2. You are planning to hide a treasure on one of three islands, Island 1, Island 2, or Island 3. Your adversary gets a chance to look for the treasure on exactly one of the islands. If you hide the treasure on Island j and your adversary looks there, she finds it with probability 1/j. If your adversary does not find the treasure, both of your payoffs are zero. If she finds it, your payoff is -1 and hers is 1. (a) Formulate this problem as a game, i.e, write down the game matrix. (b) Find a Nash equilibrium for this game. (c) Find all Nash equilibria for this game. (d) Suppose there are n islands. For every n = : 1, 2,..., find a Nash equilibrium express equilibrium mixing probabilities as functions of j and n.