    VALUE OF PERFECT INFORMATION

IN THE SCENARIO TO THIS PROGRAM THERE ARE SEVERAL
POSSIBLE STATES OF NATURE, ONE OF WHICH IS THE TRUE STATE.
WE DO NOT KNOW WHAT THE TRUE STATE OF NATURE(S OF N) IS BUT
WE KNOW THE PROBABILITY OF OCCURRENCE OF EACH S OF N.
IN ADDITION THERE ARE SEVERAL ALTERNATIVE ACTIONS WE MAY TAKE
EACH OF WHICH HAS A CERTAIN EXPECTED VALUE(OR AVERAGE RETURN).
EXPECTATION THEORY SAYS TO CHOOSE THE ACTION WITH THE HIGHEST
EXPECTED VALUE. IF WE KNEW WHAT THE TRUE STATE OF NATURE WAS
THEN WE WOULD KNOW WHAT ACTION TO TAKE. THE EXPECTED VALUE OF
PERFECT INFORMATION IS THE EXPECTED VALUE OF DECISIONS WITH
KNOWLEDGE OF THE S OF N MINUS THE MAXIMUM EXPECTED VALUE OF
ACTIONS WITHOUT THIS KNOWLEDGE.

PRESS ENTER TO CONTINUE? 
IN THIS PROGRAM THERE ARE UP TO 25 S OF N'S AND 8 POSSIBLE
ACTIONS. THE MAXIMUM EXPECTED VALUE OF THESE ACTIONS IS
COMPUTED. THEN THE EXPECTED VALUE WITH PERFECT INFORMATION
ABOUT THE S OF N IS COMPUTED. THEIR DIFFERENCE IS THE EVPI.

PRESS ENTER TO BEGIN? 
ENTER NUMBER OF POSSIBLE STATES OF NATURE? 2

ENTER PROBABILITY OF S OF N 1 ? 111
ENTER PROBABILITY OF S OF N 2 ? 222

PROBABILITIES DO NOT SUM TO 1.
ENTER 1 TO STANDARDIZE,0 TO BEGIN OVER? 1

ENTER NUMBER OF POSSIBLE DECISIONS(<=8)? 2

DECISION  1 
    PAYOFF WHEN S OF N IS 1 ? 123
    PAYOFF WHEN S OF N IS 2 ? 456

DECISION  2 
    PAYOFF WHEN S OF N IS 1 ? 789
    PAYOFF WHEN S OF N IS 2 ? 395
COMPUTING
    DECISION          EXPECTED VALUE
       1                    345.00
       2                    526.33

MAXIMUM EXPECTED VALUE =  526.333 

EVWPI                  =  567 
EXPECTED VALUE OF PERFECT INFORMATION =  40.6667 

