х Problem 5 Four thousand cars must travel from point A to point B every morning. Travel can take place on either the path A-C-B or the path A-D-B. Travel time on segments C-B and A-D equal 20 minutes each regardless of how many cars are in the respective segment. Segments A-C and D-B are subject to congestion: if there are x cars on segment A-C it takes minutes to complete the segment whereas if there are if there are x cars on segment D-B it takes minutes to complete the segment. A Nash equilibrium of this game is a distribution of the cars on the transportation network such that no driver has incentives to deviate from their choices as represented on that distribution. 40 х 120 Find the Nash equilibrium of this game. What is the travel time each driver experience in going from A to B in equilibrium? Problem 6. Take the network traffic configuration depicted in Problem 5. The authorities add to the network a new highway that goes directly from A to B. It will be subject to congestion as follows: If there are x cars on this new segment A-B it takes minutes to complete the segment. х 80 Find the Nash equilibrium of this game. What is the travel time each driver experience in going from A to B in equilibrium?
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