Decisions under Uncertainty and Risk

Anatol Rapoport

Chapter 3 in Decision Theory and Decision Behaviour, 1998, pp 50-81 from Palgrave Macmillan

Abstract: Abstract We will now suppose that the outcome of a decision (regarded as a choice of action among a finite number of alternatives) depends not only on the course of action chosen but also on a particular state of nature that obtains at the time. In our model the alternatives will be represented by the rows of a matrix, the states of nature by the columns. The entries in the matrix will represent the utilities of the outcomes determined jointly by the actor’s choices and by the states of nature: Matrix 3.1 % MathType!MTEF!2!1!+- % feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaqbaeqabCqaaa % aabaaabaGaamyqamaaBaaaleaacaaIXaaabeaaaOqaaiaadgeadaWg % aaWcbaGaaGOmaaqabaaakeaaaeaacaWGbbWaaSbaaSqaaiaadMgaae % qaaaGcbaaabaGaamyqamaaBaaaleaacaWGTbaabeaaaaGcdaWadaqa % auaabeqahyaaaaaabaGaam4uamaaBaaaleaacaaIXaaabeaaaOqaai % aadofadaWgaaWcbaGaaGOmaaqabaaakeaacqWIVlctaeaacaWGtbWa % aSbaaSqaaiaadMgaaeqaaaGcbaGaeS47IWeabaGaam4uamaaBaaale % aacaWGUbaabeaaaOqaaiaadwhadaWgaaWcbaGaaGymaiaaigdaaeqa % aaGcbaGaamyDamaaBaaaleaacaaIXaGaaGOmaaqabaaakeaacqWIVl % ctaeaacaWG1bWaaSbaaSqaaiaaigdacaWGQbaabeaaaOqaaiabl+Ui % mbqaaiaadwhadaWgaaWcbaGaaGymaiaad6gaaeqaaaGcbaGaamyDam % aaBaaaleaacaaIYaGaaGymaaqabaaakeaacqWIVlctaeaacqWIVlct % aeaacqWIVlctaeaacqWIVlctaeaacqWIVlctaeaacqWIVlctaeaacq % WIVlctaeaacqWIVlctaeaacqWIVlctaeaacqWIVlctaeaacqWIVlct % aeaacaWG1bWaaSbaaSqaaiaadMgacaWGSbaabeaaaOqaaiabl+Uimb % qaaiabl+UimbqaaiaadwhadaWgaaWcbaGaamyAaiaadQgaaeqaaaGc % baGaeS47IWeabaGaamyDamaaBaaaleaacaWGPbGaamOBaaqabaaake % aacqWIVlctaeaacqWIVlctaeaacqWIVlctaeaacqWIVlctaeaacqWI % VlctaeaacqWIVlctaeaacaWG1bWaaSbaaSqaaiaad2gacaWGSbaabe % aaaOqaaiabl+Uimbqaaiabl+Uimbqaaiabl+Uimbqaaiabl+Uimbqa % aiaadwhadaWgaaWcbaGaamyBaiaad6gaaeqaaaaaaOGaay5waiaaw2 % faaaaa!9A1A! $$\begin{array}{*{20}{c}} {} \\ {{A_1}} \\ {{A_2}} \\ {} \\ {{A_i}} \\ {} \\ {{A_m}} \\ \end{array} \left[ {\begin{array}{*{20}{c}} {{S_1}} & {{S_2}} & \cdots & {{S_i}} & \cdots & {{S_n}} \\ {{u_{11}}} & {{u_{12}}} & \cdots & {{u_{1j}}} & \cdots & {{u_{1n}}} \\ {{u_{21}}} & \cdots & \cdots & \cdots & \cdots & \cdots \\ \cdots & \cdots & \cdots & \cdots & \cdots & \cdots \\ {{u_{il}}} & \cdots & \cdots & {{u_{ij}}} & \cdots & {{u_{in}}} \\ \cdots & \cdots & \cdots & \cdots & \cdots & \cdots \\ {{u_{ml}}} & \cdots & \cdots & \cdots & \cdots & {{u_{mn}}} \\ \end{array} } \right]$$

Keywords: Mass Function; Single Actor; Certainty Equivalent; Fair Coin; Minimax Regret (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1057/9780230377769_4

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