Mind the Gap: Crowdfunding and the Role of Seed Money

We analyze voluntary private contributions to public goods and the role seed money plays in signaling the public good's quality to potential subsequent contributors. We present a theoretical model and analyze two sets of naturally occurring data from crowdfunding platforms. After developing the theoretical background, we find statistically significant switch points that distinguish between seed contributions and subsequent contributions. A positive change in contribution behavior after the switch suggests an increase in the perceived value of the public good. We find that the signal comprises the number of contributors and the average contribution (as a proportion of the targeted goal). Copyright © 2015 John Wiley & Sons, Ltd.     

Stackelberg leadership and transfers in private provision of public goods

We consider transfers in a Stackelberg game of private provision of a public good. It turns out that the agent who is the follower in the process of making voluntary contributions to a public good may have an incentive to make monetary transfers to the Stackelberg leader even in a situation where neither has a comparative advantage in making contributions to the public good. The Stackelberg leader is willing to accept such transfers if the actual contribution game is fully non-cooperative because the transfer generates a Pareto superior outcome. If the contributions in the Stackelberg equilibrium is the threat point of a possible cooperative Nash bargaining game, the Stackelberg leader will refuse to accept the transfer if she can. Received: 30 June 1995 / Accepted: 18 February 1997     

Threshold uncertainty in discrete public good games: an experimental study

A discrete public good is provided when total contributions equal or exceed the contribution threshold. Recent theoretical work shows that an increase in threshold uncertainty will increase (decrease) equilibrium contributions when the public good value is sufficiently high (low). In an experiment designed to test these predictions, I find only limited verification of the prediction. Using elicited beliefs data to represent subjects’ beliefs, I find that behavior is not consistent with expected payoff maximization, however, contributions are increasing in subjects’ subjective pivotalness. Thus, wider threshold uncertainty will sometimes—but not always—hinder collective action.     

Allocation of Prizes in Contests with Participation Constraints

We study all‐pay contests with an exogenous minimal effort constraint where a player can participate in a contest only if his effort (output) is equal to or higher than the minimal effort constraint. Contestants are privately informed about a parameter (ability) that affects their cost of effort. The designer decides about the size and number of prizes. We analyze the optimal prize allocation for the contest designer who wishes to maximize either the total effort or the highest effort. It is shown that if the minimal effort constraint is relatively high, the winner‐take‐all contest in which the contestant with the highest effort wins the entire prize sum does not maximize the expected total effort or the expected highest effort. Rather, a random contest in which the entire prize sum is equally allocated to all the participants yields a higher expected total effort as well as a higher expected highest effort.     

Social pressure,uncertainty, and cooperation

We analyse the role of uncertainty in a sequential game where players have to decide whether to contribute to a public project or not. A player's payoff may depend on his belief about the other player's action which allows us to model social pressure. Using the theory of psychological games, we show that the players' propensity to choose an individually costly action such as cooperation in a public project may increase if there is some uncertainty about who has cooperated before. A central agency, e.g. the government, can induce incomplete information by using a randomization policy, thus crowding in private contributions. Received: November 16, 1998 / Accepted: May 31, 1999     

投标人参考点效应与最优公开保留价博弈分析

本文从行为经济学出发,用博弈论的方法研究存在参考点效应时,投标人在第一价格和第二价格密封招标中的报价策略以及招标人的最优公开保留价定价策略,并对不同招标方式下投标人的期望收益进行比较。本文给出存在参考点效应时招标最优公开保留价的定价公式,分析了参考点效应和投标人数对最优公开保留价的影响。研究表明,在采用公开保留价的情况下,考虑投标人参考点效应对报价策略的影响时,不同招标方式给投标人带来的期望收益是相等的,即此时招标支付等价性命题仍然成立。此外,随着投标人参考点效应的增强和投标人数的增加,招标人的最优公开保留价下降。     

A model of selective tendering: Does bidding competition deter opportunism by contractors?

Under contractual incompleteness, a bid-taker is obliged to depend on a self-enforcing contract where a winning bidder puts his reputation at stake. In this case the winning bidder will renege on contractual obligations if any one-shot gain from opportunism is greater than a long-term gain from maintaining his reputation. Since the long-term gain is decreasing in the number of competing bidders, excessive bidding competition may provoke the winning bidder's opportunism. We derive an optimum number of bidders which ensures the self-enforcing contract at the lowest expected procurement cost. We also show how excessive bidding competition leads to the phenomenon of cost overruns.     

