Testing static game theory with dynamic experiments: A case study of public goods

Game theory provides predictions of behavior in many one-shot games. On the other hand, most experimenters usually play repeated games with subjects, to provide experience. To avoid subjects rationally employing strategies that are appropriate for the repeated game, experimenters typically employ a “random strangers” design in which subjects are randomly paired with others in the session. There is some chance that subjects will meet in multiple rounds, but it is claimed that this chance is so small that subjects will behave as if they are in a one-shot environment. We present evidence from public goods experiments that this claim is not always true.     

Common fate,game harmony and contributions to public goods: experimental evidence

We experimentally study the effects of common fate on voluntary contributions to linear public goods. In each period, earnings are assigned to subjects according to the outcome of a lottery. In ‘common fate’, ‘independent fate’ and ‘rival fate’ treatments, the lottery outcomes of group members are (respectively) positively correlated, stochastically independent and negatively correlated. We observe the highest contributions and strongest reciprocity under common fate. Contrary to the game harmony hypothesis, contributions are not lower under rival fate than under independent fate. Surprisingly, under rival fate, having won the lottery in one period induces higher contributions in the next period.     

An experimental comparison of collective choice procedures for excludable public goods

This paper compares three collective choice procedures for the provision of excludable public goods under incomplete information. One, serial cost sharing (SCS), is budget balanced, individually rational, anonymous and strategy proof. The other two are “hybrid” procedures: voluntary cost sharing with proportional rebates (PCS) and with no rebates (NR). PCS satisfies all these properties except strategy proofness, and NR satisfies all the properties except for strategy proofness and budget balance. However, PCS and NR do not exclude any potential users, and they do not require equal cost shares, thereby overcoming the two main sources of inefficiency with SCS. We characterize the Bayesian Nash equilibria (BNE) of the hybrid mechanisms and conduct laboratory experiments to compare the performance of the three mechanisms. We find that PCS produces significantly more efficient allocations than either SCS or NR.     

Foreign aid and weakest-link international public goods: An experimental study

In this paper, we investigate efficiency differences between income and in-kind transfers as distribution mechanisms of foreign aid to weakest-link international public goods in a laboratory environment. We find that if there is relatively small difference in country size, then income transfers seem to provide a higher provision of the international public good, and thus higher overall welfare level than that of in-kind transfers. However, if there is a large disparity in country size, then in-kind transfers appear to provide a higher level of IPG provision and higher accompanying global welfare.     

Ambiguity on audits and cooperation in a public goods game

We investigate the impact of various audit schemes on the provision of public goods, when contributing less than the average of the other group members is centrally sanctioned and the probability of an audit is unknown. We study how individuals update their beliefs about the probability of being audited, both before and after audits are permanently withdrawn. We find that when individuals have initially experienced systematic audits, they decrease both their beliefs and their contributions almost immediately after audits are withdrawn. In contrast, when audits were initially less frequent and more irregular, they maintain high beliefs and continue cooperating long after audits have been withdrawn. This identifies the compliance effect of irregularity and uncertainty due to learning difficulties. By increasing both the frequency of audits and the severity of sanctions, we also identify an educative effect of frequent and high sanctions on further cooperation.     

Learning dynamics for mechanism design: An experimental comparison of public goods mechanisms

In a repeated-interaction public goods economy, incomplete information and dynamic behavior may affect the realized outcomes of mechanisms known to be efficient in a complete information one-shot game. An experimental test of five public goods mechanisms indicates that subjects with private information appear to best respond to recent observations. This provides predictions about which mechanisms will generate convergence to their efficient equilibrium allocations. These predictions match the experimental result that globally stable efficient mechanisms realize the highest efficiency in practice. The simplicity of the suggested best response model makes it useful in predicting stability of mechanisms not yet tested.     

Institutions, motivations and public goods: An experimental test of motivational crowding

Contributions to public goods can be motivated by intrinsic factors such as warm glow altruism and fairness, as well as extrinsic incentives such as sanctions and payments. However, psychological studies suggest that formal extrinsic incentives may crowd out intrinsic motivations. In an experimental study of individual contributions to a public good we find that suasion crowded in voluntary contributions, while an extrinsic incentive in the form of a regulation led to crowding out. This has implications for the design of public policy where ranges of motivations are present.     

The ratio equilibrium and a voting game in a public goods economy

An economic model of the allocation process with public goods is presented. We define a concept of equilibrium and prove the existence. Next we present a voting game in which a level of the public goods to be produced is decided. We prove that the core of the voting game and the equilibria exist simultaneously, and that they coincide.     

