Game Theory AH2205

I refuse to answer on the grounds that… May 27, 2010

During the Exam, I got the question on what happened in an Auction game if there was a tie. After some thoughts, my response to this was: “I would not like to answer this question”. And I added: “But there is information in this statement”.

Huh? The argument was this: You were asked to find a mixed NE. But the action set was continuous. If I would have said that “Oh, yes, sorry, I forgot to add that information to the exam question”, then I would have suggested that the answer was a mixed strategy on a discrete distribution. But on the other hand, if I said that “it does not matter”, then I would have implied that it was a continuous distribution, with a zero probability of ties.

On the third hand, since I did not want to add any more information to the Exam Question, then I really provided information that it was a continuous distibution anyway, didn’t I…?

Another more boring answer to this is that it won’t matter much because of the revenue equivalence theorem, and that was the second part of the same question.