abstract: In each step two players, m and M claim unclaimed elements of \binom{[n]}{k}, such that the claimed elements form an intersecting family. Let gsat(F) be the length of this game. m would like to minimize, M would like to maximize it.

We prove that with optimal strategies Omega(n^(k/3-2)) < gsat(F) < O(n^{k-Omega(k^(1/2))}).

Joint work with B. Patkos.