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Optimal Adaptive Testing: Informativeness and Incentives

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Listed:
  • Rahul Deb
  • Colin Stewart

Abstract

We introduce a learning framework in which a principal seeks to determine the ability of a strategic agent. The principal assigns a test consisting of a finite sequence of questions or tasks. The test is adaptive: each question that is assigned can depend on the agent's past performance. The probability of success on a question is jointly determined by the agent's privately known ability and an unobserved action that he chooses to maximize the probability of passing the test. We identify a simple monotonicity condition under which the principal always employs the most (statistically) informative question in the optimal adaptive test. Conversely, whenever the condition is violated, we show that there are cases in which the principal strictly prefers to use less informative questions.

Suggested Citation

  • Rahul Deb & Colin Stewart, 2015. "Optimal Adaptive Testing: Informativeness and Incentives," Working Papers tecipa-551, University of Toronto, Department of Economics.
  • Handle: RePEc:tor:tecipa:tecipa-551
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    Keywords

    testing; learning; sequential choice of experiments;

    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

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