{E , E , …,E n } or Ω = {θ , θ , θ } For example, if a washing powder is marketed, it may be highly liked by outcomes (outcome θ ) or it may not appeal at all (outcome θ ) or it may satisfy only a small fraction, say % (outcome θ ) ∴ Ω = {θ , θ , θ } A A A E E E E E E Events Acts In a tree diagram the places are next to acts. We may also get another act on the happening of events as follows: In a matrix form, they may be represented as either of the two ways. States of nature Acts S S A A or Acts States of nature A A , ... A n S S Pay-off: The result of combinations of an act with each of the states of nature is the outcome and monetary gain or loss of each such outcome is the pay-off.
This means that the expression pay-off should be in quantitative form. Pay -off may be also in terms of cost saving or time saving. In general, if there are k alternatives and n states of nature, there will be k × n outcomes or pay-offs. These k × n payoffs can be very conveniently represented in the form of a k × n pay-off table.
States of nature Decision alternative A A .............. A k E a a .............. a k E a a .............. a k .
a nk Where a ij = conditional outcome (pay-off) of the i th event when j th alternative is chosen. The above pay-off table is called pay-off matrix. . .
Situations- Certainty and uncertainty Types of decision making: Decisions are