Econ 367 PS1 - Kaushik Basu Spring 2008 Econ 367...

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Kaushik Basu Spring 2008 Econ 367 : Game-Theoretic Methods Problem Set 1 1. In the game of Hex we proved that Black does not have a winning strategy. The proof took the form of showing that if Black has a winning strategy then White can always win (which is of course a contradiction). Why can we not construct a similar proof to show that White does not have a winning strategy? Being able to answer this question to your satisfaction will help you understand properly the original proof (that is, of why Black does not have a winning strategy). ANSWER: The reason we cannot construct a similar proof for White is because White moves first. Since White is the first mover, Black cannot put his stone where White has put his should the book indicate to do so. 2. Try to write down in words why in chess you cannot use the kind of argument used in Hex to show that Black does not have a winning strategy. ANSWER: Remember that in the proof in Hex, we assume Black has a winning strategy, and posit that this implies White has a winning strategy.
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