Game Theory: Unusual Question #3 and #4

[Bozeman]

Sorry, it looks like I was not careful enough in saying that there was agreement. I looked at most of the points in well's result, found them to agree, and then just scanned the rest to make sure no strange #'s appeared. I found JA's results exactly, and apparently well made a typographical error in that one of his 3/4's should have been 5/6.

As for your supposed improvement, I can only guess that you made an arithmetic error (easy to do here), or miscalculated the EV or size of one of the areas.

As for how I reached the solution, sop: define several decision points, and then note that at each decision point a player is indifferent to 2 possibilities. For example, if b is Player B's minimal value raise, then EVraise(b)=EVcall(b). These 7 eqs. then let you solve for the 7 decision points. To get game value, I look at the square [0,1] x [0,1]. The diagonal denotes a tie if showdown is reached, and each region divided by the diagonal and the lines corresponding to decision pts. has a particular expectation value and a probability of occuring equal to its area, so I just add them up. Many terms, so I occasionally make arithmetic mistakes here since I am not using Mathematica or Maple.

Craig