1. (20 points) Consider the following story. Two travellers, 1 and 2 are travelling from one remote island to another part of the world. Each travellers is carrying a suitcase containing an identical object on the flight. The value of the object is known to be between $180 and $300. The suitcases are lost and the airline has to compensate the travellers. The exact value of the object is known to the travellers but not to the airline company. The airline asks each traveler to name an integer between 180 and 300. Each traveler gets (in dollars) the smaller of the numbers chosen, and, if the numbers differ, in addition $5 is transferred from the traveler who names the larger number to the one who names the smaller number. Thus if x, and a, are the integer amounts reported by the travellers i and j respectively, i, j E {1, 2}, i # j, then the payoff to traveller i is, I; +5, if r, xj. Model the above as a normal/strategic form game, and find all pure strategy NE in the game