On the performance of rule-based contribution schemes under endowment heterogeneity

We experimentally test different rule-based contribution mechanisms in a repeated 4-player public goods game with endowment heterogeneity and compare them to a VCM, distinguishing between a random and an effort-based allocation of endowments. We find that endowment heterogeneities limit the efficiency gains from these rule-based contribution schemes under random allocation. Under effort-based allocations, substantial efficiency gains relative to a VCM occur. These are largely driven by significant reductions of contributions in VCM, while the rule-based mechanisms generate stable efficiency levels, even though falling short in realizing the maximal efficiency gains. Our results indicate that the procedure of endowment allocation impacts the perception of what constitutes a fair burden sharing.     

A Case for Bundling Public Goods Contributions

We extend the model of voluntary contributions to multiple public goods by allowing for bundling of the public goods. Specifically, we study the case where agents contribute into a common pool which is then allocated toward the financing of two pure public goods. We explore the welfare implications of allowing for such bundling vis‐à‐vis a separate contributions scheme. We show that for high income inequality or for identical preferences among agents bundling leads to higher joint welfare. Interestingly, a welfare improvement can in some cases occur despite a decrease in total contributions. On the contrary, when agents are heterogenous, for low income inequality bundling can lead to lower total contributions and may decrease welfare compared to a separate contribution scheme. Our findings have implications for the design of charitable institutions and international aid agencies.     

Dissertation abstract: A status theory of collective action

The “collective action problem” describes situations where each person in a group can individually profit more by withholding contributions to group goals. However, if all act in their material self-interest no public good is produced and all are worse off. I present a new solution to the collective action problem based on status. I argue that contributions to collective action increase an individual’s status in the group because contributions create perceptions of high group motivation, defined as the relative value an individual places on group versus individual welfare. Individuals are predicted to receive a variety of social and material benefits for their contributions to the group. These rewards can help explain why individuals contribute to collective action. Four laboratory studies tested the theory. In Study 1, following interaction in a 6-person public goods game, participants reported viewing higher contributors as more group motivated and higher status. Higher contributors also wielded more interpersonal influence in task interactions with participants. Participants also cooperated with higher contributors more, and allocated greater altruism to them in a Dictator game. Study 2 addressed an exchange-theoretic alternative explanation for the findings of Study 1, showing that observers of collective action who did not benefit from higher contributors’ contributions to the public good, nonetheless rated them as higher status, cooperated with them more, and gave them greater altruistic gifts. These results show that collective action contributors can earn social and material benefits even outside the group. Study 3 more directly tested the mediating role of group motivation. Contributors who sacrificed a greater proportion of resources for the collective action were rated as more group motivated and higher status than a moderate proportional contributor, even though the amounts they contributed were the same. These findings support the theory, and underscore the significance of self-sacrifice in the acquisition of status in collective action. Study 4 investigated the effects of status rewards on contributors’ behavior towards and perceptions of the group. Participants who received positive status feedback for their contributions subsequently contributed more than those who did not. Rewarded participants also identified more with the group and saw it as having greater solidarity and cohesion. I conclude by discussing theoretical implications and future research. JEL Classification C71     

Voluntary Contributions to Multiple Public Projects

The problem of financing a set of discrete public goods (facilities, projects) by private contributions is studied. The corresponding cooperative game, the realization game , is shown to be convex. For the noncooperative setting we study a realization scheme that induces a strategic game. This contribution game is shown to be a generalized ordinal potential game ; a best–response in the contribution game implies a best response in a coordination game in which the payoff to all players is the utilitarian collective welfare function, i.e., the sum of the utility functions of the players. Strategy profiles maximizing utilitarian welfare are strong Nash equilibria of the contribution game. Each strong Nash equilibrium corresponds in a natural way with a core element of the realization game, and vice versa. Moreover, each strong Nash equilibrium is coalitional proof.     

