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.     

A folk theorem for minority games

We study a particular case of repeated games with public signals. In the stage game an odd number of players have to choose simultaneously one of two rooms. The players who choose the less crowded room receive a reward of one euro (whence the name “minority game”). The players in the same room do not recognize each other, and between the stages only the current majority room is publicly announced. We show that in the infinitely repeated game any feasible payoff can be achieved as a uniform equilibrium payoff, and as an almost sure equilibrium payoff. In particular we construct an inefficient equilibrium where, with probability one, all players choose the same room at almost all stages. This equilibrium is sustained by punishment phases which use, in an unusual way, the pure actions that were played before the start of the punishment.     

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.     

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.     

Garbling of signals and outcome equivalence

In a game with incomplete information players receive stochastic signals about the state of nature. The distribution of the signals given the state of nature is determined by the information structure. Different information structures may induce different equilibria.Two information structures are equivalent from the perspective of a modeler, if they induce the same equilibrium outcomes. We characterize the situations in which two information structures are equivalent in terms of natural transformations, called garblings, from one structure to another. We study the notion of ‘being equivalent to’ in relation with three equilibrium concepts: Nash equilibrium, agent normal-form correlated equilibrium and the belief invariant Bayesian solution.     

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.     

Cooperative vs non-cooperative truels: little agreement, but does that matter?

It is well-known that non-cooperative and cooperative game theory may yield different solutions to games. These differences are particularly dramatic in the case of truels, or three-person duels, in which the players may fire sequentially or simultaneously, over one round or n rounds. Representative solution concepts (Nash and subgame-perfect equilibrium; two notions of core) are compared, and little agreement is found among them. Although it might be desirable to subsume these different solutions within a common framework, such unification seems unlikely since they are grounded in fundamentally different notions of stability.     

Technology Strategy And Product Diversity

This paper considers a three-stage game of a differentiated oligopoly: firms first make their entry decisions, then they choose production technologies and in the third stage of the game they decide product prices. The technology choice can be understood as selecting one from a pool of those recently available as well as developing a new technology through innovative activities. The resulting market equilibrium is then compared with the social optimum. The main conclusions are that a monopolistically competitive market will typically undersupply both product variety and production scale. R&D competition in a free entry differentiated oligopoly will lead to insufficient R&D investment at firm and industry levels.     

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. The dissertation is composed of three parts and six chapters. The first chapter expresses the various theoretical mechanisms of production of a public good, while the second one presents an overview of the experimental literature using voluntary contribution mechanisms. The second part carries on the introduction of an interior solution in a public good game in order to distinguish an explanation of overcontribution in terms of mistakes or strategies. While chapter three presents the most important works in literature that use an interior solution, the fourth chapter constitutes a personal contribution consisting in an experiment with an interior optimum. Our main result is that individuals contribute a constant part of their social optimum and that overcontribution is not explained by error. We test then the simple learning model R.L. using the observed data on the aggregate level. This model predicts well the observed behaviour. The third part is composed of two experiments where the environment of players is modified. We introduce in chapter five promises as cheap talk and find that they increase contributions at the aggregate level. In chapter six, various conditions of information on individual contributions are tested. The parameter tested is the level of information on “neighbours” contributions given to players. One of the treatments presents full information about individual contributions of the members of the group, while this information is incomplete in the other treatments. Our results show that information has no effect on the level of contribution. We simulate then the EWA learning model both at the aggregate and the individual levels and compare the simulated data to the experimental one. These simulations predict a level of contribution that is higher that the one observed in the experiment. JEL Classification C91, C92, H41 Dissertation Committee: Alan Kirman (Ph.D. Advisor), Université d’Aix-Marseille III Marie-Claire Villeval (Chair), GATE, Lyon, France Jordi Brandts, Universitat Autonoma Barcelona, Spain Charles Noussair, Emory University, Alanta, GA, U.S.A. Sylvie Thoron, GREQAM & Université du Var, France Marc Willinger, Université de Montpellier I, France     

Existence of equilibrium and stratification in local and hierarchical Tiebout economies with property taxes and voting

