Contribution Game Research Articles

Individual, Dictator, and Democratic punishment in public good games with perfect and imperfect observability

In the context of repeated public good contribution games, we experimentally compare the institution of democratic punishment, where members of a group decide by majority voting whether to inflict punishment on another member, with individual peer-to-peer and dictatorial punishment institutions. Democratic punishment leads to more cooperation and higher average payoffs, both under perfect and imperfect monitoring of contributions. A comparison with dictatorial punishment suggests that the effect relative to traditional peer-to-peer punishment primarily works by curbing anti-social punishment and thereby establishing a closer connection between a member's contribution decision and whether subsequently being punished by others.

ネットワーク上のcontribution gameを不平等回避モデルで考察した際のナッシュ均衡・absorbing setの導出

ネットワーク上のcontribution gameを不平等回避モデルで考察した際のナッシュ均衡・absorbing setの導出

Promoting Socially Desirable Behaviors: Experimental Comparison of the Procedures of Persuasion and Commitment

In a series of experiments, we test the relative efficiency of persuasion and commitment schemes to increase and sustain contribution levels in a Voluntary Contribution Game. The design allows to compare a baseline consisting of a repeated public good game to, respectively, four manipulation treatments relying on: an information strategy, a low commitment strategy, a high commitment strategy and a promise strategy. We confirm the advantages of psychologically orientated policies as they increase the overall level of contribution and for some, that is commitment and promises, question the decreasing trend traditionally observed in long term contributions to public goods.

Protocol invariance and the timing of decisions in dynamic games

We characterize a class of dynamic stochastic games that we call separable dynamic games with noisy transitions and establish that these widely used models are protocol invariant provided that periods are sufficiently short. Protocol invariance means that the set of Markov perfect equilibria is nearly the same irrespective of the order in which players are assumed to move within a period. Protocol invariance can facilitate applied work, and renders the implications and predictions of a model more robust. Our class of dynamic stochastic games includes investment games, research and development races, models of industry dynamics, dynamic public contribution games, asynchronously repeated games, and many other models from the extant literature.

Environmental awareness: The case of climate change

The extent of provision of a public good often relies on social awareness and public support for it. This applies, in particular, to global reduction of greenhouse gases and its relevance for mitigating climate change. We examine the concept of “public awareness” by introducing a formal model that analyzes efforts to mitigate climate change in a setting with heterogeneous countries. In the theoretical part we examine the Nash equilibrium of the contribution game. The effects of awareness and economic parameters on mitigation efforts can be disentangled, raising the possibility of linking awareness of climate change with economic wealth. The second part provides some empirical observations and offers the rankings of countries regarding awareness for climate change, as well as an empirical relationship between awareness and economic wealth.

Identifying discrete behavioural types: a re-analysis of public goods game contributions by hierarchical clustering

We propose a framework for identifying discrete behavioural types in experimental data. We re-analyse data from six previous studies of public goods voluntary contribution games. Using hierarchical clustering analysis, we construct a typology of behaviour based on a similarity measure between strategies. We identify four types with distinct stereotypical behaviours, which together account for about 90% of participants. Compared to the previous approaches, our method produces a classification in which different types are more clearly distinguished in terms of strategic behaviour and the resulting economic implications.

Noncooperative Dynamic Contribution to a Public Project

We consider a dynamic contribution game in which a group of agents collaborates to complete a public project. The agents exert efforts over time and get rewarded upon completion of the project, once the cumulative effort has reached a pre-specified level. We explicitly derive the cooperative solution and a noncooperative Markov-perfect Nash equilibrium. We characterize the set of socially efficient projects, i.e., projects that cooperative groups find worth completing. Comparing with the Markov-perfect Nash equilibrium, we find that noncooperative groups give up large socially efficient projects. Moreover, they take too much time to complete the projects that they undertake.

Cooperation and Strategic Complementarity: An Experiment with Two Voluntary Contribution Mechanism Games with Interior Equilibria

In public goods game experiments, designs implementing non-linearities in the production are less common than the standard linear setting, especially so under the assumption that the private goods production and public goods aggregation function are both non-linear. We study a voluntary contribution game (VCM) in which returns from the private project have diminishing marginal benefits and the contributions to the joint project exhibit pairwise strategic complementarities. As a control, we use a public goods game with an identical private production technology, but with the standard linear public goods aggregation. In addition to the aggregation technology, we manipulate the group size variable: In both treatments, the subjects will first play a VCM game in groups of five for 20 rounds, after which the group size is reduced to two, and the game is played for another 20 rounds. A significant over-contribution is observed in both settings when the group size is five. The rate of over-contribution is much higher under the complementary technology, but as predicted by theory, the contributions drop drastically when the group size is reduced from n = 5 to n = 2 within this treatment. Our experiment also provides empirical evidence that the so-called group size effect is present in both treatments, but it is much weaker under the standard aggregation technology.

