Voluntary Contribution Game Research Articles

Networks of Many Public Goods with Non-Linear Best Replies

We model a bipartite network in which links connect agents with public goods. Agents play a voluntary contribution game in which they decide how much to contribute to each public good they are connected to. We show that the problem of finding a Nash equilibrium can be posed as a non-linear complementarity one. The existence of an equilibrium point is established for a wide class of individual preferences. We then find a simple sufficient condition, on network structure only, that guarantees the uniqueness of the equilibria, and provide an easy procedure for building networks that respects this condition.

“Do the right thing:” The effects of moral suasion on cooperation

The use of moral appeals to affect the behavior of others is pervasive (from the pulpit to ethics classes) but little is known about the effects of moral suasion on behavior. In a series of experiments we study whether moral suasion affects behavior in voluntary contribution games and the mechanisms by which behavior is altered. We find that observing a message with a moral standard according to the golden rule or, alternatively, utilitarian philosophy, results in a significant but transitory increase in contributions above the levels observed for subjects that did not receive a message or received a message that advised them to contribute without a moral rationale. When players have the option of punishing each other after the contribution stage, the effect of the moral messages on contributions becomes persistent: punishments and moral messages interact to sustain cooperation. We also investigate the mechanisms through which moral suasion operates and find that it affects both expectations and preferences.

Meritocratic Matching Stabilizes Public Goods Provision

We study the stability and welfare properties of merit-based (meritocratic) group-matching mechanisms in voluntary contribution games. Meritocratic matching in this context means that players tend to be assortatively grouped according to their contributions. We let regimes di ffer from one another with respect to their matching fidelity. The stability analysis summarizes as follows. When there is not enough meritocracy, the only equilibrium state is universal free-riding. Above a first threshold, several Nash equilibria above free-riding emerge, but only the free-riding equilibrium is stochastically stable. There exists a second meritocratic threshold, above which an equilibrium with high contributions becomes the unique stochastically stable state. This operationalization of meritocracy sheds light on critical transitions, that are enabled by contribution-assortative matching, between equilibria related to tragedy of the commons

Trust in Trade: Studying the Causal Role of Trust on Public Support for Free Trade in a Field Survey Experiment

While most explanations of individual trade policy preferences center on the re-distributional implications of trade, recent research is particularly interested in the role of non-economic determinants. We join the latter line of work by studying the effect of a fundamental socio-psychological determinant of trade preferences: generalized social trust. The hypothesized causal effect of social trust is tested in a field survey experiment that combines a voluntary contribution game with a survey. The empirical work was carried out in Hanoi, Vietnam. The findings offer robust support for the argument that social trust has a positive causal effect on public support for international trade.

Paretian dictators: constraining choice in a voluntary contribution game

We explore individuals’ preferences over limiting the choice sets of others in an environment with externalities. Specifically, we conduct public goods games in which participants can mandate the contributions of others or restrict choices to a subset of feasible contributions levels. We find that, relative to a baseline treatment in which individuals make choices from the set of all contribution alternatives, allowing individuals to constrain the choices of others results in more efficient outcomes. We discuss these results in light of the literature on behavioral theories of reciprocity and conditional cooperation and in regards to the literature on pre-constitutional design, political institutions, and social choice.

Not Just Like Starting Over: Leadership and Revivification of Cooperation in Groups

We conduct a laboratory experiment to study how, after a history of decay, cooperation in a repeated voluntary contribution game can be revived in an enduring way. Simply starting the repeated game over - a simple fresh start - leads to an initial increase of cooperation, but to a subsequent new decay. Motivated by cooperation decay in organizations we study the potential of three interventions of triggering higher and sustained cooperation, which take place at the same time as a restart. Surprisingly, we find that the detailed explanation of the causes of the decay in cooperation of Fischbacher and Gaechter (2010) combined with an advice on how to prevent decay do not have an effect beyond that of just starting over. In contrast, a one-way free form communication message sent by the leader to the followers strongly revives cooperation. We find evidence that repeated free form communication by the leader further strengthens the reviving effect on cooperation. Combining the two previous interventions does not outperform the pure effect of communication. Our content analysis reveals that leader communication is more people oriented than the expert advice.

Enforcing Compliance with Environmental Agreements in the Absence of Strong Institutions: An Experimental Analysis

This paper uses laboratory experiments to evaluate the performance of a deposit-refund mechanism used to enforce compliance with voluntary public-good commitments made in the absence of strong regulatory institutions. With this mechanism agents decide whether to join an agreement and pay a deposit prior to making their contribution decisions. If an agreement receives sufficient membership to form, members then make their contribution decisions and compliant members are refunded their deposits. If an agreement does not form, then deposits are immediately refunded and a standard voluntary contribution game is played. We find that the deposit-refund mechanism achieves nearly full efficiency when agreements require full participation, but is far less effective, and in some cases disruptive, when agreements require only partial participation. As the mechanism does not require the existence of strong sanctioning institutions, it is particularly suited for enforcing compliance with international environmental agreements.

