Question 170
Two players, Alice and Bob, play a game on $n$ vertices labelled $1, 2, \dots, n$. Alice and Bob take turns adding edges $\{i, j\}$, with Alice going first. Both players are banned from creating a cycle, and the game ends after $n-1$ total turns.
Let the weight of the edge $\{i, j\}$ be $|i - j|$, and let $W$ be the total weight of all edges at the end of the game. If Alice plays to maximize $W$ and Bob plays to minimize $W$, what will $W$ be?
Let the weight of the edge $\{i, j\}$ be $|i - j|$, and let $W$ be the total weight of all edges at the end of the game. If Alice plays to maximize $W$ and Bob plays to minimize $W$, what will $W$ be?