzed and compared with the Cournot-Nash provision. The main results for economies with heterogeneous agents state that the asymptotic Lindahl allocation of the pure public bad is the null allocation. In contrast, the asymptotic Cournot-Nash provision of the public bad might approach infinity. Other results were obtained in concert with the broad analysis of the large finite economies with pure public bad commodities. Received: July 26, 2001; revised version: March 12, 2002 RID="*" ID="*" We are indebt to Nicholas Yannelis and anonymous referee for their valuable comments and suggestions. Correspondence to: B. Shitovitz