Endogenous Move Structure and Voluntary Provision of Public Goods: Theory and Experiment

AbstractIn this paper, we examine voluntary contributions to a public good, embedding Varian's (1994) voluntary contribution game in extended games that allow players to choose the timing of their contributions. We show that predicted outcomes are sensitive to the structure of the extended game, and also to the extent to which players care about payoff inequalities. We then report a laboratory experiment based on these extended games. We find that behavior is similar in the two extended games: subjects avoid the detrimental move order of Varian's model, where a person with a high value of the public good commits to a low contribution, and instead players tend to delay contributions. These results suggest that commitment opportunities may be less damaging to public good provision than previously thought.

All but one free ride when wealth effects are small

Quasilinear preferences on a public good and a numeraire good are limits of preferences where both goods are normal. The set of equilibria of the voluntary contribution (or private provision) game is easily characterized under quasilinearity by: top valuators aggregately contribute their common stand-alone contribution, whereas non-top valuators contribute nothing. Because, as long as preferences are randomly selected, there will typically be a single top valuator, it follows that, typically, the equilibrium is unique, with all players but one contributing nothing, hence “free riding” in the sense of the ordinary English usage of the expression. The upper-hemicontinuity of the Nash equilibrium correspondence implies that this is also the case when both goods are strictly normal, but the wealth effects on the public good are small.

Words versus actions as a means to influence cooperation in social dilemma situations

We use a sequential voluntary contribution game to compare the relative impact of a first-mover’s non-binding announcement versus binding commitment on cooperation. We find that a non-binding announcement and a binding commitment increase individual contributions to a similar extent. Since announced contributions systematically exceed commitments, in sessions with a non-binding announcement, second-movers tend to contribute more to the group activity than in sessions with a binding commitment. Yet, second-movers appear to be more motivated towards achieving a social optimum when the first-mover uses commitment. We also find that a non-binding announcement has a higher impact on individual propensity to cooperate than the ex post contribution of the first-mover. However, the failure to make announced contributions decreases cooperation even though the first-mover is reassigned in every period.

Leadership by Example and by Pre-Game Communication in Social Dilemma Situations

This paper compares the effects of two leadership styles: leading by pre-game communication and leading by example using an iterated voluntary contribution game. We find that pre-game communication increases the level of individual contributions in the game and has essentially the same impact on the level of individual contributions as leading by example. Yet, followers appear to be more motivated towards achieving a socially optimal outcome in leading by example than in leading by pre-game communication. We also find that the content of pre-game communication has a higher impact on individual decisions than the ex post contribution of the leader. However, false messages cause an erosion of trust: participants decrease their contributions if they have received a false message from the leader in the previous period even though leaders are re-assigned in every period.

Public Good and Private Good Valuation for Waiting Time Reduction - A Laboratory Study

In a laboratory experiment with salient rewards, subjects were endowed with money and waiting time. Preferences for waiting time were elicited both as a private good by means of a series of second price auctions, i.e., in a non-induced values framework, and as a public good in the scope of a voluntary contribution game. Our data supports the Lindahl equilibrium as a descriptive model of behavior. Private goods valuations turned out to be good predictors of public goods valuations. Furthermore, positive expectations about other subjects' contributions lead to a significant increase of one's own contribution. We did not find evidence of waiting time being discounted.

Achievable Outcomes in Smooth Dynamic Contribution Games

This paper studies a class of dynamic voluntary contribution games in a setting with discounting and neoclassical payoffs (differentiable, strictly concave in the public good, and quasilinear in the private good). An achievable prole is the limit point of a subgame perfect equilibrium path - the ultimate cumulative contribution vector of the players. A prole is shown to be achievable only if it is in the undercore of the underlying coalitional game, i.e., the prole cannot be blocked by a coalition using a component-wise smaller prole. Conversely, if free-riding incentives are strong enough that contributing zero is a dominant strategy in the stage games, then any undercore prole is the limit of achievable proles as the period length shrinks. Thus, in this case when the period length is very short, (i) the set of achievable contributions does not depend on whether the players can move simultaneously or only in a round-robin fashion; (ii) an efcient prole can be ap- proximately achieved if and only if it is in the core of the underlying coalitional game; and (iii) any achievable prole can be achieved almost instantly.

