Continuous-Time Public Good Contribution Under Uncertainty

Insights from sexual selection and costly signalling theory suggest that competition for females underlies men's public good contributions. We conducted two public good experiments to test this hypothesis. First, we found that men contributed more in the presence of an opposite sex audience, but there was no parallel effect for the women. In addition, men's public good contributions went up as they rated the female observer more attractive. In the second experiment, all male groups played a five round public good game and their contributions significantly increased over time with a female audience only. In this condition men also volunteered more time for various charitable causes. These findings support the idea that men compete with each other by creating public goods to impress women. Thus, a public good is the human equivalent of a peacock's tail.

Before coming to the discussion of stochastic integrals, it will be useful to introduce some terminology from the general theory of stochastic processes. Some of the concepts have been defined earlier in these notes. We shall repeat the definitions for the sake of completeness.KeywordsSample PathLocal MartingalePredictable ProcessOptional SamplingMartingale Convergence TheoremThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

K. Ito invented his famous stochastic calculus on Brownian motion in the 1940s. In the 1960s and 1970s, the “Strasbourg school,” headed by P.A. Meyer, developed a modern theory of martingales, the general theory of stochastic processes, and stochastic calculus on semimartingales. It turned out soon that semimartingales constitute the largest class of right continuous adapted integrators with respect to which stochastic integrals of simple predictable integrands satisfy the theorem of dominated convergence in probability. Stochastic calculus on semimartingales not only became an important tool for modern probability theory and stochastic processes but also has broad applications to many branches of mathematics, physics, engineering, and mathematical finance.

d1. Filip Lundberg's works on risk theory were all written at a time when no general theory of stochastic processes existed, and when collective reinsurance methods, in the present day sense of the word, were entirely unknown to insurance companies. In both respects his ideas were far ahead of his time, and his works deserve to be generally recognized as pioneering works of fundamental importance.

We model a stream of cash flows as an optional stochastic process, and value the cash flows by using a continuous and strictly positive linear functional. By applying a representation theorem from the general theory of stochastic processes we are able to study this valuation principle, as well as properties of the stochastic discount factor it implies. This approach to valuation is useful in the non-presence of a financial market, as is often the case when valuing cash flows arising from insurance contracts and in the application of real options.

A laboratory study of voluntary public goods provision with imperfect monitoring and communication

There has been substantial recent interest in determining why there is cooperation in public goods experiments even in environments that provide all subjects with the incentive to free ride (see e.g., John O. Ledyard, 1995). Theories used to explain such cooperation generally posit either that subjects are “confused” in the sense that they make errors or do not understand the game’s incentives, or that subjects contribute due to social factors such as altruism and reciprocity. Although several authors have pointed out the importance of distinguishing between these alternatives, the roles that confusion and social motives play in determining public contributions remain poorly understood. This paper provides new evidence on the way that confusion and social motives determine contributions in public goods games by reporting data from experiments that use a new design with the Voluntary Contribution Mechanism (VCM). Two important and often replicated findings in the experimental public goods literature are (1) that subjects’ public contributions are much greater than predicted by standard economic theories of free-riding and (2) that these contributions decay over the course of multiple-round games (see e.g., Douglas D. Davis and Charles A. Holt, 1993). Models that employ social factors to explain cooperation and its decay usually assume that subjects are motivated by altruism, reciprocity, or fairness (see e.g., Andreoni, 1990; Rachel T. A. Croson, 1998; Anna Gunthorsdottir et al., 2001). It has been argued, for instance, that subjects make contributions in order to elicit like contributions from reciprocators in subsequent rounds and that decay in public contributions might result from “frustrated attempts at kindness” (Andreoni, 1995 p. 892). Specifically, because there is generally heterogeneity in the willingness to contribute to the public good, initially cooperative players will likely reduce their public contributions after being grouped with relatively low contributors. In contrast, confusion theories postulate that players make public contributions either in error or because they do not understand how to pursue their self-interest. These theories argue that high initial contributions decay primarily because subjects gradually come to understand the game’s incentives. Recently, Andreoni (1995) conducted an interesting series of experiments in the first and, to our knowledge, only effort to discriminate between these competing theories of cooperative play. He provides two reasons that doing this is important. The first is that knowing the relative importance of confusion and social motives in generating cooperative decay can provide a useful guide to future research. While Andreoni argues that such knowledge could be used to inform research on learning models, note also that to the extent confusion is found to be important, shedding light on the way different sorts of instructions affect confusion could help to improve pedagogics. A second compelling reason Andreoni gives is that the outcomes of experiments designed to test theories of social giving are difficult to interpret if confusion is a primary source of cooperation. * Houser: Department of Economics and Economic Science Laboratory, University of Arizona, Tucson, AZ 85721; Kurzban: Economic Science Laboratory, University of Arizona, Tucson, AZ 85721. We thank Mark Isaac, Kevin McCabe, David Porter, Vernon Smith, Bart Wilson, seminar participants at the University of Arizona, and two anonymous referees for valuable comments on this research. The authors gratefully acknowledge the research support of fellowships from the International Foundation for Research in Experimental Economics. This research was supported by Russell Sage Foundation Grant No. 98-00-01. The authors are responsible for any errors. 1 See, for example, James Andreoni (1995), Martin Sefton and Richard Steinberg (1996), and Thomas R. Palfrey and Jeffrey E. Prisbrey (1997). 2 This paper focuses on only standard linear games in which to contribute zero to the public good is the dominant strategy.

