Show that tacit collusion is more likely to be stable when there are fewer firms using the basic n-firm Cournot model (i

Show that tacit collusion is more likely to be stable when there are fewer firms using the basic n-firm Cournot model (i.e. n identical firms, each with marginal cost of c, and fixed cost of zero, all facing inverse market demand given by p = a-bQ). How does the alpha required to sustain tacit collusion in equilibrium vary with n? HINT: You will first need to figure out what would constitute collusion and defection in this model! You already know that the "punishment" outcome is the n-firm Cournot equilibrium. Figure out the rest of the elements of the alpha inequality, and then figure out how alpha varies with n.