Eliciting performance: deterministic versus proportional prizes

Author

Listed:

() (Stony Brook University
Yale University)

• Siddhartha Sahi

(Rutgers University)

Abstract

Abstract Two standard schemes for awarding a prize have been examined in the literature. The prize is awarded $$(\pi _{D})$$ ( π D ) deterministically: to the contestant with the highest output; $$(\pi _{P})$$ ( π P ) probabilistically: to all contestants, with probabilities proportional to their outputs. Our main result is that if there is sufficient diversity in contestants’ skills, and not too much noise on output, then $$\pi _{P}$$ π P will elicit more output on average than $$\pi _{D}$$ π D . Indeed if contestants know each others’ skills (the complete information case) then the expected output at any Nash equilibrium selection under $$\pi _{P}$$ π P exceeds that at any individually rational selection under $$\pi _{D}$$ π D . If there is incomplete information, the inequality continues to hold when we restrict to Nash selections for both schemes.

Suggested Citation

• Pradeep Dubey & Siddhartha Sahi, 2016. "Eliciting performance: deterministic versus proportional prizes," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(1), pages 239-267, March.
• Handle: RePEc:spr:jogath:v:45:y:2016:i:1:d:10.1007_s00182-015-0503-9
DOI: 10.1007/s00182-015-0503-9
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References listed on IDEAS

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Full references (including those not matched with items on IDEAS)

Keywords

Principal; Contestant; Proportional and deterministic prizes; Complete and incomplete information; Nash equilibrium; Individually rational strategies;

JEL classification:

• C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
• C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
• C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
• D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
• D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
• D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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