Leírás
We consider a four-player game on the discrete hypercube $Q_n = \{0,1\}^n$, where each of the four players has chosen a single vertex of the hypercube. Such a position is referred to as a profile. Imagine there is a voter at every vertex, and each voter gives their vote to whichever player is closest to them, in terms of Hamming distance. The score of a player is the total number of votes they get. We say that a profile is an equilibrium if no player can strictly increase their score by moving to a different vertex, while the other players maintain their original positions. Moreover, a profile is balanced if, in each of the $n$ coordinates, two players have chosen 0, and two players have chosen 1. We prove that a four-player profile is an equilibrium if and only if it is balanced, proving a conjecture of Day and Johnson.
Zoom link for the lecture:
https://us06web.zoom.us/j/2572885125?omn=84501050120