On delays in project completion with cost reduction: an experiment.

• Author: Sarkar, Shubhro

1. Introduction

   The focus of this article is on the effects of externalities on delays in completion of a public project. It is often the case that the individual cost of contribution for a public good decreases as the number of contributions already made increases. Allegations of corruption against public officials can be viewed as a public project with these features. If the corrupt official can be identified and removed, everyone receives some benefit, but this can happen only if a sufficient number of individuals are willing to implicate the official. The person bringing the first allegation not only faces the social stigma that such allegations could bring, but potentially, could also have to deal with retaliation from the person or parties against whom such allegations have been made. As more allegations are brought forward, the private cost of bringing similar allegations is reduced because these allegations become more credible. Thus, individuals have an incentive to free ride on the contributions made by others. Individuals with access to information that might bring the official to justice face a dilemma: They could contribute now with the hope that the official is brought to justice sooner rather than later, or they could choose to wait, hoping others contribute first. This process of whistle blowing is only one example of a public project with cost reduction; another example includes early adoption of a new technology standard.

   We construct a multiperiod voluntary contributions public project model designed to capture the vital features of the problem described above. Agents can choose to make an irrevocable, binary contribution at any point of time before a contribution deadline. The cost of contribution decreases as the number of prior contributors increases. If a sufficient number of contributions is received, the project is completed, and all agents get a benefit. The benefit of the project decreases over time. If the project is not completed before the contribution deadline, none of the agents receive any benefit, but agents who chose to contribute still incur their cost of contribution.

   When there is no cost reduction, there is a Pareto-dominant, subgame perfect equilibrium where the project is completed without delay. We show that as long as cost reduction is sufficiently large, there is no pure-strategy subgame perfect equilibrium that does not involve delay. Although all equilibria must result in completion of the project, the effect of cost reduction is to lead to excessive delay in project provision and, because benefits decline over time, inefficient outcomes. Both with and without cost reduction, there exist multiple pure-strategy subgame perfect Nash equilibria. We design an experiment based on the same theoretical framework, where we consider two treatments, one with and one without cost reduction. The objective of the experiment was to determine whether the actions of human participants are consistent with the theoretical predictions of the model. Because there are many possible equilibria, the experiment might provide insights into which outcomes are more likely. Specifically, we designed the experiment in the hope of answering the following questions:

   (1) Does cost reduction result in significantly more delay?

   (2) Is the project completed under both conditions?

   (3) In both treatments, do the players manage to coordinate on Pareto-superior equilibria?

   We find that the project is completed in the treatment with cost reduction with more delay than it is in the treatment without cost reduction. We also find that the Pareto-dominant subgame perfect outcome is played frequently in both treatments. However, the players do not appear to completely overcome the significant coordination problems prevalent in this setup. For example, the actual project completion rates are significantly below what might be expected. We hypothesize that coordination problems are exacerbated in this model because of the highly asymmetric payoffs in pure-strategy equilibria.

   Because choices in laboratory experiments appear inherently mixed, we solve for the symmetric mixed-strategy subgame perfect Nash equilibria for both the games with and without cost reduction and find that observed choice frequencies appear to be similar to those predicted by the purely mixed-strategy subgame perfect Nash equilibrium in the case with cost reduction, such that it is possible that mixed strategies were used by the players in that game. Most players were also observed to follow a strategy of rotation, according to which each player chose to contribute about 60% of the time. While analyzing individual behavior, we find that although contribution rates did not vary significantly over the two treatments, there is evidence that suggests that players chose to contribute with more delay and to contribute more frequently in histories where one or two prior contributions were already made in the treatment with cost reduction than without cost reduction. Three contributions were the modal choice in the data. How groups managed to coordinate on three contributions is a fundamental question. We find that such coordination rates varied widely across the groups, and we discuss features that account for such (un)successful coordination.

   The article is organized as follows. In section 2 we discuss some related literature. In section 3 we present the model and our theoretical results. The design of the experiment is described in section 4. We present the experiment results in section 5 and conclude in section 6.

2. Related Literature

   There is a substantial theoretical and experimental literature on public projects with binary contributions. A review of the extensive experimental literature on public goods provision is provided by Ledyard (1995).

   A series of papers by Palfrey and Rosenthal (1984, 1988, 1991, 1994) examine a model of public project completion with binary contributions. They examine the model under complete and incomplete information and examine human participants' behavior in the laboratory under a number of treatments. Their models differ from ours in several key aspects. First, contributions are made simultaneously, so dynamics are not considered, and, second, in most cases, each agent's cost of contribution is private information.

   Seminal works by Schelling (1978) and Olson (1982) recognized that dynamics may play a vital role in problems of collective action. Bliss and Nalebuff (1984) develop a model where the public good is provided if one individual makes a contribution. With a finite population, equilibrium involves inefficient waiting, but as the population size approaches infinity, the inefficiency vanishes in the sense that the public good is provided almost immediately and by the lowest-cost contributor. Our model differs from Bliss and Nalebuff in that multiple contributions may be required for completion allowing for cost reduction. We also examine the situation under the assumption of complete information. With complete information, the Bliss and Nalebuff model is a special case of our model without cost reduction, and we show that there exists an equilibrium without delay. Gradstein (1992) examines a binary contribution model where the public benefit is strictly increasing in the number of contributions. Gradstein finds that when two contribution periods are allowed, inefficiency in the form of delay and underprovision may persist even for infinite populations. Marx and Matthews (2000), on the other hand, show that in an environment where players can make multiple contributions before a contribution horizon is reached but have incomplete information about the actions of the other players, perfect Bayesian equilibria exist that essentially complete the project. They do this by constructing equilibria involving punishment strategies where future contributions depend upon the observed level of previous contributions. Duffy, Ochs, and Vesterlund (2007) experimentally examine the Marx and Matthews model and find that sequential play not only increases average contributions, but also increases the probability that groups reach the threshold level of the public good. Although Duffy et al. focus on the potential benefits of sequential giving, our experiment highlights the potential coordination pitfalls that sequential contributions might create.

   Our approach differs most substantially from the literature mentioned above on two key dimensions: First, our model has the twin features of cost reduction as other players make contributions and benefit reduction as players fail to complete the project sooner rather than later. These features are both likely to be prevalent in many public project settings and can make the efficiency issues of public project provision more salient. Second, although almost all of these models utilize an incomplete information setting, we assume complete information. Under these other models, cost differences are determined exogenously by nature. Although this has the advantage of allowing one to identify a single, unique equilibrium, they potentially abstract from important coordination issues. In our model with complete information, the actual costs of each player are determined endogenously by the order of contribution. This creates a complex coordination problem that we believe is likely to be prevalent in many real world public project applications and, because it involves potential coordination between different equilibria, is ideally suited to experimental examination.

3. The Model

   We begin the theoretical analysis by describing a generalized version of the discrete-time, finite horizon model with n players. We assume that each player i [member of] {1, ..., n}, must choose whether and when to contribute for a public goods project during a contribution horizon lasting T periods. In each period t, player i must make an irreversible decision to either contribute (C) or not to...