ECON212A (Queen's)

Submitted by pabsta on Wed, 09/16/2009 - 16:04

Some comments on question 2 of Quiz 5

Part a) :
- Some students gave the definition of a dominant strategy rather than a dominated strategy. As they are somewhat opposed, they yield different answers.
- Almost all of you forgot to write that a dominant strategy will never be played regardless of what the other player plays. Accordingly, a dominated strategy does not depend on some other player's action. Some wrote their answer as if it depended on both players.
Part b) :
- A Nash equilibrium is a pair of strategies from player A and B such that no player wants to deviate (choose another strategy) given what the other player is playing. It is a pair in this case since there are only two players. If there were n players, it would be an n-tuple. Some wrote, that it was the "best response" given what the other player is playing. This is not complete as the "nobody wants to deviate" condition is missing.
- A Nash equilibrium is not necessarely the best outcome of the game, as we can see by the sample example below :
  
  Left Right
  
  up (3,3) (0,4)
  
  down (4,0) (1,1)
  
  In this example, (1,1) is a Nash equilibrium while (3,3) is clearly a pareto amelioration for both players.

Part a) :
- 9600$ refers to the amount of money lost, not the amount you would get if your car is vandalised.
- A "sure thing" has to be sure (e.g P(event) = 1). If you get 10000$ with probability 0.9, it is not a sure thing.
Part b) :
- Some wrote something like "A risk averse person will accept a bet only if the expected utility of the bet is higher than the utility of a sure thing". While what you mean can be implicitely understood, it is a wrong statement. What sure thing are you talking about ? Everybody will accept a bet of 1$ with probability equal to one half compared to a sure value of 0$, risk averse persons included. Hence, you must specify what is the "sure thing" (that is the expected value of the bet).
- Some wrote that risk aversion is . This is a special case. For instance, the utility $u =(1+ I^b)^{1/b}, 0<b<1$ also defines risk averse preferences.