Imagine, if both sides want to take the edge of 1000 over 800 and pick April, they both end up as losers. But, if one constantly concedes and takes June, the other side would always get that trace of advantage and be ahead - which is not a very good thing.
So ...?
A naive solution, following the analogy of the football penalty kick, seems to be using the mixed strategy. In other words, you should pick the month by random, so that there is 50% chance of not having the conferences clash, and, if your opponent keeps choosing April, they have price to pay.
In an ideal world with the two sides being identical, both would end up with the same strategy, and the model predicts that both sides would pick the month by random.
It sounds great, eh? Do you see the flaw here?
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