5. Assume that you are at the Christchurch airport waiting to board a ight to visit your family for Christmas. Let us say 190 passengers (including you) want to board the ight. Assume that ight attendants are absent to guide you properly. So, everyone is rushing for no reason. There are two doors to enter the ight (front and back), and each passenger decides which one to take. The satisfaction! utility of entering the front door is 10 units (the way to the front door has a footpath bridge that protects you from the rain). In contrast, the back door is the least preferred and has 0 satisfaction! utility (because it takes more time to reach the seat, you must go out of the terminal, and it is raining heavily). In deciding which door to take, each passenger cares only about net satisfaction! utility. Passengers' payoff is assumed to be their net utility. Net Utility of a Passenger = Satisfaction of Taking a Door Time Cost to Reach the Seat If m passengers are taking the front door, the time cost for a passenger to reach the seat is assumed to be m units. In contrast, ifm passengers take the back door, the time cost is 2m units to reach the seat. Passengers make simultaneous decisions as to whether to take the front or back door. a. Derive each passenger's payoff function (3 marks). b. Find a Nash Equilibrium (2 marks). 6. Players are getting ready for the FIFA world cup. Two cloth brands are thinking to sponsor the jestsey for team Croatia and Maldoxa: Alleson Athletic and Boxercraft The Croatia's and Moldova's team managers has asked their players to choose the one among the two. Let us now assume the intrinsic superiority of Alleson Athletic is not as great, and that network effects are stronger for Boxercraft. These modifications are reflected in different payoffs. Now, the payoff from wearing Boxercraft is 100b and from wearing Alleson Athletic is 15 + 5a; n number of soccer players are The Banshees of Inisherin Row Player Alex Alex simultaneously deciding between Alleson Athletic and Boxercraft Hint: Lecture 8 (Operating System game). a. Find all Nash Equilibria (3 marks). b. Let us now assume that a third option exists, which is to wear brand Augusta; it has a payoff of 200. Players simultaneously decide among Alleson Athletic, Boxercraft, and Augusta. Find all Nash equilibria (2 marks)