PAYOFF TABLE POINTERS

  1. Rows listvarious actions that we might choose/decide to do. They are listed to the left of the main grid,which contains a series of numerical payoffs.
  2. Columns headings list the various events or states of nature that could influence the amount of the payoff derived from doing an action. These states of nature may appear abstractly as N1, N2, or concretely as RAIN, WAR, etc.
  3. All states of nature in a payoff table must
  4. be mutually exclusive (no overlap or joint occurrence, e.g., SUNNY and COOL could both be true and thus are not mutually exclusive)
  5. and together exhaust all the possibilities in nature that need to be considered, e.g., WAR, PEACE—there is no other possibility here.
  6. While payoffs can be given as monetary units, we will most often use UTILS.
  7. UTILS can INFORMALLYbe considered units of pleasureif expressed by a positive number, e.g., +5, or of pain if expressed by a negative number,e.g., -2.
  8. However, use this definition: UNITS OF SATISFACTION OR DISSATISFACTION
  9. The advantages to using utils rather than money all the time are that
  10. not everything is valued in dollars, e.g., a spouse’s love
  11. the payoff numbers expressed in utils are easier to deal with mathematically, because they are often small integers.
  12. There are various functions used to evaluate a set of (action) payoffs on a row, e.g., SUM, MEDIAN, MAX, etc. Such numbers will be called the scores and are listed in columns to the right of the payoffs.
  13. Often some coefficient (i.e., a multiplier) is applied to a payoff, e.g., the probability that some state of nature will occur.
  14. If the plain payoff of an action is 4 (when a certain state of nature occurs) and if the probability of that state of nature is .2; then the probabilistic payoffcan be computed by Excel, i.e., 4 * .2 = .8
  15. As a matter of logic, a possible action choice cannot sensibly cause a state of nature to occur. This restriction is often overlooked and can cause a paradox.
  16. You should use Excel to calculate row scores and todetermine the winning action by selecting the action with the MOST FAVORABLErow-score. Thus a score of -4 is MORE FAVORABLE than a score of -5.
  17. Methods of REGRET and DELIGHT are based on COLUMN maximums and minimums, respectively.