Optimal scrutiny in multi-period promotion tournaments |
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| Institution: | 1. Center for Game Theory in Economics, SUNY at Stony Brook, NY 11794, USA;2. Department of Economics, Ben-Gurion University, Beer Sheva 84105, Israel;1. Department of Economics, Ben-Gurion University of the Negev, Beer Sheva 84105, Israel;2. IZA, Germany;3. Swiss Institute for Empirical Economic Research (SEW), University of St. Gallen, Varnbüelstrasse 14, CH-9000 St. Gallen, Switzerland;4. Department of Economics and Business Administration, Ariel University, Ariel 40700, Israel;1. UNIDEMI, FCT, Universidade NOVA de Lisboa, Portugal;2. Ernst & Young, Portugal;3. FCT, Universidade NOVA de Lisboa, Portugal;1. Department of Transportation Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran;2. Department of Industrial and Systems Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran |
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| Abstract: | Consider a principal who hires heterogeneous agents to work for him over T periods, without prior knowledge of their skills, and intends to promote one of them at the end. In each period the agents choose effort levels that influence their outputs, and are fully informed of the past history of outputs. The principal's major objective is to maximize the expected total 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 promotes 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 η(T) is the maximal optimal sample size, then η(T)/T→0 as T→∞. |
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