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by OneLessThing
654 days ago
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Okay I did the simulation. I don't think this strategy actually works, but I initially thought it might like you did. One such nash equillibrium my sim found was having the Ballmer player mix between picking either end of the range (not always 1 or 100 but around those numbers). I have the Ballmer player winning with around $.85-$1.00 EV per round. The resulting player strategy was to also try to start their binary search at the extreme ends of the range and hope they guessed the right side. It's kind of like the soccer penalty kick dynamic between the shooter and goalie. Goalie wants to pick the same side, shooter wants opposite sides. But with 100 choices, the goal is too wide I think. I now think that not constraining the players remaining choices to follow binary search pattern would completely change the resulting equilibrium and improve the results for the player. But that would be more computationally demanding to calculate because there's a strategy choice for every range of choices. And also I've avoided work for 2 hours by working on this so that's not great haha. I _am_ curious what not constraining the player to binary search would do though... |
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