Summary. This paper present the first fully closed general equilibrium model of hierarchical and local public goods economies with the following features: (i) multiple agent types who are endowed with both some amount of private good (income) and a house, who are mobile between houses and jurisdictions, and who vote in local and national elections; (ii) multiple communities that finance a local public good through property taxes which are set in accordance with absolute majority rule; and (iii) a national government that produces a national public good financed through an income tax whose level is determined through majority rule voting. In contrast to previous models, no overly restrictive assumptions on preferences and technologies are required to prove the existence of an equilibrium in the presence of property taxation and voting. Thus, the existence of an equilibrium is proved without any of the major restrictions used in the past, and sufficient conditons for stratification of agents into communities based on their public good preferences and their wealth levels are found. This model lays the groundwork for a positive applied analysis of local public finance and intergovernmental relations. It furthermore builds the foundation for the first parameterized computable general equilibrium model of local public goods and fiscal federalism. Received: February 1, 1996; revised version August 9, 1996     

Private provision of a discrete public good: efficient equilibria in the private-information contribution game

We study the voluntary provision of a discrete public good via the contribution game. Players independently and simultaneously make nonrefundable contributions to fund a discrete public good, which is provided if and only if contributions cover the cost of production. We characterize nonconstant continuous symmetric equilibria, giving sufficient conditions for their existence. We show the common normalization by which players’ values are distributed over [0, 1] is not without loss of generality: if the distribution over this interval has continuous density f with f(0) >  0, then no (nonconstant) continuous symmetric equilibrium exists. We study in detail the case in which players’ private values are uniformly distributed, showing that, generically, when one continuous equilibrium exists, a continuum of continuous equilibria exists. For any given cost of the good, multiple continuous equilibria cannot be Pareto ranked. Nevertheless, not all continuous equilibria are interim incentive efficient. The set of interim incentive efficient equilibria is exactly determined. The authors thank Manfred Dix, George Mailath, Andrew Postlewaite, and an anonymous referee for their comments.     

Demand fluctuations and capacity utilization under duopoly

Summary.  This paper studies the impact of uncertain demand on firms’ capacity decisions when they operate in an oligopolistic environment. We define a two-stage game where firms choose capacity in the first stage without knowing which state of Nature is going to realize, and output levels in the second, knowing which state is realized. We prove the existence of a symmetric subgame perfect equilibrium at which firms are in excess capacity compared with the capacity they would choose in the Cournot certainty equivalent game. Received: May 17, 1996; revised version July 31, 1996     

Network architecture, salience and coordination

This paper reports the results of an experimental investigation of dynamic games in networks. In each period, the subjects simultaneously choose whether or not to make an irreversible contribution to the provision of an indivisible public good. Subjects observe the past actions of other subjects if and only if they are connected by the network. Networks may be incomplete so subjects are asymmetrically informed about the actions of other subjects in the same network, which is typically an obstacle to the attainment of an efficient outcome. For all networks, the game has a large set of (possibly inefficient) equilibrium outcomes. Nonetheless, the network architecture makes certain strategies salient and this in turn facilitates coordination on efficient outcomes. In particular, asymmetries in the network architecture encourage two salient behaviors, strategic delay and strategic commitment. By contrast, we find that symmetries in the network architecture can lead to mis-coordination and inefficient outcomes.     

Endogenous transfers in the Prisoner's Dilemma game: An experimental test of cooperation and coordination

We test a two-stage compensation mechanism for promoting cooperation in Prisoner's Dilemma games. Players first simultaneously choose binding non-negative amounts to pay their counterparts for cooperating, and then play the induced game knowing these amounts. In our games, all payment pairs consistent with mutual cooperation in subgame-perfect equilibrium transform these games into coordination games, with both mutual cooperation and mutual defection as Nash equilibria in the second stage. When endogenous transfer payments are not permitted, cooperation is much less likely. Mutual cooperation is most likely when the (sufficient) payments are identical, and it is also substantially more likely with payment pairs that bring the mutual-cooperation payoffs closer together. Both the Fehr–Schmidt and Charness–Rabin models predict that transfers that make final payoffs closer are preferred; however, they do not explain why equal transfers are particularly effective. Transfers are also effective in sustaining cooperation even when they are imposed and not chosen.     

