The best-shot all-pay (group) auction with complete information

We analyze an all-pay group contest in which individual members’ efforts are aggregated via the best-shot technology and the prize is a public good for the winning group. The interplay of within-group free-riding and across-group competition allows for a wide variety of equilibria, according to how well groups overcome internal free-riding. In contrast with the existing literature, we derive equilibria of a symmetric model in which multiple agents per group are active. Our findings differ qualitatively from those of the individualistic all-pay auction: rents are not necessarily dissipated in equilibrium, total expected efforts vary across equilibria, and participation is expected to be greater. Moreover, equilibria with greater symmetry of behavior within a group are shown to have more “wasted” effort but also greater payoffs as overall efforts are lower. In contrast to standard economic intuition, free-riding can be beneficial for players as it reduces competition among groups. Examples of asymmetric group contests are also studied.     

Private provision of a discrete public good: efficient equilibria in the private-information contribution game

We study the voluntary provision of a discrete public good via the contribution game. Players independently and simultaneously make nonrefundable contributions to fund a discrete public good, which is provided if and only if contributions cover the cost of production. We characterize nonconstant continuous symmetric equilibria, giving sufficient conditions for their existence. We show the common normalization by which players’ values are distributed over [0, 1] is not without loss of generality: if the distribution over this interval has continuous density f with f(0) >  0, then no (nonconstant) continuous symmetric equilibrium exists. We study in detail the case in which players’ private values are uniformly distributed, showing that, generically, when one continuous equilibrium exists, a continuum of continuous equilibria exists. For any given cost of the good, multiple continuous equilibria cannot be Pareto ranked. Nevertheless, not all continuous equilibria are interim incentive efficient. The set of interim incentive efficient equilibria is exactly determined. The authors thank Manfred Dix, George Mailath, Andrew Postlewaite, and an anonymous referee for their comments.     

Behavioral explanations of efficient public good allocations

Theorists have studied decentralized allocation mechanisms by characterizing the Cournot-Nash equilibria of the mechanism. However, when a mechanism is operationalized by an iterative decision process, and agents derive utility only from the final outcome, Cournot behavior may not be an appropriate solution concept. We suggest two alternative behavioral models, reservation behavior and satisficing behavior, which recognize the impact of the iterative process upon incentives, yet maintain some of the critical simplifications that have made Cournot behavior an attractive model.We report on nine public good experiments with a Groves-Ledyard general equilibrium mechanism. Overall, the experiments attain highly efficient allocations, despite widespread violations of Cournot behavior. We suggest the explanation that most subjects initially followed reservation behavior, and then came to adopt satisficing behavior.     

Adoption externalities as public goods

A public good problem arises naturally in situations characterized by positive externalities or negative externalities. For positive externalities, agents furnish a public good by taking an action. Similarly, for negative externalities, agents furnish a public good by not taking an action. We examine these externalities in a binary choice problem, i.e. adoption externalities. In each case, there is a potential role for government intervention, even when equilibrium transfers are not allowed, since one equilibrium Pareto dominates all others. We analyze the positive and normative features of equilibria in these models, and we explore the possibility of useful government intervention.     

Tiebout equilibria in local public good economies with spillovers

This paper analyzes the effects of spillovers on the equilibrium population distribution across jurisdictions in a local public good economy with free mobility. Spillovers are parametrized by a matrix [α_ij] where α_ij ∈ [0, 1]. When spillovers are symmetric and close to 0 or 1 (pure local public goods and pure public goods), all equilibrium jurisdiction structures are symmetric. However, any population distribution can be sustained in equilibrium for some value of the spillover parameter α. In the class of utility functions with additive externalities, we identify the unique family of utility functions for which equilibria are symmetric except for an isolated value of α. This is a class of utility functions which are linear in the public good and a power function of the private good, u(c, γ) = − A(1 − c)^β + γ. With this specification of utility, we show that an increase in α results in a more fragmented equilibrium population distribution, and that when spillovers are asymmetric and large, a jurisdiction which is more centrally located (i.e. benefits more from the public goods provided in other jurisdictions) has a larger population in equilibrium.     

