Consider two groups of citizens, each group can either choose to drive x = d or to take public transport x = p. The first group, group 1, enjoys driving and has the following benefit from using their car within the ULEZ area: B1(x1 = d) = 18. The second group, group 2, does not enjoy driving and has a benefit of B2(x2 = d) = 0 from driving their car. If they don’t drive, citizens can use public transport to get around. The benefit of doing so is the same for both groups: B1(x1 = p) = B2(x2 = p) = 10. Both groups drive cars that do not meet the ULEZ requirements and therefore create excessive pollution. For simplicity, we consider that pollution, and the health problems it induces, are the main cost of driving. This cost is imposed on both groups and is equal to Ci(x1 = d, x2 = d) = 10 if both groups drive, Ci(x1 = p, x2 = d) = Ci(x1 = d, x2 = p) = 5 if only one group drives and Ci(x1 = p, x2 = p) = 0 if neither group drives, where i represents either group 1 or group 2. The utility of each group from choosing action xi is equal to the benefits minus the costs: Ui(xi , xj ) = Bi(xi) − Ci(xi , xj ), where i ∈ {1, 2}. 1. Compute the utility of group 1 from driving when group 2 takes public transport: U1(x1 = d, x2 = p). Compute the utility of group 1 from taking public transport when group 2 takes public transport: U1(x1 = p, x2 = p). Does group 1 prefer to drive or take public transport, given that group 2 takes public transport?
Consider two groups of citizens, each group can either choose to drive x = d or to take public transport x = p. The first group, group 1, enjoys driving and has the following benefit from using their car within the ULEZ area: B1(x1 = d) = 18. The second group, group 2, does not enjoy driving and has a benefit of B2(x2 = d) = 0 from driving their car. If they don’t drive, citizens can use public transport to get around. The benefit of doing so is the same for both groups: B1(x1 = p) = B2(x2 = p) = 10. Both groups drive cars that do not meet the ULEZ requirements and therefore create excessive pollution. For simplicity, we consider that pollution, and the health problems it induces, are the main cost of driving. This cost is imposed on both groups and is equal to Ci(x1 = d, x2 = d) = 10 if both groups drive, Ci(x1 = p, x2 = d) = Ci(x1 = d, x2 = p) = 5 if only one group drives and Ci(x1 = p, x2 = p) = 0 if neither group drives, where i represents either group 1 or group 2. The utility of each group from choosing action xi is equal to the benefits minus the costs: Ui(xi , xj ) = Bi(xi) − Ci(xi , xj ), where i ∈ {1, 2}.
1. Compute the utility of group 1 from driving when group 2 takes public transport: U1(x1 = d, x2 = p). Compute the utility of group 1 from taking public transport when group 2 takes public transport: U1(x1 = p, x2 = p). Does group 1 prefer to drive or take public transport, given that group 2 takes public transport?
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