Assurance payments on the coordination of threshold public goods provision: An experimental investigation

We investigate the assurance payment mechanism (APM) in a single-unit threshold public good game. APM offers an assurance payment ($AP$) as compensation to would-be contributors if the group fails to provide the good and individual contributions reach a pre-determined price. We characterize the set of pure-strategy Nash equilibria for APM under complete information and show that assurance payments substantially reduce the multiplicity of equilibria and eliminate the set of non-provision equilibria in a general setup. We find strong evidence that APM improves upon the baseline provision point mechanism without assurance in lab experiments. Assurance payments act as a coordination device and induce more contributions concentrated on $AP$, especially for agents with values above $AP$, leading to more frequent successful provision, higher group contributions, and an overall welfare improvement. Our experimental findings highlight the non-equilibrium mis-coordination as the main reason for the non-provision of threshold public goods and indicate that the format of assurance payments plays a key role in successful coordination even when provision is the unique equilibrium outcome.     

Rotating group representatives and group members’ requests in repeated public goods game

ABSTRACT

This study investigated the effect of group representatives on contribution behaviour in response to group members’ requests in repeated public goods games. Data came from 135 students in 15 groups enrolled in the experiment, grouped in the following treatments: no group representatives (NR, NRG) and group representatives (R1, R2). We also tested initial requests wherein the group members’ initial requests (i.e. NRG, R2) mediated the positive relationship between individual-level contribution preferences and group contributions. We used a fixed-effects GLS regression and IV regression to analyse the effect of group representatives and group members’ requests. The results indicated the following: (a) rotating group representative/group members’ requests was related to group contributions at the session (within-members) and group (between-group) levels; (b) the reactions to members’ requests positively predicted group contributions; (c) subjects in the no group representatives treatment formed their requests by relying more on previous group contributions than subjects in the group representatives treatment, who relied more on the previous group members’ requests; and (d) the initial requests explained long-term contribution levels, which resulted in variations in group contributions observed between the NRG and R2 treatments. Our findings highlight the role of rotating group representatives in stimulating cooperation among members, while group members’ requests impel individuals to make contribution decisions at the group level.     

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.     

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.     

Rewards and the private provision of public goods on dynamic networks

We study an evolutionary model of a public good game with rewards played on a network. Giving rewards to contributors transforms the game but gives rise to a second-order dilemma. By allowing for coevolution of strategies and network structure, the evolutionary dynamics operate on both structure and strategy. Players learn with whom to interact and how to act and can overcome the second-order dilemma. More specifically, the network represents social distance which changes as players interact. Through the change in social distance, players learn with whom to interact, which we model using reinforcement dynamics. We find that, for certain parameter constellations, a social institution, prescribing prosocial behavior and thus solving the second-order dilemma, can emerge from a population of selfish players. Due to the dynamic structure of the network, the institution has an endogenous punishment mechanism ensuring that defectors will be excluded from the benefits of the institution and the public good will be supplied efficiently.     

Technology and public goods

This paper presents a theory of public goods based on production theory where public goods are viewed as inputs to the production process. We examine the pure case of public inputs (no private inputs) as well as the mixed case (private and public inputs). We show how the case of public inputs is related to certain forms of nonjoint production, and we characterize it in terms of variable profit and joint cost functions. Comparative statics results are derived graphically in the two-by-two case.     

Power and public goods

A game-theoretic analysis using the Harsanyi-Shapley nontransferable utility value indicates that the choice of public goods in a democracy is not affected by who has voting rights. This is corroborated by an independent economic argument based on the implicit price of a vote.     

The role of risk aversion in public goods dilemmas with environmental uncertainty: an experimental analysis

The purpose of this study is to extend earlier research on environmental uncertainty in public goods dilemmas. The present paper reports the results of an experiment designed to examine the effect of risk aversion on public goods provision. A von Neumann–Morgenstern utility function with constant coefficient of relative risk aversion is used to investigate the impact of risk attitudes within a threshold public goods environment. The outcome of the threshold public goods experiment shows that subjects are indifferent to the changes in environmental conditions. Additionally, the analysis indicates that risk aversion is a significant determinant of voluntary public goods contribution level.     

On the consistency of conjectures with public goods

This note addresses Sugden's criticisms, levelled against our Non-Nash theory for public goods. In particular, we argue that our previous exercise was not to present a theory of public goods that could escape the voluntary contribution problem by relaxing Nash conjectures. Rather, our non-Nash model was merely an analytical exercise, meant to encompass a widevariety of behaviour. This note also indicates when positive conjectures might be realistic and, therefore, potentially consistent. Finally, we extend our specific example to include negative, zero, and positive conjectures.