Contests with size effects

In this paper we analyze the structure of contest equilibria with a variable number of individuals. First we analyze a situation where the total prize depends on the number of agents and where every single agent faces opportunity costs of investing in the contest. Second we analyze a situation where the agents face a trade-off between productive and appropriative investments. Here, the number of agents may also influence the productivity of productive investments. It turns out that both types of contests may lead to opposing results concerning the optimal number of individuals depending on the strength of size effects. Whereas in the former case individual utility is u-shaped when the number of agents increases, the opposite holds true for the latter case. We discuss the implications of our findings for the case of anarchic societies and market competition.     

Contests with Multi-tasking*

The standard contest model in which participants compete in a single dimension is well understood and documented. Multi‐dimension extensions are possible but are liable to increase the complexity of the contest structure, mitigating one of its main advantages: simplicity. In this paper we propose an extension in which competition ensues in several dimensions, and a competitor that wins a certain number of these is awarded a prize. The amount of information needed to run the contest is hence limited to the number of dimensions won by each player. We look at the design of this contest from the point of view of maximising effort in the contest (per dimension and totally), and show that there will be a tendency to run small contests with few dimensions. The standard Tullock model and its results are encompassed by our framework.     

Contests with limited resources

Many interesting phenomena (electoral competition, R&D races, lobbying) are instances of multiple simultaneous contests with unconditional commitment of limited resources. Specifically, the following game is analyzed. Two players compete in a number of simultaneous contests. The players have limited resources (budgets) and must decide how to allocate these to the different contests. In each contest the player who expends more resources than his adversary wins a corresponding prize. Mixed-strategy equilibria are characterized in the case of identical values and budgets and the connections with the classical Blotto game are analyzed.     

Sustained output growth under uncertainty: A simple model with human capital

In a model where agents use their labour/education choice to adjust their consumption profile over time, I show that the impact of uncertainty on growth depends, critically, on agents’ attitudes towards risk, reflected by the coefficient of relative risk aversion. In this respect, the well known result from the literature on ‘saving under uncertainty’ can be extended into a broader context, whereby the intertemporal profile of consumption is determined via human capital accumulation rather than saving and physical capital investment.     

Repeated Contests with Asymmetric Information

The same contestants often meet repeatedly in contests. Behavior in a contest potentially provides information with regard to one's type and can therefore influence the behavior of the opponents in later contests. This paper shows that if effort is observable, this can induce a ratchet effect in contests: high ability contestants sometimes put in little effort in an early round in order to make the opponents believe that they are of little ability. The effect reduces overall effort and increases equilibrium utility of the contestants when compared with two unrelated one-shot contests. It does, however, also introduce an allocative inefficiency since sometimes a contestant with a low valuation wins. The model assumes an imperfectly discriminating contest. In an extension I show that, qualitatively, results are similar in a perfectly discriminating contest (all pay auction).     

On Elimination in Contests: A Perspective on Output Maximization

This paper investigates the desirability of adding a preliminary elimination stage for output maximization in a winner‐take‐all contest framework in which the contestant who achieves the highest (random) output wins. We find that, generally, the desirability of an elimination stage does not monotonically depend on the productivity of the effort; adding a preliminary stage can improve output for both concave and convex production functions. This result contrasts sharply with current insight from effort maximization, which argues that adding a preliminary stage can increase effort supply only if the production function is concave.     

Cost information sharing with uncertainty averse firms

Summary. A homogeneous Cournot duopoly with asymmetric information is analyzed. Every firm learns its own marginal cost parameter, but not the marginal cost parameter of the opponent. Every firm can commit to revealing its private information to the other firm, i.e. to share information. The influence of uncertainty aversion on the readiness of the duopolists to share cost information is analyzed. Uncertainty aversion is modeled according to the Choquet utility theory. It is shown that low uncertainty aversion leads the firms to share information, while high uncertainty aversion leads the firms not to share. A simple economic explanation for this result is given.Received: 5 January 2001, Revised: 7 May 2003, JEL Classification Numbers: D43, D81, D82.I wish to thank Jürgen Eichberger, Volker Krätschmer, Willy Spanjers, seminar participants at Universität des Saarlandes, seminar participants at University College London, participants in the conference of the Verein für Socialpolitik in Mainz 1999 and an anonymous referee for helpful comments. The views expressed in this paper are those of the author and do not necessarily reflect the views of the European Central Bank.     