A game of timing and visibility

We consider the following abstraction of competing publications. There are n players in the game. Each player i chooses a point x_i in the interval [0,1], and a player's payoff is the distance from its point x_i to the next larger point, or to 1 if x_i is the largest. For this game, we give a complete characterization of the Nash equilibrium for the two-player game, and, more important, we give an efficient approximation algorithm to compute numerically the symmetric Nash equilibrium for the n-player game. The approximation is computed via a discrete version of the game. In both cases, we show that the (symmetric) equilibrium is unique. Our algorithmic approach to the n-player game is non-standard in that it does not involve solving a system of differential equations. We believe that our techniques can be useful in the analysis of other timing games.     

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.     

On the voluntary provision of “weakest‐link” public goods: The case of private information

We characterize equilibria in a private‐provision public‐good game where individuals are allowed arbitrary contribution levels and the level of the public good equals the least contribution made by an individual. Equilibrium comparative statics are derived for the interim Pareto‐dominant equilibrium. First, improvements in the cost distribution of even only one player benefit all. Second, even with such “weakest‐link” public goods, for which greater similarity of preferences would seem to facilitate coordination, decreased heterogeneity can actually decrease payoffs. Indeed, increasing the riskiness of cost distributions has an ambiguous effect on welfare. Two mechanisms are provided for improving equilibrium payoffs: Technology transfer and cheap‐talk communication. While substantial welfare gains are possible, examples show that (a) technology transfer may be futile if a “regularity” condition is not satisfied and (b) cheap talk may be useless if the language for communication is not sufficiently rich.     

Simple search methods for finding a Nash equilibrium

We present two simple search methods for computing a sample Nash equilibrium in a normal-form game: one for 2-player games and one for n-player games. Both algorithms bias the search towards supports that are small and balanced, and employ a backtracking procedure to efficiently explore these supports. Making use of a new comprehensive testbed, we test these algorithms on many classes of games, and show that they perform well against the state of the art—the Lemke–Howson algorithm for 2-player games, and Simplicial Subdivision and Govindan–Wilson for n-player games.     

Uncertainty and the Voluntary Provision of a Pure Public Good in a Two‐Moment Decision Model

In this paper, we explore the potential benefits of uncertainty that may arise in a two‐moment model of the voluntary provision of a pure public good. We find that an increase in a given contributor i’s risk associated with the aggregate contribution level of the other contributors (i.e., an increase in social uncertainty) induces that contributor to increase his own contribution level if and only if the uncertainty's incremental effect on the expected value of his net marginal utility is negative. Contributor i’s welfare likewise increases when a closely related condition is met, namely that the uncertainty's marginal effect on his expected marginal utility value of the public good exceeds its countervailing effect on the numeraire. Further, the corresponding aggregate contribution to the public good increases in the presence of free‐riding if and only if the incremental effect of contributor i’s contribution on the aggregate expected value of all other contributors’ net marginal utilities is small‐enough positive. We derive similar conditions for the case of private uncertainty, where the increase in contributor i’s risk is associated with his own marginal valuation of the public good. A simple example illustrates these conceptual results. Numerical analysis demonstrates that an increase in private uncertainty can have a nonmonotonic impact on contributor i’s welfare.     

The optimal treatment of tax expenditures

This paper analyzes the optimal treatment of tax expenditures. It develops an optimal tax model where individuals derive utility from spending on a “contribution” good such as charitable giving. The contribution good has also a public good effect on all individuals in the economy. The government imposes linear taxes on earnings and on the contribution good so as to maximize welfare. The government may also finance directly the contribution good out of tax revenue. Optimal tax and subsidy rates on earnings and the contribution good are expressed in terms of empirically estimable parameters and the redistributive tastes of the government. The optimal subsidy on the contribution good is increasing in the size of the price elasticity of contributions, the size of the crowding out effect of public contributions on private contributions, and the size of the public good effect of the contribution good. Numerical simulations show that the optimal subsidy on contributions is fairly sensitive to the size of these parameters but that, in most cases, it should be lower than the earnings tax rate.     