Sequential equilibrium in monotone games: A theory-based analysis of experimental data

A monotone game is an extensive-form game with complete information, simultaneous moves and an irreversibility structure on strategies. It captures a variety of situations in which players make partial commitments and allows us to characterize conditions under which equilibria result in socially desirable outcomes. However, since the game has many equilibrium outcomes, the theory lacks predictive power. To produce stronger predictions, one can restrict attention to the set of sequential equilibria, or Markov equilibria, or symmetric equilibria, or pure-strategy equilibria. This paper explores the relationship between equilibrium behavior in a class of monotone games, namely voluntary contribution games, and the behavior of human subjects in an experimental setting. Several key features of the symmetric Markov perfect equilibrium (SMPE) are consistent with the data. To judge how well the SMPE fits the data, we estimate a model of Quantal Response Equilibrium (QRE) [R. McKelvey, T. Palfrey, Quantal response equilibria for normal form games, Games Econ. Behav. 10 (1995) 6–38; R. McKelvey, T. Palfrey, Quantal response equilibria for extensive form games, Exp. Econ. 1 (1998) 9–41] and find that the decision rules of the QRE model are qualitatively very similar to the empirical choice probabilities.

Strategic behavior and learning in repeated voluntary contribution experiments

Voluntary contribution experiments systematically find that contributions decline over time. We use a two-stage voluntary contribution game to investigate whether this decrease is caused by learning or strategic behavior. Using a strategy method we find a robust pattern of declining contributions: contributions in stage 2 are 45 percent lower than in stage 1. Repeating the game five times we find that experience generates a smaller decline in contributions: stage 1 contributions decrease by around 7 percent per game. Finally we find no significant differences between the strategy and direct-response method, which suggests that our results help explain behavior in the latter.

Giving little by little: Dynamic voluntary contribution games

Charitable contributions are frequently made over time. Donors are free to contribute whenever they wish and as often as they want, and are frequently updated on the level of contributions by others. A dynamic structure enables donors to condition their contribution on that of others, and, as Schelling [Schelling, Thomas C., The Strategy of Conflict Cambridge, MA: Harvard University Press, 1960.] suggested, it may establish trust thereby increasing charitable giving. Marx and Matthews [Marx, Leslie, and Steven Matthews, “A Dynamic Voluntary Contribution to a Public Project,” Review of Economic Studies, 67, 2000, 327–358.] build on Schelling's insight and show that multiple contribution rounds may secure a provision level that cannot be achieved in the static, one-shot setting, but only if there is a discrete, positive payoff jump upon completion of the project. We examine these two hypotheses experimentally using static and dynamic public good games. We find that contributions are indeed higher in the dynamic than in the static game. However, in contrast to the predictions, the increase in contributions in the dynamic game does not depend critically on the existence of a completion benefit jump or on whether players can condition their decisions on the behavior of other members of their group.

Aggregative Public Good Games

AbstractWe exploit the aggregative structure of the public good model to provide a simple analysis of the voluntary contribution game. In contrast to the best response function approach, ours avoids the proliferation of dimensions as the number of players is increased, and can readily analyze games involving many heterogeneous players. We demonstrate the approach at work on the standard pure public good model and show how it can analyze extensions of the basic model.

Dissertation abstract: Contribution to a public good - Theoretical analysis and experimental evidence

The work undertook is located between Public Economic Theory and Experimental Economics. The object of the thesis consists in analysing the aggregate behavior and the individual heterogeneity in a voluntary contribution game. The thesis defended here is that overcontribution in comparison to the Nash equilibrium of the game, can not be explained neither by judgement errors, nor by the information on the individual behaviour of the members in a one given group. The level of contribution observed remains nevertheless inferior to the one simulated using the E.W.A. learning model.

Leading-by-example and signaling in voluntary contribution games: an experimental study

We report experimental results on the effect of leadership in a voluntary contribution game. Consistent with recent theories we find that leading-by-example increases contributions and earnings in an environment where a leader has private information about the returns from contributing (Hermalin in Am Econ Rev 88:1188–1206, 1998; Vesterlund in J Public Econ 87:627–657, 2003). In contrast the ability to lead-by-example has no effect on total contributions and earnings when such returns are commonly known. In our environment the success of leadership therefore appears to be driven by signaling rather than by nonpecuniary factors such as reciprocity.

Cheap talk, efficiency and egalitarian cost sharing in joint projects

Rarely, if ever, do parties contemplating a joint project commit resources without engaging in non-binding discussions about who does what. To examine the role of such discussions, we model the investment decision as a voluntary contribution game where each player is privately informed of her benefit from project's completion. Efficiency of every equilibrium of this game is improved when a prior stage of communication is allowed. Interestingly, this improvement can be achieved in “simple equilibria” where a player simply announces whether (not how much) she plans to contribute. With symmetric priors, the simple equilibrium that maximizes either utilitarian ex ante welfare or the probability of completion has a curiously egalitarian feature—whenever the project is completed, each party contributes exactly half the cost, independent of private information.