Theory and Decision

, Volume 52, Issue 3, pp 233-260

First online:

The Minimax, the Minimin, and the Hurwicz Adjustment Principle

  • Bernhard F. ArnoldAffiliated withInstitut für Statistik und Ökonometrie, Universität Hamburg
  • , Ingrid GrößlAffiliated withHochschule für Wirtschaft und Politik
  • , Peter StahleckerAffiliated withInstitut für Statistik und Ökonometrie, Universität Hamburg

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In this paper the Hurwicz decision rule is applied to an adjustment problem concerning the decision whether a given action should be improved in the light of some knowledge on the states of nature or on other actors' behaviour. In comparison with the minimax and the minimin adjustment principles the general Hurwicz rule reduces to these specific classes whenever the underlying loss function is quadratic and knowledge is given by an ellipsoidal set. In the framework of the adjustment model discussed in this paper Hurwicz's optimism index can be interpreted as a mobility index representing the actor's attitude towards new external information. Examples are given that serve to illustrate the theoretical findings.

Adjustment model Ellipsoidal information Hurwicz principle Minimax principle Minimin principle Quadratic loss function