Effect of an audience in public goods provision

This paper investigates a novel public goods game where contributions to the public goods require effort that is observable. When the players are observed, they exert more effort to contribute to the public goods, and free-riding diminishes significantly compared to the no observer case. These effects are absent when no effort is required in order to contribute to the public goods. Furthermore, in the presence of an audience, the contributions to the public goods do not diminish when the game is repeated in the effort-required environment. Being observed does not affect the performance of the players if there is no strategic aspect of the game, in other words, when they play a private goods game. These results indicate that an individual wants to avoid appearing lazy when her effort helps the society.     

Woodsy the optimal owl: Environmental campaigns, norms, and implications for public goods policy

Norms regarding private provision of a public good (e.g. cutting down on energy use, not littering) can affect the marginal gains from contributing to a public good and therefore people's decisions about contributing to the public good. A model is proposed in which norms of private contributions to a public good can be influenced by public policy, and these norms affect people's self-image, which derives from a comparison of one's own contribution with the norm contribution. In this context, we examine the conditions under which private contributions to a public good are efficient, and the conditions under which policy affecting these norms improves social welfare. We find that (1) a benevolent social planner who fails to account for private provision norms will underprovide the public good, and (2) public policy that attempts to raise the norm contribution of private provision can increase social welfare if the effect of raising the norm does not have an extreme negative effect - either extremely small or extremely large - on peoples' self-image.     

Providing public goods in the absence of strong institutions

This paper proposes a simple two-stage mechanism to establish positive contributions to public goods in the absence of powerful institutions to provide the public good and to sanction free-riders. In this mechanism players commit to the public good by paying a deposit prior to the contribution stage. If there is universal commitment, deposits are immediately refunded whenever a player contributes her specified share to the public good. If there is no universal commitment, all deposits are refunded and the standard game is played. For suitable deposits, prior commitment and full ex post contributions are supported as a subgame-perfect Nash equilibrium for the resulting game. As the mechanism obviates the need for any ex post prosecution of free-riders, it is particularly suited for situations where players do not submit to a common authority as in the case of international agreements.     

Leadership and motivation for public goods contributions

Results from a leader–follower public goods game are presented. An individual, when randomly selected to make a contribution knowing others will observe the selection, gives more than in the simultaneous‐move public goods game. Followers adopt a quasi‐matching strategy where they systematically donate less than the leader, but contribute more when the leader does and contribute less when the leader free rides. The net result is increased provision of a public good when contributions are sequential. The results highlight that psychological preferences, rather than solely social preferences, can explain behavior.     

Revisiting the impact of impure public goods on consumers’ prosocial behavior: A lab experiment in Shanghai

In this study, we implemented a dictator game experiment to examine how the increase of the public characteristic in an impure public good affects individuals’ prosocial behaviour. A within‐subject design was used in the experiment. The dictator game was repeated six times with an impure public good introduced in four of them. We observe that the increase of the public characteristic in an impure public good partly crowds out individuals’ subsequent donations, which could be explained by a seemingly ‘mental accounting’ mental process. In addition, we also find that the selfish behaviour of individuals in dictator games with impure public goods, to some extent, has an inertia influence on their subsequent donations when the impure public good is removed.     

A comparative study of environmental amenity valuations

The paper reports on a comparative study of direct and indirect approaches to valuing environmental amenities (i.e., public goods), specifically, air quality in terms of its human health effects. The application of three indirect valuation methods (via market goods) is reported here: the health production method, a consumer preferences (for nonmarket goods) model, and the cost of illness method. The first and second methods are (economic) behavior-based approaches where willingness to pay for an environmental good is derived by exploiting relationships in consumption between the public good and market good(s). The third method is based on a physical relationship—a dose-response function—between the environmental good and health. The direct valuation approach encompassed three contingent valuation elicitation formats: open-ended, modified iterative bidding game, and referenda-style binary choice. The application of all four methods was based on data from a survey of a large, stratified sample of households from the Haifa metropolitan area in northern Israel. The estimates of welfare change derived by the various methods are discussed and compared.     

