The benefits of voluntary leadership in experimental public goods games

We study the effects of voluntary leadership in experimental public goods games when each group member can volunteer to contribute before the other members. We find that voluntary leadership increases contributions significantly, compared to a treatment where leadership is enforced exogenously.     

Public goods in directed networks

We study the provision of a public good in a social network where links are directed, i.e., the information flows one way. Our results relate, through stochastic dominance, the equilibrium outcome of such a process with the out-degree distribution of the network.     

Incentive effects: The case of belief elicitation from individuals in groups

Non-incentivized belief elicitation has a negative effect on the belief accuracy of experienced observers predicting choices in 2 × 2 matrix games. This negative impact extends to the accuracy of group beliefs and revised beliefs after forecasters know each other's initial beliefs.     

An experimental investigation of overdissipation in the all pay auction

Pervasive overbidding represents a well-documented feature of all-pay auctions. Aggregate bids exceed Nash predictions in laboratory experiments, and individuals often submit bids that guarantee negative profits. This paper examines three factors that may reduce pervasive overbidding: (a) repetition (experience), (b) reputation (strangers vs. partners), and (c) active participation. Reputation and repetition reduce aggregate overdissipation, but they eliminate it only in conjunction with active participation.     

Optimal ownership of public goods reconsidered

Consider a non-governmental organization (NGO) that can invest in a public good. Should the government or the NGO own the public project? In an incomplete contracting framework with split-the-difference bargaining, Besley and Ghatak (2001) argue that the party who values the public good most should be the owner. We demonstrate the robustness of their insight when the split-the-difference rule is replaced by the deal-me-out solution. Our finding is in contrast to the private good results of Chiu (1998) and De Meza and Lockwood (1998), who show that the optimal ownership structure crucially depends on whether the split-the-difference rule or the deal-me-out solution is used.     

Core equivalence with congested public goods

Summary This paper examines a model of an infinite production economy with a finite number of types of agents andsemi- public goods, which are subjected to crowding and exclusion. The utility of an agent depends not only on the vector of public commodities produced by the coalition to which she belongs, but also on the mass of agents of her type who are the members of this coalition. The main purpose of the paper is to derive necessary and sufficient conditions on the local degrees of congestion which would guarantee the equivalence between the core and the set of equal treatment Lindahl equilibria. We prove that this equivalence holdsif and only if there are constant returns to group size for each type of agents. It implies that linearity of each agent's congestion function with respect to the mass of the agents of her own type is necessary for the core equivalence to hold.The final version of this paper was written while Shlomo Weber was visiting the Technical University of Dresden as the Fellow of the Alexander von Humboldt Foundation, whose support is gratefully acknowledged. The authors are grateful to Peter Meyer, Nicholas Yannelis and the anonymous referees for useful remarks and suggestions.     

Public goods in networks

This paper considers incentives to provide goods that are non-excludable along social or geographic links. We find, first, that networks can lead to specialization in public good provision. In every social network there is an equilibrium where some individuals contribute and others free ride. In many networks, this extreme is the only outcome. Second, specialization can benefit society as a whole. This outcome arises when contributors are linked, collectively, to many agents. Finally, a new link increases access to public goods, but reduces individual incentives to contribute. Hence, overall welfare can be higher when there are holes in a network.     

Learning in games with strategic complementarities revisited

Fictitious play is a classical learning process for games, and games with strategic complementarities are an important class including many economic applications. Knowledge about convergence properties of fictitious play in this class of games is scarce, however. Beyond games with a unique equilibrium, global convergence has only been claimed for games with diminishing returns [V. Krishna, Learning in games with strategic complementarities, HBS Working Paper 92-073, Harvard University, 1992]. This result remained unpublished, and it relies on a specific tie-breaking rule. Here we prove an extension of it by showing that the ordinal version of strategic complementarities suffices. The proof does not rely on tie-breaking rules and provides some intuition for the result.     

Weak links, good shots and other public good games: Building on BBV

We suggest an alternative way of analyzing the canonical Bergstrom-Blume-Varian model of non-cooperative voluntary contributions to a public good that avoids the proliferation of dimensions as the number of players is increased. We exploit this approach to analyze models in which the aggregate level of public good is determined as a more general social composition function of individual gifts — specifically, as a CES form — rather than as an unweighted sum. We also analyze Hirshleifer's weakest-link and best-shot models. In each case, we characterize the set of equilibria, in some cases establishing existence of a unique equilibrium as well as briefly pointing out some interesting comparative static properties. We also study the weakest-link and best-shot limits of the CES composition function and show how the former can be used for equilibrium selection and the latter to establish that equilibria of some better-shot games are identical to those of the much simpler best-shot game.     

Testing the TASP: An experimental investigation of learning in games with unstable equilibria

We report experiments studying mixed strategy Nash equilibria that are theoretically stable or unstable under learning. The Time Average Shapley Polygon (TASP) predicts behavior in the unstable case. We study two versions of Rock-Paper-Scissors that include a fourth strategy, Dumb. The unique Nash equilibrium is identical in the two games, but the predicted frequency of Dumb is much higher in the game where the NE is stable. Consistent with TASP, the observed frequency of Dumb is lower and play is further from Nash in the high payoff unstable treatment. However, Dumb is played too frequently in all treatments.     

