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Increasing Risk and Increasing Informativeness: Equivalence Theorems

Mechanical and Industrial Engineering, University of Massachusetts, 220 Engineering Laboratory, Amherst, Massachusetts 01003
edbaker{at}ecs.umass.edu

When considering problems of sequential decision making under uncertainty, two of the most interesting questions are: How does the value of the optimal decision variable change with an increase in risk? How does the value of the optimal decision variable change with a more informative signal? In this paper, we show that if the payoff function is separable in the random variable, then one model can simultaneously answer both questions. This result holds for the reaction functions and equilibria of noncooperative games, as well as for single decision makers, with virtually no restrictions on the payoff functions. This is useful because otherwise it is very difficult to get at general results on the impact of learning. Furthermore, we clarify why the impacts of risk and a more informative signal are different when the payoff function is nonlinear in the random variable. It is because the directional impacts of informativeness are independent of risk attitude; the impacts of risk are not.

Subject classifications: decision analysis; theory; comparative statics of risk and learning; games; stochastic; impact of learning on equilibrium; natural resources; energy; climate change policy.
History: Received October 2002; revision received August 2003; revision received May 2004; revision received September 2004; accepted September 2004.