Coordination failure in repeated games with private monitoring

Players coordinate continuation play in repeated games with public monitoring. We investigate the robustness of such equilibrium behavior with respect to ex-ante small private-monitoring perturbations. We show that with full support of public signals, no perfect public equilibrium is robust if it induces a “regular” 2×2$2\times 2$ coordination game in the continuation play. This regularity condition is violated in all belief-free equilibria. Indeed, with an individual full rank condition, every interior belief-free equilibrium is robust. We also analyze block belief-free equilibria and point out that the notion of robustness is sensitive to whether we allow for uninterpretable signals.     

Parametric persistence of multiple equilibria in an economy directly calibrated to 5 equilibria

In existing literature, there are few concrete examples of multiple equilibria and the only ones known to us have 3 equilibria, but multiplicity remains a major concern for applied models used in policy work. Here, we report numerical examples for a 3 individual 2 good CES/LES pure exchange economy directly calibrated to 5 equilibria. We are able to use analytical methods of the model to show that for certain parameterizations there are no more than 5 equilibria (given the parameter values). We are also able to explore the size of the regions of the parameter space for which 5 equilibria persist, and show these ranges to be very small. Other features of the equilibrium manifolds are explored. Findings are only suggestive and indicative for the special cases we consider rather than definitive, but informative relative to existing work.     

Group size and the private supply of a best-shot public good

This paper examines the relationship between group size and the likelihood that a best-shot public good is voluntarily provided. Holding fixed each member's individual probability of supplying the public good, the likelihood of supply increases as the group grows. This is the size effect. However, as group size increases, the probability that each individual member supplies decreases. This is the strategic effect. The net effect of group size on the likelihood is thus ambiguous. As group size increases without bounds, the two effects are offset—the likelihood approaches a finite limit.     

A three-player dynamic majoritarian bargaining game

We analyze an infinitely repeated divide-the-dollar bargaining game with an endogenous reversion point. In each period a new dollar is divided among three legislators according to the proposal of a randomly recognized member—if a majority prefer so—or according to previous period's allocation otherwise. Although current existence theorems for Markovian equilibria do not apply for this dynamic game, we fully characterize a Markov equilibrium. The equilibrium is such that irrespective of the discount factor or the initial division of the dollar, the proposer eventually extracts the whole dollar in all periods. We also show that proposal strategies are weakly continuous in the status quo that equilibrium expected utility is not quasi-concave, and the correspondence of voters’ acceptance set (the set of allocations weakly preferred over the status quo) fails lower hemicontinuity.     

A graphic representation of the Nash and Lindahl equilibria in an economy with a public good

In an economy with a public good the noncooperative Nash equilibrium and the cooperative Lindahl equilibrium are represented graphically. The Nash equilibrium is shown to be non-optimal, while the Lindahl equilibrium is shown to be optimal. Simple stability analyses are undertaken. Finally, the two equilibria are compared. It appears that more public good will be allocated in the Lindahl than in the Nash equilibrium, and that in a sufficiently large economy a transition from a Nash to a Lindahl equilibrium will be advantageous for everyone.     

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.     

Volunteering a public service: an experimental investigation

In some public goods environments it may be advantageous for heterogeneous groups to be coordinated by a single individual. This “volunteer” will bear private costs for acting as the leader while enabling each member of the group to achieve maximum potential gains. This environment is modeled as a War of Attrition game in which everyone can wait for someone else to volunteer. Since these games generally have multiple Nash equilibria but a unique subgame-perfect equilibrium, we tested experimentally the predictive power of the subgame-perfection criterion. Our data contradict that subjects saw the subgame-perfect strategy combination as the obvious way to play the game. An alternative behavioral hypothesis—that subjects were unable to predict accurately how their opponents would play and tried to maximize their expected payoff—is proposed. This hypothesis fits the observed data generally well.     

