Consider an n-player game in which each player i I chooses a level of participation i in [0, 1]. 1. Determine all the symmetric Nash equilibria (in pure strategies), for < 1 and also for > 1, when the utility function is ui() = jI j i 2. Propose a modification of the utility function that will determine an interior equilibrium value of i for some value of n and . 3. Under which utility function (between your proposed one and the one we gave) do we find higher level of participation i for < 1 and for > 1? What about welfare, which one leads to the highest total welfare? Provide an intuition for your results.