1/1 Some extensions of the Traveller's Dilemma October 1, 2015 1. Two players simultaneously choose numbers between 1 and 15. If they both choose the same number they get that number in dollars. If they choose different numbers, the one with the lower number can get his number plus 5 and the one with the higher number gets her number minus 5. 2. Modification 3. No restrictions except, of course, each needs to choose a number from 1 to 15. Here things are somewhat more difficult. Consider some possibilities. (a) Each says 15; is this an equilibrium? No. Player 2, say, can deviate and say 14. Then she gets a payoff of 19, which is higher than 15. (b) Each says 12? One says 10 and the other says 15? . The equilibrium is in mixed strategies; Each chooses a number between 6 and 15, each with probability 10