Choice in uncertain situations:

In the presence of uncertain situations, people tend to show some behavioural traits. Look at the following observations:

1)  People often do not want to play actuarially fair games.

2)  People won't necessarily play actuarially favourable games.

3)  People would not  pay  large amounts  of money  to  play  gambles with huge upside potential.

Example

Suppose Rita and Sita agree to flip a coin one time. If a head comes up, Rita will pay  Sita Re. 1; in the event of the appearance of a tail Sita will pay Rita Re. 1. Try to understand this game taking Rita's view points. She expects two prizes available in the game:

X₁  head prize  -+  her payoff =  -1,  (as she loses Re.  1)
X₂  tail prize  -+  her payoff = +1 (as she wins Re. 1).

Expectations of the other  player  also  run in  the  same line except for the reversed values of XI  and X2. Thus, the expected value of this game is

Remember  that  even  when  this  game  is  played  a number  of  times,  the expected gains of the participants will not change. Change this game  slightly to assign X₁ = Rs.10  and X₂ = Re.1. Its expected value is

When  this  game  is  played  a  large number  of  times,  Sita will  be a distinct gainer. Perhaps,  Sita  could  pay  Rita a small amount  as  an  entry  fee to participate  in  the game.  In  both  its versions,  the  above game  is  called  an actuariallyfair game.  It  is observed that  in many situations, people refuse to play actuarially  fair games. One way of appreciating above idea is to note your reaction if you are invited to participate  in the above game with a bait of Rs. 10,000  instead of Re. 1. You will, in all  likelihood, decline to accept the offer. People often avoid playing games with bigger  risk even if  these are fair ones. For a formal  treatment of the theme, it will be useful to touch upon the St. Petersburg Paradox.