Beliefs and Public Good Provision with Anonymous Contributors

We analyze a static game of public good contributions where finitely many anonymous players have heterogeneous preferences about the public good and heterogeneous beliefs about the distribution of preferences. In the unique symmetric equilibrium, the only individuals who make positive contributions are those who most value the public good and who are also the most pessimistic; that is, according to their beliefs, the proportion of players who most like the public good is smaller than it would be according to any other possible belief. We predict whether the aggregate contribution is larger or smaller than it would be in an analogous game with complete information and heterogeneous preferences, by comparing the beliefs of contributors with the true distribution of preferences. A trade‐off between preferences and beliefs arises if there is no individual who simultaneously has the highest preference type and the most pessimistic belief. In this case, there is a symmetric equilibrium, and multiple symmetric equilibria occur only if there are more than two preference types.     

Competition and coordination in experimental minority games

This work presents experimental results on a coordination game in which agents must repeatedly choose between two sides, and a positive fixed payoff is assigned only to agents who pick the minoritarian side. We conduct laboratory experiments in which stationary groups of five players play the game for 100 periods, and manipulate two treatment variables: the amount of information about other players’ past choices and the salience of information regarding the game history (i.e., the length of the string of past outcomes that players can see on the screen while choosing). Our main findings can be summarized as follows: aggregate efficiency in the game is in most cases significantly higher than the level corresponding to the symmetric mixed strategy Nash equilibrium. In addition, providing players with information about individual choices in the group does not improve aggregate efficiency with respect to when such information is absent. Displaying information about more rounds than just the previous one, on the other hand, seems to have a positive effect on aggregate efficiency. At the individual level, we find a stronger statistical relation between players’ current choices and their own past choices than between players’ choices and previous aggregate outcomes. In addition, the depth of the relation between present and past choices seems to be affected by the prompt availability of information about the game history. Finally, we detect evidence of a mutual co-adaptation between players’ choices over time that is partly responsible for the high level of efficiency observed.      

Confusion and learning in the voluntary contributions game

We use a limited information environment to assess the role of confusion in the repeated voluntary contributions game. A comparison with play in a standard version of the game suggests, that the common claim that decision errors due to confused subjects biases estimates of cooperation upwards, is not necessarily correct. Furthermore, we find that simple learning cannot generate the kind of contribution dynamics commonly attributed to the existence of conditional cooperators. We conclude that cooperative behavior and its decay observed in public goods games is not a pure artefact of confusion and learning.     

An Experimental Investigation of Excludable Public Goods

This paper extends the research on incentive compatible institutions for the provision of public goods by imposing a minimum contribution that must be met in order for an individual to enjoy the benefits of the public good. Excluding individuals who do not contribute at least the minimum transforms the linear n-player pure public goods game to an n-player coordination game with multiple, Pareto-ranked Nash equilibria. The experimental results show that exclusion increases contributions to the public good in most cases. However, an increase in contributions may not be sufficient to increase social welfare because there is a welfare cost to excluding individuals when the good is non-rival. Furthermore, exclusion can decrease both contributions and welfare in environments in which individuals fail to coordinate their contributions. The results are sensitive to the minimum contribution requirement and to the relative returns from the public and private alternatives.     

Kindness,confusion, or … ambiguity?

Other-regarding preferences or decision errors are the main explanations put forward to justify contributions exceeding the non-cooperative optimum in VCM games. An alternative rationale relies on ambiguity aversion. Ambiguity aversion increases the perceived marginal benefit of own contributions, which in equilibrium will exceed the Nash level. We present a series of experiments testing this hypothesis. To control for other-regarding preferences, we run a two-player game in which a human player plays with a virtual agent. Players are assigned either to a risky setting (known probabilities of opponent’s choices) or to an ambiguity setting (probabilities of opponent’s contribution are vague). Results show that ambiguity affects contributions. However, attitude to ambiguity appears to be affected by the location of the aggregate Nash optimum inside the decision space.     

