1. [30 Points] We will continue with our model of the petrol crisis. Assume that there are two people living on an island and each person has two actions: keep buying petrol as normal or rush to the petrol station and ll up the tank. When both players buy as normal, the petrol supply would be enough for the two, and hence no single player has any incentives to rush. In fact, when all players keep buying as n01mal, rushing unilaterally will incur a small cost (e.g. one has to give up their normal routine, go to the gas station with half ill tanks etc.). If one player rushes, however, the other has incentives to do so too, for waiting when the other player rushes results in the worst outcome for the player who waits. a) Create a game using this scenario assuming that players decide simultaneously. Assign payoffs for all possible strategy combinations, carefully arguing and justifying why you assigned a particular payo to a particular strategy combination. Any reasonable payoffs are allowed, provided that the game is within the general framework given above and the payoffs are justied well. Find all Nash equilibria and all evolutionarily stable strategies in this game you created. b) Find all Nash equilibria and all evolutionarily stable strategies of this game if we assume that actors convert the payo's above into utilities using the social orientation model: Ui(X,y:6i] = x + 6;}! with 1