Optimal Scrutiny in Multi-Period Promotion Tournaments

Consider a principal who hires heterogeneous agents to work for him over T periods, without prior knowledge of their respective skills, and intends to promote one of them at the end. In each period the agents choose effort levels and produce random outputs, independently of each other, and are fully informed of the past history of outputs. The principal's major objective is to maximize the total expected output, but he may also put some weight on detecting the higher-skilled agent for promotion. To this end, he randomly samples n out of the T periods and awards the promotion to the agent who produces more on the sample. This determines an extensive form game Gamma (T,n), which we analyze for its subgame perfect equilibria in behavioral strategies. We show that the principal will do best to always choose a small sample size n. More precisely, if eta(T) is the maximal optimal sample size, then eta(T)/T approaches 0 as T approaches infinity.Multi-period promotion tournaments, extensive form games, subgame perfect equilibria, undominated sample sizes

Optimal Scrutiny in Multi-Period Promotion Tournaments

Consider a principal who hires heterogeneous agents to work for him over T periods, without prior knowledge of their respective skills, and intends to promote one of them at the end. In each period the agents choose effort levels and produce random outputs, independently of each other, and are fully informed of the past history of outputs The principal’s major objective is to maximize the total expected output, but he may also put some weight on detecting the higher-skilled agent for promotion. To this end, he randomly samples n out of the T periods and awards the promotion to the agent who produces more on the sample. This determines an extensive form game Γ( T,n ), which we analyze for its subgame perfect equilibria in behavioral strategies. We show that the principal will do best to always choose a small sample size n . More precisely, if ε( T ) is the maximal optimal sample size, then ε( T )/ T → 0 as T → ∞

Job Promotion Tournaments and Imperfect Recall

In this paper, a promotion tournament is considered, where, at the beginning of the tournament, it is unknown how long the tournament lasts. Further, the promotion decision is based on the assessments of a supervisor with imperfect recall. In line with psychological research, the supervisor is assumed to either value early or recent impressions more strongly. It is shown that effort may increase or decrease, as the probability of promotion in a certain period gets higher. The single effects determining the sign of the effort change oftentimes depend on how the supervisor processes information

Tournaments with Midterm Reviews

In many tournaments investments are made over time and conducting a review only once at the end, or also at points midway through, is a strategic decision of the tournament designer. If the latter is chosen, then a rule according to which the results of the different reviews are aggregated into a ranking must also be determined. This paper takes a first step in the direction of answering how such rules are optimally designed. A characterization of the optimal aggregation rule is provided for a two-agent two-stage tournament. In particular, we show that treating the two reviews symmetrically may result in an equilibrium effort level that is inferior to the one in which only a final review is conducted. However, treating the two reviews lexicographically by first looking at the final review, and then using the midterm review only as a tie-breaking rule, strictly dominates the option of conducting a final review only. The optimal mechanism falls somewhere in between these two extreme mechanisms. It is shown that the more effective the first-stage effort is in determining the final review’s outcome, the smaller is the weight that should be assigned to the midterm review in determining the agents’ ranking

Lab Labor: What Can Labor Economists Learn from the Lab?

This paper surveys the contributions of laboratory experiments to labor economics. We begin with a discussion of methodological issues: why (and when) is a lab experiment the best approach; how do laboratory experiments compare to field experiments; and what are the main design issues? We then summarize the substantive contributions of laboratory experiments to our understanding of principal-agent interactions, social preferences, union-firm bargaining, arbitration, gender differentials, discrimination, job search, and labor markets more generally.personnel economics, principal-agent theory, laboratory experiments, labor economics

Tournaments with Midterm Reviews

In many tournaments investments are made over time and conducting a review only once at the end, or also at points midway through, is a strategic decision of the tournament designer. If the latter is chosen, then a rule according to which the results of the different reviews are aggregated into a ranking must also be determined. This paper takes a first step in the direction of answering how such rules are optimally designed. A characterization of the optimal aggregation rule is provided for a two-agent two-stage tournament. In particular, we show that treating the two reviews symmetrically may result in an equilibrium effort level that is inferior to the one in which only a final review is conducted. However, treating the two reviews lexicographically by first looking at the final review, and then using the midterm review only as a tie-breaking rule, strictly dominates the option of conducting a final review only. The optimal mechanism falls somewhere in between these two extreme mechanisms. It is shown that the more effective the first-stage effort is in determining the final review’s outcome, the smaller is the weight that should be assigned to the midterm review in determining the agents’ ranking.

The hierarchical structure of a firm: a geometric approach

This paper develops a novel, geometric approach to modelling a firm's hierarchical structure. We model the firm''s hierarchy as the sector of a circle, in which the radius represents the height of the hierarchy and the angle of the sector represents the width of the hierarchy. The firm then chooses the height and angle in order to maximise profit. We analyse the impacts of changes in economies of scale, input substitutability and labour productivity on the firm''s hierarchical structure. We find that the firm will unambiguously become more hierarchical as specialisation of its workers increases or as its output price increases. The effect of changes in scale economies is contingent on the level of task specialisation and output price.

Lab Labor: What Can Labor Economists Learn from the Lab?

This chapter surveys the contributions of laboratory experiments to labor economics. We begin with a discussion of methodological issues: why (and when) is a lab experiment the best approach; how do laboratory experiments compare to field experiments; and what are the main design issues? We then summarize the substantive contributions of laboratory experiments to our understanding of principal-agent interactions, social preferences, union-firm bargaining, arbitration, gender differentials, discrimination, job search, and labor markets more generally.

The Hierarchical Structure of the Firm: A Geometric Perspective

This paper incorporates hierarchical structure into the neoclassical theory of the firm. Firms are hierarchical in two respects: the organization of workers in production and the wage structure. The firm’s hierarchy is represented as a sector of a circle, where the radius represents the hierarchy’s height, the width of the sector represents the breadth of the hierarchy at a given height, and the angle of the sector represents span of control. A perfectly competitive firm chooses height and width, as well as capital, in order to maximize profit. We analyze the short run and long run impact of changes in scale economies, input substitutability, and input and output prices on the firm’s hierarchical structure. We find that the firm grows as the specialization of its workers increases or as its output price increases relative to input prices. The effect of changes in scale economies is contingent on the price of output. The model also brings forth an analysis of wage inequality within the firm, which is found to be independent of the firm’s hierarchical organization of workers, and only depends on the firm’s wage schedule.Theory of the firm; Hierarchical structure; Economies of scale; Input substitutability; Inequality