代理人能力分布不均情形下首位晋升制与末位淘汰制的比较研究

在基于相对业绩比较的锦标赛激励机制中,首位晋升制与末位淘汰制是两种常见的竞赛激励机制。在代理人能力分布不均情形下,将代理人之间的拆台行为引入传统的锦标赛模型,可以研究代理人能力分布不同时首位晋升制与末位淘汰制下代理人的行为以及对委托人收益的影响。通过数理模型推导可获得以下结论:第一,首位晋升制下代理人的努力水平和拆台水平均比较高,委托人采用首位晋升制更有利,能力分布对委托人最优选择不产生影响。第二,低能力代理人占多数时,高能力代理人努力水平过高,受到的拆台也更多,高能力代理人占多数时,低能力代理人努力水平更高受到的拆台更多,能力分布对代理人的行为产生影响。     

Collusion and biased tournaments

Tournaments are vulnerable to collusion. This paper finds that biased tournaments can be more effective at preventing collusion than unbiased ones. When agents can collude to exert low effort, introducing some bias into tournaments generates opposite effects on favored and disfavored agents׳ respective incentives to exert high effort and provides strong incentives for the favored agent to deviate from collusion. Introducing an adequate degree of bias reduces the principal׳s incentive cost for preventing collusion; however, granting excessive bias instead increases the incentive cost. We show that the optimal level of bias can be endogenously determined.     

On the Competition of Asymmetric Agents

Abstract. Rank-order tournaments are usually implemented in organizations to provide incentives for eliciting employees' effort and/or to identify the agent with the higher ability, for example in promotion tournaments. We close a gap in the literature by experimentally analyzing a ceteris paribus variation of the prize spread – being the major design feature of tournaments – in a symmetric and an asymmetric setting. We find that effort significantly increases with the prize spread as predicted by standard theory. However, only for sufficiently large prize spreads weak players competing against strong players strain themselves all the more and sorting of agents is feasible.     

Rank-order tournaments and selection

Rank-order tournaments are often presented as devices for aligning incentives in a principal-agent setting. In most of this literature agents are expected to be identical so that the principal is indifferent ex ante as to who wins the contest, implying that the selection properties of the tournament can be ignored. In this paper we consider a tournament which is not necessarily symmetric, and in which agent type is private information. The principal cares about who wins, but the basic tournament will not achieve perfect selection; the lower-type agent may sometimes win. In a two-player tournament we present a simple reward system in which the winner's reward depends upon which (if any) of two “test standards” is passed; conditions are presented under which this system allows the principal to choose the best agent. This system can be extended in a simple manner to rank types in ann-player tournament. We suggest that the theory can be applied to internal labor markets and research contests.     

A comparison of cardinal tournaments and piece rate contracts with liquidity constrained agents

A celebrated result in the theory of tournaments is that relative performance evaluation (tournaments) is a superior compensation method to absolute performance evaluation (piece rate contracts) when the agents are risk-averse, the principal is risk-neutral or less risk-averse than the agents and production is subject to common shocks that are large relative to the idiosyncratic shocks. This is because tournaments get closer to the first best by filtering common uncertainty. This paper shows that, surprisingly, tournaments are superior even when agents are liquidity constrained so that transfers to them cannot fall short of a predetermined level. The rationale is that, by providing insurance against common shocks through a tournament, payments to the agents in unfavorable states increase and payments in favorable states decrease which enables the principal to satisfy tight liquidity constraints for the agents without paying any ex ante rents to them, while simultaneously providing higher-power incentives than under piece rates. The policy implication of our analysis is that firms should adopt relative performance evaluation over absolute performance evaluation regardless of whether the agents are liquidity (wealth) constrained or not.     

Splitting Leagues

Splitting leagues or tournaments is puzzling when agents are homogeneous and splitting leads to a negative competition effect. However, a principal can benefit from splitting under some circumstances. First, splitting can be used as a divide-and-rule strategy by the principal to create additional incentives when collusion among the agents is possible. Second, splitting leagues gives the principal the opportunity to introduce promotions and relegations between nested tournaments.     

On the Incentive Effects of Sample Size in Monitoring Agents – A Theoretical and Experimental Analysis

When agents compete for a bonus and their productivity in each of several possible occasions depends stochastically on (constant) effort, the number of times this is checked to assign the bonus affects the level of uncertainty in the selection process. Uncertainty, in turn, is expected to increase the effort made by competing agents (Cowen and Glazer, 1996; Dubey and Haimanko, 2003; Dubey and Wu, 2001). Theoretical predictions are derived and experimental evidence is collected for two competing agents, with the bonus awarded to that agent who outperforms the other. Sampling occasions (1 or 3), cost of production (high or low), cost symmetry (asymmetric or symmetric), and piece‐rate reward are manipulated factorially to test the robustness of the effects of uncertainty. For control, a single‐agent case is included. Results indicate that, for tournaments, greater uncertainty does indeed lead to greater than expected effort and lower average variable costs.     