Designing feedback in voluntary contribution games: the role of transparency

We analyze the effects of limited feedback on beliefs and contributions in a repeated public goods game setting. In a first experiment, we test whether exogenously determined feedback about a good example (i.e., the maximum contribution in a period) in contrast to a bad example (i.e., the minimum contribution in a period) induces higher contributions. We find that when the type of feedback is not transparent to the group members, good examples boost cooperation while bad examples hamper it. There is no difference when the type of feedback is transparent. In a second experiment, feedback is endogenously chosen by a group leader. The results show that a large majority of the group leaders count on the positive effect of providing a good example. This is true regardless whether they choose the feedback type to be transparent or non-transparent. Half of the group leaders make the type of feedback transparent. With endogenously chosen feedback about good examples no difference in contributions can be observed among transparent and non-transparent feedback selection. In both experiments feedback shapes subjects’ beliefs. With exogenously chosen feedback, transparent feedback tends to reduce beliefs when good examples are provided as feedback and tends to increase beliefs in when bad examples are provided as feedback compared to the respective non-transparent cases. Our results shed new light on the design of feedback provision in public goods settings.

Does Social Trust Affect Public Support for International Trade? Insights from an Experiment in Vietnam

In view of recent political backlash against various trade agreements, we are interested in understanding how social trust influences public opinion on international trade. Recent correlational studies suggest that such an effect might exist, but further research is needed to establish whether social trust does indeed play a causal role in shaping the mass public’s trade attitudes. We use an experimental approach to assess whether higher levels of social trust lead to more public support for free trade. To induce variation in levels of social trust, we expose study participants to different versions of a voluntary contribution game and examine the effect of such variation on trade preferences. The experiment was carried out in Vietnam, whose economy has experienced a rapid process of trade liberalization. We show that our treatment design effectively induces differing levels of social trust, with higher levels of social trust generating greater support for free trade.

Warm-glow giving in networks with multiple public goods

This paper explores a voluntary contribution game in the presence of warm-glow effects. There are many public goods and each public good benefits a different group of players. The structure of the game induces a bipartite network structure, where players are listed on one side and the public good groups they form are listed on the other side. The main result of the paper shows the existence and uniqueness of a Nash equilibrium. The unique Nash equilibrium is also shown to be asymptotically stable. Then the paper provides some comparative statics analysis regarding pure redistribution, taxation and subsidies. It appears that small redistributions of wealth may sometimes be neutral, but generally, the effects of redistributive policies depend on how public good groups are related in the contribution network structure.

Reciprocity and resistance to change: An experimental study

Many uncertain organizational changes fail because of resistance by employees. This paper studies the circumstances under which acceptance to change occurs. We propose that reciprocity towards the employer helps to increase change approval. Subjects in our experiment play a combination of a gift exchange and a threshold contribution game. In each group, one employer chooses a wage and then five employees decide on their effort. A ‘reform’ is adopted if the employees exert at least a minimum threshold of effort. The reform is efficiency enhancing but also raises inequality among employees. We find that uncertainty over payoffs does not necessarily lead to resistance. The likelihood of reform approval is especially high if the employer is able to trigger reciprocal behavior in employees by offering a fair wage, which confirms our hypothesis.

Pledge-and-Review Bargaining

Real-world negotiations differ fundamentally from existing bargaining theory. Inspired by the Paris Agreement on climate change, this paper develops a novel bargaining game in which each party quantities its own contribution (to a public good, for example), before the set of pledges must be accepted. I first show that, if the tolerance for delay is uncertain, each equilibrium pledge coincides with an asymmetric Nash bargaining solution. The weights placed on others. payouts reflect the underlying uncertainty, but they vary from pledge to pledge, so the set of equilibrium pledges is inefficient. This bargaining outcome is embedded in a dynamic contribution game, with endogenous technology, participation, enforcement, and contract terms, to investigate when pledge-and-review bargaining is desirable. The model’s predictions can rationalize the key differences between the climate agreements signed in Kyoto (1997) and Paris (2015) as well as the development from the former to the latter.

