imperfect competition - oligopoly

Problem 3. Consider the Hotelling model with three hot dog stands. If the three stands are located at different positions, then each consumer goes to the nearest stand. If the three stands are all located at the same position, then each stand gets 1/3 of the beach. If two are located at the same position while the third is at a di'erent position, then the third one gets the part of the beach closer to it than to the other two, and the other two equally share the rest of the beach. Show that there is no Nash equilibrium. Problem 4. Consider the Cournot model with three oil companies. Suppose p = 70 (11 + 12 + (13) and 01(q) = 02(q) = 03(q) = 10g. Find a Nash equilibrium