Nash as an Organizing Principle in the Voluntary Provision of Public Goods: Experimental Evidence

Experiments are reported that add to the growing literature on the voluntary provision of public goods. Information conditions are manipulated to address whether early findings of above-equilibrium contributions to a public good are a result of complete information regarding the symmetry of the game. No significant information effect was found. Further, by examining designs with an interior Nash equilibrium, this research suggests that the nonzero contributions observed in the previous dominant strategy environments, where the prediction was a zero level of provision of the public good, were not simply transitional errors as the system converged to a boundary equilibrium.     

The Colonel Blotto game

In the Colonel Blotto game, two players simultaneously distribute forces across n battlefields. Within each battlefield, the player that allocates the higher level of force wins. The payoff of the game is the proportion of wins on the individual battlefields. An equilibrium of the Colonel Blotto game is a pair of n-variate distributions. This paper characterizes the unique equilibrium payoffs for all (symmetric and asymmetric) configurations of the players’ aggregate levels of force, characterizes the complete set of equilibrium univariate marginal distributions for most of these configurations, and constructs entirely new and novel equilibrium n-variate distributions.I am grateful to Jason Abrevaya, Dan Kovenock, James C. Moore, Roger B. Nelsen, and three anonymous referees for very helpful comments. A version of this paper was presented at the 2005 Midwest Economic Theory Meetings. This paper is based on the first chapter of my Ph.D. dissertation     

Rebate rules in threshold public good provision

This paper considers how six alternative rebate rules affect voluntary contributions in a threshold public-good experiment. The rules differ by (1) whether an individual can receive a proportional rebate of excess contributions, a winner-takes-all of any excess contributions, or a full rebate of one's contribution in the event the public good is provided and excess contributions exist, and (2) whether the probability of receiving a rebate is proportional to an individual's contribution relative to total contributions or is a simple uniform probability distribution set by the number of contributors. The paper adds to the existing experimental economics literature on threshold public goods by investigating both aggregate and individual demand revelation under the winner-take-all and random full-rebate rules. Half of the rules (proportional rebate, winner-take-all with uniform probability among all group members, and random full-rebate with uniform probability) provide total contributions that nearly equal total benefits, while the rest (winner-take-all with proportional probability, winner-take-all with uniform probability among contributors only, and random full-rebate with proportional probability) exceed benefits by over 30%. Only the proportional rebate rule is found to achieve both aggregate and individual demand revelation. Our experimental results have implications for both fundraisers and valuation practitioners.     

An experimental study of coordination and learning in iterated two-market entry games

Summary. Tacit coordination in large groups is studied in an iterated market entry game with complete information and multiple market capacities that are varied randomly from period to period. On each period, each player must decide independently whether to enter any of the markets, and if entering, which of the two markets to enter. Across symmetric and asymmetric markets, we find remarkable coordination on the aggregate level, which is accounted for by the Nash equilibrium, together with considerable individual differences in frequency of entry and decision rules. With experience, the decisions of most players converge to decision rules with cutoff values on the combined market capacity that determine whether or not to enter but not which of the two markets to enter. This latter decision is determined probabilistically by the differential market capacities. The aggregate and individual results are accounted for quite well by a reinforcement-based learning model that combines deterministic and probabilistic elements.     

Intragroup competition in public good games: The role of relative performance incentives and risk attitudes

We analyze a public good game (PGG) with intragroup competition in which, generally but not always, the dominant strategy is to not contribute; therefore, free riding is the unique Nash equilibrium, not achieving Pareto efficiency. We propose a PGG setup where subjects' contributions are rewarded with different individual returns following a rank‐order voluntary contribution mechanism. It is found that the resulting competition for a better return significantly increases contributions. This effect is sensitive to the salience of return differences rewarding higher contributions. Furthermore, the positive effect of return differences on contribution levels depends on an individual's return‐to‐risk sensitivity as elicited through an independent risk elicitation task.     