Game of Variable Contribution to Common Good under Uncertainty

We consider a stochastic game of contribution to the common good in which the players have continuous control over the degree of contribution, and we examine the gradualism arising from the free rider effect. This game belongs to the class of variable concession games which generalize wars of attrition. Previously known examples of variable concession games in the literature yield equilibria characterized by singular control strategies without any delay of concession. However, these no-delay equilibria are in contrast to mixed strategy equilibria of canonical wars of attrition in which each player delays concession by a randomized time. We find that a variable contribution game with a single state variable, which extends the Nerlove-Arrow model, possesses an equilibrium characterized by regular control strategies that result in a gradual concession. This equilibrium naturally generalizes the mixed strategy equilibria from the canonical wars of attrition. Stochasticity of the problem accentuates the qualitative difference between a singular control solution and a regular control equilibrium solution. We also find that asymmetry between the players can mitigate the inefficiency caused by the gradualism.

Aiming for the Goal: Contribution Dynamics of Crowdfunding

We study reward-based crowdfunding, a new class of dynamic contribution games where a private good is produced only if the funding goal is reached by a deadline. Buyers face a problem of coordination rather than free-riding. A long-lived donor may alleviate this coordination risk, signaling his wealth through dynamic contributions. We characterize platform-, donor-, and buyer-optimal equilibrium outcomes, attained by Markov equilibria with simple donation strategies. We test the modeli?½s predictions using high-frequency data collected from the largest crowdfunding platform, Kickstarter. The model i?½ts the data well, especially for predictions concerning comparative statistics, donation dynamics, and properties of successful campaigns.

Assortative Matching with Inequality in Voluntary Contribution Games

Voluntary contribution games are a classic social dilemma in which the individually dominant strategies result in a poor performance of the population. However, the negative zero-contribution predictions from these types of social dilemma situations give way to more positive (near-)efficient ones when assortativity, instead of random mixing, governs the matching process in the population. Under assortative matching, agents contribute more than what would otherwise be strategically rational in order to be matched with others doing likewise. An open question has been the robustness of such predictions when heterogeneity in budgets amongst individuals is allowed. Here, we show analytically that the consequences of permitting heterogeneity depend crucially on the exact nature of the underlying public-good provision efficacy, but generally are rather devastating. Using computational methods, we quantify the loss resulting from heterogeneity vis-a-vis the homogeneous case as a function of (i) the public-good provision efficacy and (ii) the population inequality.

Contribution-Based Grouping under Noise

Many real-world mechanisms are “noisy” or “fuzzy”, that is the institutions in place to implement them operate with non-negligible degrees of imprecision and error. This observation raises the more general question of whether mechanisms that work in theory are also robust to more realistic assumptions such as noise. In this paper, in the context of voluntary contribution games, we focus on a mechanism known as “contribution-based competitive grouping”. First, we analyze how the mechanism works under noise and what happens when other assumptions such as population homogeneity are relaxed. Second, we investigate the welfare properties of the mechanism, interpreting noise as a policy instrument, and we use logit dynamic simulations to formulate mechanism design recommendations.

The limit to behavioral inertia and the power of default in voluntary contribution games

It is well documented that people are reluctant to switch from a default option. We experimentally test the robustness of this behavioral inertia in a collective decision-making setting by varying the default option type and the decision-making environment. We examine the impacts of automatic-participation and no-participation default options on subjects’ participation in a public goods provision and their contributions. Two variants of public goods game are employed: the linear and the threshold public goods games. The study shows the evidence of partial stickiness rather than complete stickiness of default options as indicated in empirical studies. Our experimental results square with the evidence of behavioral inertia only when the automatic-participation default is used. This default boosts contributions in the linear public goods game but not in the threshold public goods game. The evidence of partial stickiness is robust to the variation of the game employed, but the effect on contribution is sensitive to it.

Warm-Glow Giving in Networks with Multiple Public Goods

This paper explores a voluntary contribution game in the presence of warm-glow effects. There are many public goods and each public good benefits a different group of players. The structure of the game induces a bipartite network structure, where players are listed on one side and the public good groups they form are listed on the other side. The main result of the paper shows the existence and uniqueness of a Nash equilibrium. The unique Nash equilibrium is also shown to be locally asymptotically stable. Then the paper provides some comparative statics analysis regarding pure redistribution, taxation and subsidies. It appears that small redistributions of wealth may sometimes be neutral, but generally, the effects of redistributive policies depend on how public good groups are related in the contribution network structure.

Community repeated interaction and strategic delegation

A large population of fixed-type agents engage in exclusive pairwise relationships in a decentralized setting. At the onset, agents randomly meet in pairs under private information of individual time-invariant types. They play a voluntary contribution game. At the end of the first period, members of each pair either stay together in the second period, in which case reported information is common knowledge, or quit and meet randomly new partners, under private information of individual types. Thus, either long-term or short-term relationships may arise. We show that there are values of the parameters such that information extracted in the first period has a positive effect on social efficiency. We give an interpretation of our results in terms of advantageous delegation of decisions to uninformed agents. Finally, we consider several extensions of the model in which our results still hold.