Hide and seek game with heterogenous hiding places

We study a conflict with multiple battlefields where two players, the hider and the seeker, choose their respective numbers of hiding places. The hiding places have different values and the score of the hider is the sum of values of the places chosen by him and not chosen by the seeker. The score of the seeker is equal to minus the score of the hider. We characterise Nash equilibria and equilibrium payoffs of this game. We find that both players compete for a subset of top valued hiding places while equilibrium payoffs are related to the harmonic mean of the values of the competed battlefields.