Question

EuroRail and Swiss Rail are hypothetical railways that have a duopoly on the route that connects the cities of Zurich and Munich. Both are considering adding an additional daily train to this route. The payoff matrix shows the payoffs for each railway, where Swiss Rail values are in italics and EuroRail values are in bold. Assume that both companies have complete knowledge of the other's payoff matrix. Add train Add train $4,000 $1,500 $2,000 $4,000 Do not add train $7,500 $2,000 $3,000 $3,000 Do not add train Select the answer that best describes the strategies in this game. O Both companies dominant strategy is to add the train. EuroRail's dominant strategy is to add the train, whereas Swiss Rail does not have a dominant strategy. Neither company has a dominant strategy. EuroRail's dominant strategy is to not add the train, whereas Swiss Rail's dominant strategy is to add the train. Does a Nash equilibrium exist in this game? O Yes, it exists in the lower left quadrant. O No, it does not exist. Yes, it exists in the upper right quadrant. Yes, it exists in the upper left quadrant.

Answer 1

Answer:

Select the answer that best describes the strategies in this game.

• Both companies dominant strategy is to add the train.

Does a Nash equilibrium exist in this game?

• A Nash equilibrium exists where both companies add a train. (Since I'm not sure how your matrix is set up I do not know the specific location).

Explanation:

we can prepare a matrix to determine the best strategy:

                                                  Swiss Rails

                                     add train             do not add train

                                    $1,500 /             $2,000 /

           add train                     $4,000                $7,500

EuroRail

      do not add train    $4,000 /             $3,000 /

                                               $2,000                $3,000

Swiss Rails' dominant strategy is to add the train = $1,500 + $4,000 = $5,500. The additional revenue generated by not adding = $5,000.

EuroRail's dominant strategy is to add the train = $4,000 + $7,500 = $11,500. The additional revenue generated by not adding = $5,000.

A Nash equilibrium exists because both companies' dominant strategy is to add a train.