Beliefs and Public Good Provision with Anonymous Contributors

We analyze a static game of public good contributions where finitely many anonymous players have heterogeneous preferences about the public good and heterogeneous beliefs about the distribution of preferences. In the unique symmetric equilibrium, the only individuals who make positive contributions are those who most value the public good and who are also the most pessimistic; that is, according to their beliefs, the proportion of players who most like the public good is smaller than it would be according to any other possible belief. We predict whether the aggregate contribution is larger or smaller than it would be in an analogous game with complete information and heterogeneous preferences, by comparing the beliefs of contributors with the true distribution of preferences. A trade‐off between preferences and beliefs arises if there is no individual who simultaneously has the highest preference type and the most pessimistic belief. In this case, there is a symmetric equilibrium, and multiple symmetric equilibria occur only if there are more than two preference types.     

Free riders and the optimal prize in public‐good funding lotteries

We prove the existence and uniqueness of an equilibrium in a game where players, whose preferences exhibit constant absolute risk aversion or constant relative risk aversion, contribute to a public good via lottery‐ticket purchases. Contrasting models with risk neutrality, we show that an equilibrium with a strictly positive amount of the public good may not exist without a sufficient number of participants who are not too risk‐averse. We show that players who are more risk‐averse purchase fewer lottery tickets and are more likely to free ride in equilibrium. In fact, it is possible for free riders to place a larger value on the public good than do those who contribute. In a symmetric equilibrium, we show that an upper bound exists for the amount of the public good, even though there are infinitely many participants. Furthermore, we derive a lottery prize that maximizes the amount of the public good in a symmetric equilibrium and find that such a prize always results in an overprovision of the public good.     

Democratic public good provision

This paper analyzes an overlapping generation model of redistribution and public good provision under repeated voting. Expenditures are financed through age-dependent taxation that distorts human capital investment. Taxes redistribute income both across skill groups and across generations. We focus on politico-economic Markov equilibria and contrast these with the Ramsey allocation under commitment. The model features indeterminate equilibria, with a key role of forward-looking strategic voting. Due to the lack of commitment to future policies, the tax burden may be on the wrong side of the dynamic Laffer curve. Moreover, restrictions on government policies can in some cases be welfare improving.     

Seigniorage and public good in an OLG model with cash-in-advance constraints

This paper is a contribution to the theory of the optimal monetary policy in overlapping generations models with a cash-in-advance constraint applying on old age consumption purchases. We are particularly interested in the study of seigniorage when the latter is used to finance public goods valued by consumers. Assuming that a public good enters the utility function and the existence of cash-in-advance constraints, we find a Laffer curve of seigniorage at steady-state. We also analyze the dynamic optimal monetary policy when the government maximizes an intertemporal social welfare function and can only resort to seigniorage to finance the purchases of the public good. We show that the optimal rate of money growth may be strictly higher than the one which maximizes steady-state seigniorage: the optimal amount of seigniorage may lie on the decreasing part of the Laffer curve of seigniorage. We finally suppose that the government can use lump-sum taxes in addition to seigniorage. Then, the Friedman rule prevails and public expenditures are only financed through lump-sum taxes.     

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.     

Dynamic Voluntary Provision of Public Goods: A Generalization

In this note we examine if the proposition offered by Fershtman and Nitzan (1991) and Wirl (1996) in the context of a dynamic voluntary provision model with a linear production function can be generalized to a more general CES formulation. By comparing the steady-state stocks of a public good in open-loop and feedback Nash equilibria with that under the cooperative solution, we demonstrate that their ranking among the steady-state stocks is indeed preserved under the CES framework.     

A Fiscal Stimulus and Jobless Recovery

We analyze the effects of a government‐spending expansion in a dynamic stochastic general equilibrium model with Mortensen–Pissarides labor‐market frictions, deep habits in private and public consumption, investment adjustment costs, a constant elasticity of substitution (CES) production function, and adjustments in employment at both intensive and extensive margins. The combination of deep habits and CES technology is crucial. The presence of deep habits magnifies the responses of macroeconomic variables to a fiscal stimulus, while an elasticity of substitution between capital and labor in the range of available estimates allows the model to produce a scenario compatible with the observed jobless recovery.