Buchanan and public finance: The tennessee years

James Buchanan’s views on public finance have already been analyzed and they are quite well known, as are their origins and roots. However, nothing has ever been said about why Buchanan chose public finance in the first place. The first goal of this paper is to show that Buchanan had made this choice before arriving at Chicago. We show how Carlton C. Sims and Charles P. White influenced him. We also show, by analyzing Buchanan’s M.A. thesis, that he was not only interested in public finance but was also primarily concerned by ethical questions and defended a bureaucratic centralized solution to solve the problem he was discussing – how to share the benefits collected from a gasoline tax among Counties. This helps to understand that Buchanan did not choose to study public finance to learn how to fight government intervention. Quite the contrary: it was to legitimate it. Second, we also demonstrate that a lot of the ideas that will matter for Buchanan in his career – the importance of ethics and the principle of an equal treatment for equals, the need to link taxes to benefits, the importance to adapt the scale of provision of a public good to the type of public good – were already present in this first work.

     

Preemption in a real option game with a first mover advantage and player-specific uncertainty

In this paper a two-player real option game with a first-mover advantage is analyzed, where payoffs are driven by a player-specific stochastic state variable. It is shown that there exists an equilibrium which has qualitatively different properties from those in standard real option games driven by common stochastic shocks. The properties of the equilibrium are four-fold: (i) preemption does not necessarily occur, (ii) if preemption takes place, the rent-equalization property holds, (iii) for almost all sample paths it is clear ex-ante which player invests first, and (iv) it is possible that both players invest simultaneously, even if that is not optimal. It is argued from simulations that real option games with a common one-dimensional shock do not provide a good approximation for games with player-specific uncertainty, even if these are highly correlated.     

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.     

Mixed markets and crime

This paper specifies and solves a two-stage, game theoretic model of a mixed market for crime control. In the first stage of the model, private targets and the government choose levels of policing. In the second stage, criminals choose targets and the severity of the crimes that they commit.The paper's key results are as follows. First, private policing can both divert crime to targets that lack private protection and also increase the severity of the crime that these less-protected targets suffer. Second, an increase in private policing reduces the aggregate expenditure on traditional policing. This is an instance of a political incentive externality, where private policing affects the objective function of the government. Specifically, it reduces the level of traditional policing that is consistent with the Samuelson condition for efficient provision of a public good. Third, the substitution of private for public policing carries with it a change in the technology of policing. In effect, private policing leads to a shift from enforcement and punishment towards monitoring and target hardening. This, in turn, may lead to an increase in the severity of crime. Fourth, the mixed policing equilibrium is inefficient, and, in some situations, mixing may reduce the utility of all targets.     

Equilibrium binding agreements under diverse behavioral assumptions

Summary. This paper extends the work of Ray and Vohra [3]. It ascertains which partitions of players will emerge and what actions will these players choose under each partition, when they can sign binding agreements and their actions have externalities. The emphasis, however, is placed on situations with multiple outcomes and how agents behave in the presence of such multiplicity. In particular, a deviating coalition considers all the likely outcomes that may prevail upon its deviation, and selects (if possible) a subset of them. Three augmentations of Ray and Vohra's [3] solution concept are defined, capturing three distinct behavioral assumptions. Efficiency of and the relation between the three notions are discussed. Received: October 9, 2001; revised version: April 22, 2002 RID="*" ID="*" I wish to thank Licun Xue, Joseph Greenberg and the participants of PET 2000 for very helpful suggestions. I am indebted to an anonymous referee for his/her valuable comments. The paper has been previously circulated under the title Binding Agreements.     

Profitability of price and quantity strategies in a duopoly with vertical product differentiation

Using a model according to Mussa and Rosen (1978) and Bonanno and Haworth (1998) we consider a sub-game perfect equilibrium of a two-stage game in a duopolistic industry in which the products of the firms are vertically differentiated. In the industry, there are a high quality firm and a low quality firm. In the first stage of the game, the firms choose their strategic variables, price or quantity. In the second stage, they determine the levels of their strategic variables. We will show that, under an assumption about distribution of consumers' preference, we obtain the result that is similar to Singh and Vives (1984)' proposition (their Proposition 3) in the case of substitutes with nonlinear demand functions. That is, in the first stage of the game, a quantity strategy dominates a price strategy for both firms. Received: April 23, 1999; revised version: May 31, 2000