The inverse-reward optimal strategy conjecture for booby trap search games

Consider a booby trap search game played on a hypergraph whose hyperedges $S$ have positive rewards $r(S)$. A Searcher strategy assigns probabilities $p(S)$ to choosing hyperedges. Inverse-reward optimal strategy conjecture. There exists an optimal Searcher strategy such that, for every hyperedge $S$, either $p(S)=0$ or $p(S)$ is inversely proportional to its reward $r(S)$; equivalently, the Searcher can attain optimality by choosing a suitable subset of hyperedges and using the mixed strategy described in Proposition~. This conjecture proposes a common form for optimal strategies suggested by the solutions of the special cases studied in the paper; whether it holds for every hypergraph is left open.