gameLBraess

# gameLBraess - The(Braess Transportation Paradox Route 1...

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The (Braess) Transportation Paradox −→ slow road: 15 minutes −→ B Route 1 Bridge B Bridge A Route 2 A −→ slow road: 15 minutes −→ 1000 cars must commute from point A to point B. East-West roads take 15 minutes, no matter how many cars are on the road. North-South roads are fast, but the bridges can get con- gested. Ab r idgew ith F cars takes

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Modeling the Commuting Problem as a Strategic Game N = { 1 , 2 ,..., 1000 } A i = { 1 , 2 } For j =1 , 2 ,de f ne the number of cars taking Route j R j = 1000 X i =1 1 a i = j u i ( a )= [15 + R 1 100 ] if a i =1 u i ( a )= [15 + R 2 100 ] if a i =2 It is easy to see that any pure strategy Nash equilibrium has 500 cars taking each route, with a payo f of 20 (commuting time of 20 minutes). For example, a i =1 if i is odd, and a i =2 if i is even.
Now suppose that we add a new East-West road, which takes 7.5 minutes, no matter how many cars use the road. This adds another possible route, Route 3, which uses

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gameLBraess - The(Braess Transportation Paradox Route 1...

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