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Friday, Nov 28, 2008 - 00:43 SGT
Posted By: Gilbert

Xams

Health Economics and Game Theory are done and dusted (what's with holding them all the way at Sheares and Kent Ridge Hall respectively, anyway?), and I guess I'm probably okay for both (N.B. I'm usually slightly optimistic towards examinations, unlike some who appear damn sad after omitting a full stop, but that's another story).

Probably could have done a bit better for Health Economics had I spent more time on the final (short essay) question instead of spending time to confirm MCQ answers for options that were virtually eliminated, but that's hindsight. For Game Theory, indeed no proofs appeared, with the main focus being on finding perfect Bayesian equilibria (including one on Nim); I think I got most of the stuff correct, but didn't manage to finish writing the answer for the last question (after showing most of the working). Sigh, for just a minute more - now I don't know whether this is worse than realising the answer only after the examination ends.

I suppose I'm pretty lucky to be mostly "fast enough" for examination purposes, as there probably are people out there who are quite brilliant but just cannot or will not calculate quickly (as a former teacher of Grigory Perelman [of Poincaré conjecture fame] said, "...he was not fast. Speed means nothing. Math doesn't depend on speed. It is about deep.") And indeed in the real world, "all the exams are open-book, and they don't have time limits".

Well, just for interest, here's the last question (heavily modified since I don't know if direct reproduction is acceptable, but the spirit is there):


Two players, A and B, are playing a promotional card game with a dealer at the Marina Bay Sands. The game is as follows:
  • The dealer puts two cards in front of each player (four cards in total for both players). One of these cards is an Ace, and the other is a Joker.
  • Each player picks one of the two cards (thus both may have Aces, both may have Jokers, or one may have an Ace and the other a Joker), and looks at it privately.
  • Then, each player may choose to continue the game or fold (they make this decision simultaneously and do not know whether the other player continues or folds. You can think of them submitting an envelope to the dealer with their card if they want to continue, and an empty envelope if they want to fold).
  • If the player folds, he does not have to pay anything, but also cannot win anything.
  • If a player continues, and the other player does not, the player that continues wins $10 from the dealer.
  • If both players continue, their cards are revealed, and the outcome is as follows:
    • If both players have an Ace, they both pay the dealer $2.
    • If both players have a Joker, they both pay the dealer $5.
    • If one player has an Ace and the other has a Joker, the one with a Joker pays the one with an Ace $5.
What is the optimal strategy that player A should pursue? (Possible AAAAA for good enough answers up for grabs!)

Skipping a 3:30 a.m. Champions League game due to the game theory paper at 9 a.m. would have been a big sacrifice on my part, had it not been yet another nil-all draw (which sent both United and Villareal into the knockout phase, though).


Villarreal v Manchester United
by thefootie


After the amusing incident involving a certain Gerrard some weeks back, Wayne Rooney has seen fit to emulate his Scouse pal with a rather lame effort (see 5:40 in the video above) despite starting that move brightly with a clever backheel. I don't know how honest Rooney really is (at least he promptly apologized for the incident), but he certainly sucks at diving - if you want to cheat, you may as well learn from the masters. His frustratingly long layoff from scoring (which began right after I ate my words about him) probably contributed.

Well, on to the open-book General Biology. Hope I do well here.



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