Production Games The Stag Hunt Best responses in the stag hunt are again underlined. Below it is a best response diagram. The dashed lines indicate BRz. Notice there are three Nash equilibria -two pure strategy Nash equilibria and one "hidden"mixed strategy equilibrium. In any discrete action space game there is at least one Nash equilibrium Road Congestion How can game theory be applied to economic problems? Consider the following road congestion game. n students go to lectures. Should they drive(D)or take the bus(B), given they want to get there as fast as possible? If they all drive, traffic congestion implies it takes 45 minutes to get to the lecture If they all take the bus, the road is clear and it only takes 30 minntes If everyone else takes the bus and a single student takes the car, the one in the car flies to work(no other he road) in 15 minutes. If everyone else takes the car and a single student takes the bus, the one on the bus takes 60 minutes- all those cars and all those bus-stops. Everyone Else Me This is a generalisation of the prisoners'dilemma. The student will drive. In fact it is dominant to do so. All the other students will arrive at the same decision. Everyone takes the car Wouldn't it be nice if everyone took the busProduction — Games 9 The Stag Hunt • Best responses in the stag hunt are again underlined. Below it is a best response diagram. S R S 5 5 4 0 R 0 4 3 3 ................................................................................................................................................................................................................................................................................ . .......................................................................................................................................................................................................................... . . . . . . . . . ............. ............. ............. ............. ............. ............. ............. ............. ............. ..... Player 2 Player 1 BR2 BR1 S R S R • • • • The dashed lines indicate BR2. Notice there are three Nash equilibria — two pure strategy Nash equilibria and one “hidden” mixed strategy equilibrium. In any discrete action space game there is at least one Nash equilibrium. Production — Games 10 Road Congestion • How can game theory be applied to economic problems? Consider the following road congestion game. n students go to lectures. Should they drive (D) or take the bus (B), given they want to get there as fast as possible? • If they all drive, traffic congestion implies it takes 45 minutes to get to the lecture. • If they all take the bus, the road is clear and it only takes 30 minutes. • If everyone else takes the bus and a single student takes the car, the one in the car flies to work (no other cars on the road) in 15 minutes. If everyone else takes the car and a single student takes the bus, the one on the bus takes 60 minutes — all those cars and all those bus-stops. Everyone Else Me B D B 30 min 60 min D 15 min 45 min • This is a generalisation of the prisoners’ dilemma. The student will drive. In fact it is dominant to do so. All the other students will arrive at the same decision. Everyone takes the car. • Wouldn’t it be nice if everyone took the bus?