商业银行贷款担保偏好行为与信贷交易成本

商业银行具有担保偏好行为,即偏好发放担保贷款.信贷交易存在很高的不确定性.银行为了降低不确定性,有两种方案可供选择:一是商业银行进行较强的筛选、监督和审查活动,获取企业的信息;二是商业银行依靠担保,节约筛选成本、监督成本和审查成本.有限理性的商业银行当然会选择后者.但是,担保行为不能完全替代银行的筛选、监督和审查活动,因为担保品本身也存在诸如价值波动等不确定性.     

Information, flexibility, and value added

Information technologies used in production activities facilitate the acquisition of more detailed and more timely information concerning the state of the production environment. While the effects of distribution shifts on decisions under uncertainty have been much studied, less is known about the effects of information acquisition on revenue generation and choice. In this article we consider the firm level impacts of information acquisition on revenue, on input use, and on profitability. A choice made under uncertainty depends upon the distribution of a random parameter but not upon its realization, while the choice depends only on the realization when this realization is known. Impacts are determined by interactions between second and third cross derivatives of the primal revenue function.     

Information, flexibility, and value added

Information technologies used in production activities facilitate the acquisition of more detailed and more timely information concerning the state of the production environment. While the effects of distribution shifts on decisions under uncertainty have been much studied, less is known about the effects of information acquisition on revenue generation and choice. In this article we consider the firm level impacts of information acquisition on revenue, on input use, and on profitability. A choice made under uncertainty depends upon the distribution of a random parameter but not upon its realization, while the choice depends only on the realization when this realization is known. Impacts are determined by interactions between second and third cross derivatives of the primal revenue function.     

Applied welfare analysis with discrete choice models: A comment

Small and Rosen extend conventional welfare analysis to a variety of non-standard consumer choice problems. This paper unifies their results and demonstrates that they are all straightforward consequences of the envelope theorem. Additional examples include progressive and regressive taxes and fixed costs.     

Contests with a stochastic number of players

We study Tullock's (1980) n-player contest when each player has an independent probability 0 < p 1 of participating. A unique symmetric equilibrium is found for any n and p and its properties are analyzed. In particular, we show that for a fixed n > 2 individual equilibrium spending as a function of p is single-peaked and satisfies a single-crossing property for any two different numbers of potential players. However, total equilibrium spending is monotonically increasing in p and n. We also demonstrate that ex-post over-dissipation is a feature of the pure-strategy equilibrium in our model. It turns out that if the contest designer can strategically decide whether to reveal the actual number of participating players or not, then the actual number of participants is always revealed.     

Wages and profits: A comment

Clark's (1979) model for the levels of aggregate wages and profits is respecified and reestimated using modern econometric techniques. One result is a more efficient estimate of the capital-labor substitution elasticity. In addition, the presence of very strong positive autocorrelation in one of the equations sheds doubt on Clark's assertion that a model for the levels of these variables is more appropriate than a model for their year-to-year changes.     

Allocation of Prizes in Contests with Size Effects

We examine the allocation of prizes in contests in which the number of contenders affects the prizes and costs. We assume that there are two groups of contenders. The government allocates a prize to the two groups, and the contenders in each group respectively compete for the prize. Examining the prize allocation in such contests, we obtain the following results. The aggregate effort increases in the prize share of the larger group. In contests with size effects through costs, the aggregate resource expended in the contests and the aggregate payoffs are independent of group size distribution if the prize is allocated in proportion to group size. The integration of contests with size effects through prizes can yield higher aggregate effort and payoffs than the decentralized contests.