Optimal mechanism design with resale via bargaining

In this paper, we examine the optimal mechanism design of selling an indivisible object to one regular buyer and one publicly known buyer, where inter-buyer resale cannot be prohibited. The resale market is modeled as a stochastic ultimatum bargaining game between the two buyers. We fully characterize an optimal mechanism under general conditions. Surprisingly, in this optimal mechanism, the seller never allocates the object to the regular buyer regardless of his bargaining power in the resale market. The seller sells only to the publicly known buyer, and reveals no additional information to the resale market. The possibility of resale causes the seller to sometimes hold back the object, which under our setup is never optimal if resale is prohibited. We find that the seller?s revenue is increasing in the publicly known buyer?s bargaining power in the resale market. When the publicly known buyer has full bargaining power, Myerson?s optimal revenue is achieved; when the publicly known buyer has no bargaining power, a conditionally efficient mechanism prevails.     

Location and ownership of public goods

We introduce location choice for the public good in the property rights framework. We find that it can be optimal to separate location from ownership.     

Between-game rule learning in dissimilar symmetric normal-form games

Rule learning posits that decision makers, rather than choosing over actions, choose over behavioral rules with different levels of sophistication. Rules are reinforced over time based on their historically observed payoffs in a given game. Past works on rule learning have shown that when playing a single game over a number of rounds, players can learn to form sophisticated beliefs about others. Here we are interested in learning that occurs between games where the set of actions is not directly comparable from one game to the next. We study a sequence of ten thrice-played dissimilar games. Using experimental data, we find that our rule learning model captures the ability of players to learn to reason across games. However, this learning appears different from within-game rule learning as previously documented. The main adjustment in sophistication occurs by switching from non-belief-based strategies to belief-based strategies. The sophistication of the beliefs themselves increases only slightly over time.     

Learning in games with unstable equilibria

We propose a new concept for the analysis of games, the TASP, which gives a precise prediction about non-equilibrium play in games whose Nash equilibria are mixed and are unstable under fictitious play-like learning. We show that, when players learn using weighted stochastic fictitious play and so place greater weight on recent experience, the time average of play often converges in these “unstable” games, even while mixed strategies and beliefs continue to cycle. This time average, the TASP, is related to the cycle identified by Shapley [L.S. Shapley, Some topics in two person games, in: M. Dresher, et al. (Eds.), Advances in Game Theory, Princeton University Press, Princeton, 1964]. The TASP can be close to or quite distinct from Nash equilibrium.     

Local public goods, inter-regional transfers and private information

Suppose that the centre wishes to make transfers between member states of a federation to reduce inequality. However, it lacks precise information concerning the cost differences that are responsible for the initial income inequality. We examine the implications of asymmetric information for the design of the transfer scheme. We show that if member states’ inherent cost levels as local public good providers take discrete values, the first best, or ‘complete information’, transfer scheme may or may not violate incentive compatibility. If inherent cost is a continuous random variable, such a scheme certainly violates incentive compatibility. We also explore the possibility of binding participation constraints. In our model, a binding incentive compatibility constraint leads to a reduction in effort devoted to cost reduction, and a binding participation constraint will also lead to a violation of Samuelson's optimality condition for public good provision.     

A fundraising mechanism inspired by historical tontines: Theory and experimental evidence

The tontine, which is an interesting mixture of group annuity, group life insurance, and lottery, has a peculiar place in economic history. In the seventeenth and eighteenth centuries it played a major role in raising funds to finance public goods in Europe, but today it is rarely encountered outside of a dusty footnote in actuarial course notes or as a means to thicken the plot of a murder mystery. This study provides a formal model of individual contribution decisions under a modern variant of the historical tontine mechanism that is easily implemented by private charities. Our model incorporates desirable properties of the historical tontine to develop a mechanism to fund the private provision of a public good. The tontine-like mechanism we derive is predicted to outperform not only the voluntary contribution mechanism but also another widely used mechanism: charitable lotteries. Our experimental test of the instrument provides some evidence of the beneficial effects associated with implementing tontine-like schemes. We find that the mechanism has particular power in cases where agents are risk-averse or in situations where substantial asymmetries characterize individual preferences for the public good.     

Not just babble: Opening the black box of communication in a voluntary contribution experiment

We let subjects in a voluntary contribution experiment make non-binding numerical announcements about their “possible” contributions and, in some treatments, send written promises to contribute specific amounts. We find that announcements were responded to both by others’ announcements and by real play, for example announcements led to costly punishment when found to be misleading. We also find that adding pre-play announcements to treatments with punishment can increase efficiency by letting cost-free warnings substitute for costly punishment. The threat of punishing false announcements and promises helps reduce false signals, but only when promise statements can be sent is the effect sufficient for achieving greater efficiency.     

Serial cost sharing of excludable public goods: general cost functions

Summary. A group of individuals meet to share the cost and determine output allocations of a partial-excludable public good. We demonstrate that, for general cost functions and preferences that satisfy the Spence-Mirlees sorting condition, the serial cost-sharing formula (Moulin, 1994) has remarkable incentive properties. First, a direct economic mechanism that uses the serial formula is coalition strategy-proof, envy-free and satisfies the stand-alone property. Second, the serial mechanism involves partial exclusion, which is important for the reduction of the free-rider problem. Received: June 10, 1996; revised version; February 11, 1997     

Informational control and organizational design

This paper focuses on issues of allocating authority between an uninformed principal and an informed expert. We analyze the benefits of informational control—restricting the precision of the expert's information (without learning its content). In this case, the result of Dessein (2002) [8] that delegating decisions to a perfectly informed expert is better than communication when preferences between the expert and the principal are not too far apart is reversed. We demonstrate that these organizational forms—informational control and delegation—can be either complements or substitutes, depending on the principal's ability to affect the expert's discretion about the set of allowed policies.