Cross-border externalities and cooperation among representative democracies

Public Goods, Merit Goods, and the Relation Between Private and Government Consumption

Experience from climate policy suggests that full cooperation among all countries is not a likely outcome. In this paper we therefore consider the case where only members of a subgroup of countries cooperate by reciprocally matching their public good contributions. In a two‐stage game, matching rates are set at stage 1 then national contributions are chosen at stage 2. In the case of small coalitions, negative matching may result in the subgame‐perfect equilibrium that decreases global public good provision and outsiders' welfare. Moreover, a growing number of countries may paradoxically entail a reduction of equilibrium public good supply.

In a public goods game, while cooperators need to make contributions, defectors can take a free ride after the realization of the public good. The Nash equilibrium in this game is simply zero contribution from all the players. A conventional approach to encourage cooperation and achieve the public good is using rewards to compensate the difference between the cooperators’ and the defectors’ payoffs. However, the public good may not be realized due to the uncertainty in the game, and the conventional way could underestimate the required rewards to achieve the public good. On the other hand, public good did realize in human history when people cannot survive from a natural disaster, such as a big flood, without cooperating to build a solid embankment, and most of them are willing to choose cooperation without rewards. The realization of the public good leads to the reduction of the defection cost and the contribution, which has a potential to encourage the players’ cooperation. Then the conventional method may overestimate the necessary rewards to realize the public good. In this paper, a public goods game is employed to model the interaction among boundedly rational players with the rewards for large-scale cooperation, and a behavioral game-theoretic approach is developed to describe their decision making processes with the consideration of the risk and impact of public good in the game. It turns out that the conventional rewards to achieve the large-scale cooperation can be reduced for a favorable group of the players.

ObjectiveIrrelevant information, such as one's Social Security number, has been shown to influence decisions in experiments. The objective of this article is to investigate this anchoring effect with respect to the randomly assigned participant number in an economic experiment.MethodsThe game is a public good contribution game. In one session, participants write their participant number on their decision sheet while this number is printed on the decision sheet in the remaining sessions. Anchoring with respect to participant number suggests that those with higher participant numbers contribute more than those with low participant numbers.ResultsI find no evidence of anchoring. In each session, the mean contribution is not significantly different across different partitioning of the subjects according to participant numbers.ConclusionsSocial scientists using experimental methods in research are unlikely to bias results by assigning participant numbers when these numbers coincide with the decision space of the games played.

This paper theoretically and experimentally investigates the impact of information provision on voluntary contributions to a linear public good with an uncertain marginal per-capita return (MPCR). Uninformed donors make contribution decisions based only on the expected MPCR (i.e. the prior distribution), while informed donors observe the realized MPCR before contributing. The theoretical analysis predicts that the impact of information on average contributions crucially depends on the generosity level of the population, modeled as a stochastic change in the pro-social preferences. In particular, a less generous population increases contributions substantially in response to good news of higher than expected MPCR and reduces contributions relatively little in response to bad news of lower than expected MPCR. The opposite is true for a more generous population. Thus, the theory predicts that information provision increases (reduces) average contributions when the population is less (more) generous. This prediction finds strong support in a two-stage lab experiment. The first stage measures subjects’ generosity in the public good game using an online experiment. The resulting measure is used to create more and less generous groups in the public good lab experiment, which varies the information provided to these groups in the lab. The findings are in line with the theoretical predictions, suggesting that targeted information provision to less generous groups may be more beneficial for public good contributions than uniform information provision.

significant impact on intraurban business location decisions. However, he also notes that intrametropolitan property tax differentials may equal as much as 10% of a firm's profits. In these cases, one might expect that fiscal variables would affect the intraurban location decision of firms. Oakland also suggests that most studies which have examined intraurban industry location have inappropriately treated the firm's business location decision only from the demand side. Specifically, the firm's demand for space or site choice is presumed to be unrestricted by zoning or other exclusionary practices of local governments. Recent research by Fischel (1975) and Fox (1978) suggests that some local governments rationally exclude firms from locating within their boundaries or supply no industry sites. They argue that residents of communities derive utility from environmental quality, public goods and private goods. The presence of industry in a jurisdiction presumably leads to more increases in tax revenues than in expenditures, and the presence of industry permits the consumption of more local public and private goods at the expense of environmental quality. Communities with stronger preferences for environmental quality will require higher ax revenues from firms or larger increases in private and public goods in order to accept losses in environmental quality. Some communities with very strong preferences for environmental quality may want to increase their property tax rate on firms to adequately compensate them for losses of environmental quality. However, since the property tax rate must be applied uniformly to residential and nonresidential property, residents are essentially constrained to trade increased public goods for losses in environmental quality and losses in private consumption. If communities find either of these tradeoffs unacceptable, then they are likely to zone very little or no land for industrial and commercial use. Thus, Oakland argues, the inclusion of communities that zoneout firms in an analysis of firm site choice ma lead to biased estimation results, especially with regard to fiscal variables. A complete analysis of the location of firms should be based on a demand for

Interpreting a stochastic monetary growth model as a modified social planner's problem