☃️merry chrimist☃️ on Nostr: A problem, for fun: Two players, bot and graf, are standing across from each other, ...
A problem, for fun:
Two players, bot and graf, are standing across from each other, separated by a line segment of length 1. A number w between 0 and 1 is fixed ahead of time, as part of the definition of the game.
Bot chooses a point on the line segment and throws a wrench at that point.
Simultaneously, graf chooses a length-w interval inside the line segment and places a shield on that interval.
If graf's shield blocks bot's wrench, then graf wins. Otherwise, bot wins.
At a Nash equilibrium, what is the probability that bot wins (as a function of w)?
Jeff Cliff 🦝 (npub1umx…d244) nya~ (npub1wsr…7hcq) Scenes by Colleen (npub16pn…ruz4) MercurialBlack (npub17z3…he6e) CMD (npub16gg…48j5)
Two players, bot and graf, are standing across from each other, separated by a line segment of length 1. A number w between 0 and 1 is fixed ahead of time, as part of the definition of the game.
Bot chooses a point on the line segment and throws a wrench at that point.
Simultaneously, graf chooses a length-w interval inside the line segment and places a shield on that interval.
If graf's shield blocks bot's wrench, then graf wins. Otherwise, bot wins.
At a Nash equilibrium, what is the probability that bot wins (as a function of w)?
Jeff Cliff 🦝 (npub1umx…d244) nya~ (npub1wsr…7hcq) Scenes by Colleen (npub16pn…ruz4) MercurialBlack (npub17z3…he6e) CMD (npub16gg…48j5)