The incentive effects of levelling the playing field – an empirical analysis of amateur golf tournaments

Levelling the playing field is an important policy instrument to guarantee an equitable competition among heterogeneous individuals. However, the incentive effects of those policies are usually not explicitly addressed in empirical studies. In this article the performance in amateur golf tournaments is analysed to gain insights into the incentive effects of those types of policies. The empirical analysis takes advantage of the fact that tournaments in amateur golf are of two distinctive types that apply different scoring rules: while one scoring rule is based on gross scores, i.e. the total number of strokes of a player, the second scoring rule is based on net scores where the total number of strokes is normalized with respect to the respective player's handicap. Performance comparisons of players who participated in both types of tournaments suggest that levelling the playing field, as in tournaments based on net score, has positive and significant performance effects.     

Competing for promotion: Are “THE BEST” always the best?

Several selection processes use multistage tournaments to choose the best candidates. The theoretical models predict that tournaments are efficient in selecting the best candidates, as they stimulate the best to perform relatively better than their opponents. Empirical tests are difficult, as data on the agents involved in these selections are scarce. Exploiting data from field tournaments, the World Swimming Championships, I show that two- and three-stage tournaments are effective for stimulating performance and selecting the best contestants; results indicate that the winners are the players who are most able to increase their relative performance from one stage to the next.     

Altitude as handicap in rank-order football tournaments

The structure of professional sports allows us to document predictions from the theory of rank-order tournaments (Lazear and Rosen 1981). In the context of South American FIFA World Cup Qualifiers, under the presence of heterogeneous agents, handicapping the best quality players may increase the tournaments’ efficiency by making the contest more competitive. In particular, we show that playing in high-altitude stadiums (above 2500 m) constitutes a handicap as the otherwise least competitive teams benefit from the existence of an altitude advantage.     

Collusion in homogeneous and heterogeneous tournaments

In tournaments, only the relative performance of agents is important. Therefore, the agents have an incentive to collude by jointly deviating to low effort levels. Previous papers on collusion have proposed to make the tournament asymmetric to prevent agents from colluding. However, by allowing side payments between the agents and focusing on implicit enforcement of collusion, the current study demonstrates that this is not true. Often, the principal prefers to hire homogeneous agents to make collusions less stable.     

Coordination and discrimination in contracting with externalities: divide and conquer?

The paper studies bilateral contracting between N agents and one principal, whose trade with each agent generates externalities on other agents. It examines the effects of prohibiting the principal from (i) coordinating agents on her preferred equilibrium, and (ii) making different contracts available to different agents. These effects depend on whether an agent is more or less eager to trade when others trade more. The prohibitions reduce the aggregate trade in the former case, and have little or no effect in the latter case. The inefficiencies under different contracting regimes are linked to the sign of the relevant externalities, and are shown to be typically reduced by both prohibitions.     

Doping and cheating in contest-like situations

Individuals who compete in a contest-like situation (for example, in sports, in promotion tournaments, or in an appointment contest) may have an incentive to illegally utilize resources in order to improve their relative positions. We analyze such doping or cheating within a tournament game between two heterogeneous players. Besides the direct and indirect costs of doping, three major effects are identified which determine a player's decision to deviate from a no-doping situation — a cost effect, a likelihood effect and a base-salary effect. Moreover, the influence of heterogeneity and exogenous performance risk on a no-doping outcome, and the influence of ex-ante and ex-post doping tests on the players' investments are discussed.     

Tournaments, minimum wage, and money non-neutrality

To reconstruct the micro-foundation of Keynesian macro-economics, the efficiency wage theory has generally been considered a success in providing a plausible explanation for the existence of involuntary unemployment. However, little has been said about how monetary policy causes fluctuations in aggregate employment and output in the efficiency wage theory. This paper extends Lin and Yang’s [Econ. Inq. 39 (2001) 644] shirking-type efficiency wage model with tournaments to account for money non-neutrality. A distinct feature of our model is that, due to the adoption of tournaments, there will be a hierarchical wage structure rather than a flat wage in the economy. As will be argued, the labor market characterized in this paper is in a sense a reversion to Keynes’ General Theory, but also an improvement upon it.     

