show steps and ans! Drivers on the two-lane highway that passes Dogwood, Alabama

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show steps and ans!

Drivers on the two-lane highway that passes Dogwood, Alabama frequently exceed the posted speed limit of 55 miles per hour The Sheriff's Department can catch and convict speeders either through patrol-car chase, or using a radar trap (rented from the county) Speeders can be caught without radar, by patrol-car chase, but convictions are uncertain and the chases are dangerous and costly. The NET payoff to the Sheriffs Department of catching and convicting speeders through chase is considerably lower than the payoff, net of radar rental cost, of catching speeders using the radar trap. The payoff (dollar value of time saved) to drivers of speeding is higher if the Sheriffs Department does NOT use radar, as the chances of being caught and convicted through patrol car chase is small Many residents and users of the road believe that the use of radar traps makes the road much safer, n speeders obtain a positive payoff from the Sheriffs use of radar traps. If there were no speeders, if all drivers travelled WITHIN the posted speed limit, the Sheriff's department would not incur the cost of either patrol-car chases or radar-trap rental and administration The payoffs to drivers and to the Sheriff s Department are represented in the payoff matrix below. Strategies of (representative, typical) drivers are Exceed Speed Limit (Left), or Within Speed Limit (Right). Strategies of the Sheriff's Department are No Radar (Up) and Radar (Down). The first (blue) number in each cell is payoff to Sheriff, the second (red) is payoff to (typical) Driver:

Explanation / Answer

at nash equilibrium both the parties will be looking at the option which benefits them individually.

in this case

sheriff is benefited by using radar if driver exceeds speed limit as the net payoff is high

whereas the driver exceeding the speed limit is benefited from the chase as the payoff is high.

so the payoff for sheriff is less than 250 because the driver will exceed the speed limit only when there is no radar providing a payoff of 100 and will be within the speed limit if the radar is there thus providing a payoff of 200.

so in either case the payoff is less than 250.

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