Punishment,counterpunishment and sanction enforcement in a social dilemma experiment

We present the results of an experiment that explores the sanctioning behavior of individuals who experience a social dilemma. In the game we study, players choose contribution levels to a public good and subsequently have multiple opportunities to reduce the earnings of the other members of the group. The treatments vary in terms of individuals’ opportunities to (a) avenge sanctions that have been directed toward themselves, and (b) punish others’ sanctioning behavior with respect to third parties. We find that individuals do avenge sanctions they have received, and this serves to decrease contribution levels. They also punish those who fail to sanction third parties, but the resulting increase in contributions is smaller than the decrease the avenging of sanctions induces. When there are five rounds of unrestricted sanctioning, contributions and welfare are significantly lower than when only one round of sanctioning opportunities exists, and welfare is lower than at a benchmark of zero cooperation. We thank James Andreoni, participants in seminars at Emory University, the University of Wisconsin-Madison, the University of New South Wales, the University of Sydney, Deakin University, the 2004 North American Regional Meetings of the ESA in Tucson, Arizona, USA, the 2004 IMEBE Meetings in Cordoba, Spain, and the 2005 SAET meetings in Vigo, Spain, for constructive and helpful comments. We thank Elven Priour for programming and organization of the sessions. Instructions for the experiment are available from the authors.     

Improving Voluntary Public Good Provision Through a Non-governmental,Endogenous Matching Mechanism: Experimental Evidence

Social norms can help to foster cooperation and to overcome the free-rider problem in the private provision of public goods. This paper focuses on the endogenous establishment of an average-oriented norm which sanctions deviations from average public good contributions. In a laboratory experiment, we analyse whether subjects are willing to implement a punishment and reward scheme at their own expense by applying the theory of non-governmental norm enforcement put forward by Buchholz et al. (J Public Econ Theory 16(6):899–916, 2014). Based on their theory, which omits a central authority but introduces an endogenously determined enforcement mechanism, we implement a two-stage public good game. In the first stage, subjects determine the strength of the sanctioning mechanism on their own. In the second stage, they decide on their personal contributions to the public good based on the established mechanism. In line with comparable pool punishment experiments, we find that subjects are apparently willing to contribute funds in order to establish a norm enforcement mechanism. Groups over-invest in the mechanism, but this over-investment decreases over time. These investments seem to be driven by the subjects’ previous individual contributions and partly by a number of strategic considerations, i.e. the previous average contribution made to the public good lowers the investment in the sanctioning mechanism. In the second stage of our experiment, higher norm enforcement parameters tend to lead to higher public good contributions. The earnings with the mechanism are on average higher than without.     

Correlated Equilibrium in Stochastic Games

We study the existence of uniform correlated equilibrium payoffs in stochastic games. The correlation devices that we use are either autonomous (they base their choice of signal on previous signals, but not on previous states or actions) or stationary (their choice is independent of any data and is drawn according to the same probability distribution at every stage). We prove that any n-player stochastic game admits an autonomous correlated equilibrium payoff. When the game is positive and recursive, a stationary correlated equilibrium payoff exists. Journal of Economic Literature Classification Numbers: C72, C73.     

Existence,uniqueness and some comparative statics for ratio and Lindahl equilibria

We present a rigorous, yet elementary, demonstration of the existence of a unique Lindahl equilibrium under the assumptions that characterize the standard n-player public good model. Indeed, our approach, which exploits the aggregative structure of the public good model, lends itself to a transparent geometric representation. Moreover, it can handle the more general concept of the cost share or ratio equilibrium. Finally, we indicate how it may be exploited to facilitate comparative static analysis of Lindahl and cost share equilibria.