Repeated two-person zero-sum games with unequal discounting and private monitoring

We consider discounted repeated two-person zero-sum games with private monitoring. We show that even when players have different and time-varying discount factors, each player’s payoff is equal to his stage-game minmax payoff in every sequential equilibrium. Furthermore, we show that: (a) in every history on the equilibrium path, the pair formed by each player’s conjecture about his opponent’s action must be a Nash equilibrium of the stage game, and (b) the distribution of action profiles in every period is a correlated equilibrium of the stage game. In the particular case of public strategies in public monitoring games, players must play a Nash equilibrium after any public history.     

Optimal lottery

This article proposes an equilibrium approach to lottery markets in which a firm designs an optimal lottery to rank-dependent expected utility (RDU) consumers. We show that a finite number of prizes cannot be optimal, unless implausible utility and probability weighting functions are assumed. We then investigate the conditions under which a probability density function can be optimal. With standard RDU preferences, this implies a discrete probability on the ticket price, and a continuous probability on prizes afterwards. Under some preferences consistent with experimental literature, the optimal lottery follows a power-law distribution, with a plausibly extremely high degree of prize skewness.     

Recurrent crises in global games

Global games have unique equilibria in which aggregate behavior changes sharply when an underlying random fundamental crosses some threshold. This property relies on the existence of dominance regions: all players have a highest and lowest action that, for some fundamentals, is strictly dominant. But if the fundamental follows a random walk, it eventually spends nearly all of its time in these regions: crises gradually disappear. We obtain recurring crises by adding a single large player who lacks dominance regions. We also show that in order to obtain recurring crises, one must either relax dominance regions or restrict to fundamentals that continually return to or cross over a fixed region.     

The dynamics of within-group and between-group interaction

The article strengthens and provides a dynamic extension of the theory on collective rent seeking and private provision of a public good. Each individual agent within each group chooses in continuous or discrete time a continuous or discrete effort level. The combined effort within each group provides within-group public goods which are used as an input in the between-group n-group competition for an external prize. Intergroup mobility and intergroup warfare are allowed for. Each group and each individual agent within each group get a fraction of the prize based on a linear combination of equity and relative effort. A model/algorithm is developed generating analytical results and simulations illustrating how the interaction within and between groups proceeds through time.     

Satisficing with a variable threshold

We axiomatize a model of satisficing which features random thresholds and the possibility of choice abstention. Given a menu, the decision maker first randomly draws a threshold. Next, using a list order, she searches the menu for alternatives which are at least as good as the threshold. She chooses the first such alternative she finds, and if no such alternative exists, she abstains. Since the threshold is random, so is the resulting behavior. We characterize this model using two simple axioms. In general the revelation of the model’s primitives is incomplete. We characterize a specialization of the model for which the underlying preference and list ordering are uniquely identified by choice frequencies. We also show that our model is a special Random Utility Model.     

Repeated interaction in standard setting

Standardization may allow the owners of standard‐essential patents to charge higher royalties than would have been negotiated ex ante. In practice, however, standard‐setting efforts are often characterized by repeated interaction and complementarities among technologies. These features give firms that contribute technology to standards both the ability and the incentive to avoid excessive royalties by threatening to exclude other technology contributors from future rounds of standardization if they charge royalties exceeding ‘fair, reasonable, and nondiscriminatory’ (FRAND) levels. We show that such an outcome can be sustained as a subgame‐perfect equilibrium of a repeated standard‐setting game and examine how the decision‐making rules of standard‐setting organizations (SSOs) affect the sustainability of FRAND royalties. Our analysis provides a novel justification for super‐majority requirements and other rules frequently adopted by SSOs.     