The impact of endowment heterogeneity and origin on contributions in best-shot public good games

Economists and psychologists have long argued the origin of wealth influences individual behavior. In a previous study (Cherry et al., 2005), we found the origin of endowment did not significantly affect behavior in linear public good games with summation contribution technology. In such games, however, both Nash behavior (everybody gives nothing) and social optimal behavior (everybody gives the entire endowment) call for symmetric levels of contributions. Results from this new study indicate that the origin of wealth might matter in more asymmetric situations, such as in a best-shot public good game with heterogeneous groups. Electronic Supplementary Material Supplementary material is available in the online version of this article at . JEL Classification C72, C92, H41     

Do binding agreements solve the social dilemma?

We investigate experimentally whether “binding agreements” can provide a solution to the social dilemma that arises in the presence of pure public goods. Signing a binding agreement can prevent players from free riding on the contributions to the public good. However, a well known theoretical result is that the outcome of the endogenous formation of agreements is not necessarily efficient. Our setting is a bargaining game in which agreements form sequentially. The individual level of contribution to the public good increases with the size of the coalition reaching an agreement and the global agreement is always the socially optimal structure. There are two equilibrium outcomes, the global agreement and an asymmetric structure, which consists of two coalitions of different sizes, the small one free riding on the contributions of the larger one. We run an experiment which lends force to the theoretical result that outcomes may be inefficient. However, subjects do not play Nash and the experimental outcome is, on average, even more inefficient than the theory predicts. Our analysis leads to the conclusion that different types of behaviour co-exist.     

Circular reasoning. Forbonnais and the intricate history of circular flow analysis in the 1750s

Abstract

Circular flow analysis in mid-18th century France is normally associated with the writings of François Quesnay. From the early 1750?s, however, François Véron de Forbonnais developed a distinct theory of circulation in then well-known contributions to the Encyclopédie and his Elémens du commerce of 1754. This article argues that like Quesnay, Forbonnais was in part inspired by Cantillon’s Essay on the Nature of Trade in General. But while Quesnay gave original developments to the real aspects of Cantillon’’s analysis of circulation, Forbonnais focussed on developing monetary aspects, including arguments for the ‘non-neutrality’ of money and an original theory of the money interest rate.     

Non-Laplacian beliefs in a global game with noisy signaling

In standard global games, individual behavior is optimal if it constitutes a best response to agnostic—Laplacian—beliefs about the aggregate behavior of other agents. This paper considers a standard binary action global game augmented with noisy signaling by an informed policy-maker and shows that in this game, equilibrium beliefs depart in quite stark ways from the Laplacian benchmark. In the limit as signals become arbitrarily precise, so that all fundamental uncertainty is removed (leaving only strategic uncertainty), the equilibrium beliefs of the marginal individual concerning the aggregate action collapse to a discrete Bernoulli distribution, giving probability mass only to the polar extreme outcomes. By contrast in the underlying standard global game the marginal individual believes the aggregate action has a continuous uniform distribution, giving equal likelihood to all possible outcomes.     

Voluntary Contributions to a Mutual Insurance Pool

We study mutual‐aid games in which individuals choose to contribute to an informal mutual insurance pool. Individual coverage is determined by the aggregate level of contributions and a sharing rule. We analyze theoretically and experimentally the (ex ante) efficiency of equal and contribution‐based coverage. The equal coverage mechanism leads to a unique no‐insurance equilibrium while contribution‐based coverage develops multiple equilibria and improves efficiency. Experimentally, the latter treatment reduces the amount of transfers from high contributors to low contributors and generates a “dual interior equilibrium.” That dual equilibrium is consistent with the co‐existence of different prior norms which correspond to notable equilibria derived in the theory. This results in asymmetric outcomes with a majority of high contributors less than fully reimbursing the global losses and a significant minority of low contributors less than fully defecting. Such behavioral heterogeneity may be attributed to risk attitudes (risk tolerance vs risk aversion) which is natural in a risky context.     