Resource availability in the social cloud: An economics perspective

Social cloud has emerged as a case of sharing economy, where socially connected agents share their computing resources within the community. This paper considers the social cloud as an endogenous resource-sharing network, where agents are involved in closeness-based conditional resource sharing. This study focuses on (1) the impact of agents' decisions of link addition and deletion on their own local and global resource availability as well as on others' global resource availability (as spillover effects), (2) the role of agents' closeness in determining spillover effects, (3) agents' link addition behavior, and (4) stability and efficiency of the social cloud. The findings include the following: (i) Agents' decision of link addition (deletion) increases (decreases) their local resource availability. However, these observations do not hold in the case of global resource availability. (ii) In a connected network, agents experience either a positive or a negative spillover effect and there is no case with no spillover effects. Agents observe no spillover effects if and only if the network is disconnected with three or more components. Furthermore, an agent experiences negative spillover if there is no change in its closeness. Although an increase in the closeness of agents is necessary to experience positive spillover effects, the condition is not sufficient. (iii) We study the relation between agents' distance from each other, and their local as well as global resource availabilities. We prove that the local resource availability of an agent from another agent increases with decrease in the distance between them and that maximum local resource availability is obtained from the agent with the least closeness. Using these results, we discuss which agent to add a link to, so as to maximize the local resource availability. We discuss why such results are difficult to establish for global resource availability. However, in a two-diameter network, we show that for an agent, link formation always increases the global resource availability. (iv) We also study resource-sharing network formation and its efficiency in a strategic setting. We prove the existence of a pairwise stable network. Furthermore, we provide a set of conditions for a few prominent network structures (star, complete, wheel, and bipartite networks) to be pairwise stable. We show that the “connected in pairs, otherwise disconnected” network is better than a connected network, in terms of social welfare.     

Are sequential round‐robin tournaments discriminatory?

I examine sequential round‐robin tournaments with three and four symmetric players. Each player is matched once with each other player and each match is organized as a Tullock contest. A single prize is allocated to the player with the most matches won. I show that, depending on the position of their matches in the sequence of the tournament, the players' ex ante winning probabilities and expected payoffs differ. Compared to tournaments with matches organized as all‐pay auctions, however, discrimination is weaker and partially reversed. Moreover, aggregate effort in tournaments with suitable Tullock contests is larger than in tournaments with all‐pay auctions. The fairness of round‐robin tournaments may be improved by an endogenous sequence of matches or the requirement that players fix their effort ex ante.     

Wealth Effects, Incentives, and Productivity

Comparative static effects of varying the wealth level of a risk-averse agent in a moral hazard setting with limited liability constraints are investigated. There are two principal opposing effects of increasing wealth: the incentive effect, which allows stronger punishments for poor performance, thereby encouraging higher effort; and the preference effect, which reduces the agent's effort incentives owing to income effects in the demand for leisure. It is shown that optimal effort levels are initially constant, subsequently increasing and eventually decreasing in wealth. Hence agents with intermediate wealth levels are the most productive.     

Unawareness of theorems

This paper provides a set-theoretic model of knowledge and unawareness. A new property called Awareness Leads to Knowledge shows that unawareness of theorems not only constrains an agent’s knowledge, but also can impair his reasoning about what other agents know. For example, in contrast to Li (J Econ Theory 144:977–993, 2009), Heifetz et al. (J Econ Theory 130:78–94, 25 2006) and the standard model of knowledge, it is possible that two agents disagree on whether another agent knows a particular event. The model follows Aumann (Ann Stat 4:1236–1239, 1976) in defining common knowledge and characterizing it in terms of a self-evident event, but departs in showing that no-trade theorems do not hold.     

Corporate Tournaments, Human Capital Acquisition, and the Firm Size–Wage Relation

This paper provides a possible explanation for the empirically observed size–wage effect and inter-industry wage differences. It develops a model in which incentives for workers to accumulate general human capital are provided by corporate tournaments, where workers with the highest level of general human capital win promotions. Given that the prizes in such tournaments are determined by outside market conditions, the investment and the equilibrium wages depend on firm and industry characteristics. The model implies that workers in bigger firms and in more technology intensive and profitable firms and industries acquire more human capital and receive higher wages and benefits.     

Present-biased preferences,self-awareness and shirking

We model a mechanism design problem in which the principal owns a project that requires work effort by an agent, but agents may have time-inconsistent, present-biased preferences and lack complete self-awareness of these preferences. The self-control problem and naïveté of an agent may lead him to agree to a contract but later shirk or slack-off, even though doing so is observable. When the principal cannot severely punish shirking and agents are completely naïve, the second-best solution entails allowing a present-biased agent to slack-off in order to avoid a greater loss due to shirking. With greater self-awareness among present-biased agents, the principal may do better by screening some from accepting the contract. Furthermore, when shirking can be severely punished, this does not lead to contracts that eliminate effects of the self control problem. Instead the principal may exploit present-biased agents by offering a contract that allows them to slack-off (which agents fail to foresee they will choose to do) but at the expense of foregoing much compensation.