Recognizing large donations to public goods: an experimental test

Private charities often publicise generous individual contributions or contributors, possibly to encourage others to give. In contrast, public good experiments used to study voluntary giving commonly tell participants only of total contributions. This paper reports an experimental test of the effect on contributions of supplying additional selective information. A control treatment is run that reveals only total contributions over ten one‐shot decision rounds. This is compared to a second treatment that also informs subjects of the maximum contribution made in their group after each round. In a third treatment, subjects are further given the opportunity to make costly rewards to the maximum contributor. Revealing generous contributions appears to raise average contributions slightly. Surprisingly, adding the ability to reward large contributors does little to generate further increases, though it significantly raises the variance of contributions. Copyright © 2002 John Wiley & Sons, Ltd.     

Stackelberg equilibrium with multiple firms and setup costs

I provide conditions that guarantee that a Stackelberg game with a setup cost and an integer number of identical leaders and followers has an equilibrium in pure strategies. The main feature of the game is that when the marginal follower leaves the market the price jumps up, so that a leader’s payoff is neither continuous nor quasiconcave. To show existence I check that a leader’s value function satisfies the following single crossing condition: When the other leaders produce more the leader never accommodates entry of more followers. If demand is strictly logconcave, and if marginal costs are both non decreasing and not flatter than average costs, then a Stackelberg equilibrium exists. Besides showing existence I characterize the equilibrium set and provide a number of results that contribute to the applied literature. As the number of leaders increases, leaders produce more and eventually they deter entry. Leaders produce more than the Cournot best reply, but they may underinvest in entry deterrence. As the number of followers increases, leaders become more aggressive. When this number is large, if leaders can produce the limit quantity and at the same time have market power, then they deter entry.     

The Structure of Sprawl: Identifying and Characterizing Employment Centers in Polycentric Metropolitan Areas

This paper applies a consistent framework to four comparably sized metropolitan areas to identify and characterize their employment centers. Employment centers are identified as places that exceed a threshold employment density and a threshold employment level. They are also characterized as specializing on the basis of location quotient analysis. We find clear evidence of specialization in every employment center in the four metropolitan areas studied. Our interpretation is that what we are observing is a systematic change in metropolitan structure rather than a random sprawling of firms. We also find some evidence that the size distribution of employment centers follows the rank-size rule. This suggests that there is structure not only in the distribution of economic activity among the employment centers but also in their size distribution. Because less than 50 percent of metropolitan employment is within employment centers, future research should focus on understanding the more diffuse employment patterns. The rank-size rule gives some guidance as to the expected size distribution of employment throughout the metropolitan area.     

A minimum expected response model: Formulation, heuristic solution, and application

Responding to true emergencies in the shortest possible time saves lives, prevents permanent injuries and reduces suffering. Most covering models consider an emergency cover if an ambulance is available within a given time or distance threshold. From a modeling perspective, shorter or longer responses within this threshold are all tallied as covered; conversely, the emergencies immediately outside the threshold are considered uncovered. However, if the shorter responses are given more weight along with the volume of such incidents, while still meeting system-wide coverage requirements, both customers and providers can benefit from reduced response times. We formulate a model to determine the locations for a given set of ambulances to minimize the system-wide expected response distances while meeting coverage requirements. We solve the model with a heuristic search algorithm and present computational and comparative statistics using data from an existing Emergency Medical Services agency.     

Multiproject team assignments

We consider expected profit maximizing mechanisms for a principal who has to allocate a group of agents among a number of projects, assuming that the principal has incomplete information about each agent's ability type, and the agents follow the Bayes-Nash or the dominant strategy equilibrium behavior. We find that while expected profit maximizing mechanisms are similar to the optimal auction (Myerson, 1981), the incentive compatibility constraints are much more restrictive. Interestingly, these constraints are satisfied if each agent's characteristics change in a consistent manner not only with types, but also from project to project. Received: 30 April 1997 / Accepted: 22 December 1998     

Mergers between local public firms

We consider a country made up of two regions, where each region owns a local public firm and a domestic private one. A national authority decides whether or not to merge the two local public firms. The result depends on whether the goods produced by the firms are homogeneous, substitutes or complements. We find that if the two local public firms produce the same good, the national authority is indifferent as to whether to merge or not. When local public firms produce different goods two cases arise. First, if the firms in each region produce homogeneous goods the national authority merges the two local public firms when the goods are complements, independent in demand and weak substitutes. Second, if the firms in each region produce heterogeneous goods the national authority merges the two local public firms only when the goods are close complements. Therefore, there is greater scope for mergers in the former case than in the later.