Incentives in market games with asymmetric information: the core

Summary. This paper examines the ex ante core of a pure exchange economy with asymmetric information in which state-dependent allocations are required to satisfy incentive compatibility. This restriction on players' strategies in the cooperative game can be interpreted as incomplete contracts or partial commitment. An example is provided in which the incentive compatible core with nontransferable utility is empty; the game fails to be balanced because convex combinations of incentive compatible net trades can violate incentive compatibility. However, randomization of such strategies leads to ex post allocations which satisfy incentive compatibility and are feasible on average. Hence, convexity is preserved in such a model and the resulting cooperative games are balanced. In this framework, an incentive compatible core concept is defined for NTU games derived from economies with asymmetric information. The main result is nonemptiness of the incentive compatible core. Received: December 26, 2001; revised version: June 11, 2002 RID="*" ID"*" This work was financed, in part, by contract No 26 of the programme “P?le d'attraction interuniversitaire” of the Belgian government, and, in part, by research grant SBR93-09854 from the U.S. National Science Foundation. Much of my thinking about this topic was developed during a wonderful visit to CORE for the 1991–1992 academic year (on sabbatical from the University of Pennsylvania). This paper was originally circulated in December 1991 as CARESS Working Paper #91-38, Center for Analytic Research in Economics and the Social Sciences, Department of Economics, University of Pennsylvania and in February 1992 as CORE Discussion Paper 9221, Center for Operations Research and Econometrics, Université Catholique de Louvain, Louvain-la-Neuve, Belgium. RID="*" ID="*" At the very start of my research, Jean-Fran?ois Mertens was almost a co-author. Fran?ois Forges provided detailed comments at a later stage, during my visit to THEMA, Université Cergy-Pontoise, in Spring 1997. They are entitled to the customary disclaimer.     

Campaign Advertising and Voter Welfare

This paper investigates the role of campaign advertising and the opportunity of legal restrictions on it. An electoral race is modelled as a signalling game with three classes of players: many voters, two candidates, and one interest group. The group has non–verifiable insider information on the candidates' quality and, on the basis of this information, offers a contribution to each candidate in exchange for a favourable policy position. Candidates spend the contributions they receive on non–directly informative advertising. This paper shows that: (1) a separating equilibrium exists in which the group contributes to a candidate only if the insider information about that candidate is positive; (2) although voters are fully rational, a ban on campaign advertising can be welfare–improving; and (3) split contributions may arise in equilibrium (and, if they arise too often, they are detrimental to voters).     

Sustaining cooperation in social dilemmas: Comparison of centralized punishment institutions

This study investigates two centralized punishment institutions for a linear public goods game. These institutions require a certain contribution level and sanction under-contributing players. The two differ in who, among those who do not meet this requirement, receive sanctions. In one institution, all violators are sanctioned, and in the other, only the worst violator(s) is sanctioned. Theoretically, the public goods game of the latter institution yields contributions equal to or greater than that of the former institution with the same requirement and sanction level. The results of an experiment support this theoretical prediction. However, there is a discrepancy between the theory and laboratory observations in that the institution with the theoretically optimal requirement did not yield the highest profit.     

“One Man,One Dollar”? Campaign contribution limits,equal influence,and political communication

Arguably the most important campaign finance regulations in U.S. federal elections are limits imposed on individual campaign contributions. One of the principal arguments in support of these contribution limits has been that they equalize the influence of individual donors and thereby cause candidates' aggregate financial resources to more accurately reflect public support. I construct a formal model to evaluate this argument. The analysis shows that a necessary condition for it to apply is that a candidate's reliance on large contributions is negatively related to voter-preferred characteristics which cannot be credibly revealed through campaign advertisements. Using data on elections to the House of Representatives between 1992 and 2000, I find no evidence that such a relationship exists. This result casts doubt on the equalization argument in support of campaign contribution limits.     

‘Expressive’ obligations in public good games: Crowding-in and crowding-out effects

We study individual contributions in a repeated linear public good experiment in which, in each period, subjects are required to contribute a minimum amount and face a certain probability of being audited. Audited subjects who contribute less than the required amount are convicted to pay the difference between the obligation and the voluntary contribution. We investigate the ‘expressive’ force of the obligations. While at early stages subjects contribute the minimum level, with repetition contributions decline below the required amount. We observe that expressive obligations exert a rather robust crowding-out effect on voluntary contributions as compared to a linear public good game. Crowding-out is stronger when payments collected through the auditing procedure are distributed to subjects rather than when they are a deadweight loss.