Final answer:
The game between Eurorail and Swissrail, two railway companies considering adding an additional train on the Zurich to Munich route, is described by the Oligopoly version of the Prisoner's Dilemma. Swissrail has a dominant strategy: to add the train.
Step-by-step explanation:
A Nash equilibrium exists where Eurorail adds a train, and Swissrail does not, in the upper right quadrant of the payoff matrix.
In the scenario presented, where Eurorail and Swissrail, two railway companies, consider adding an additional daily train on the Zurich to Munich route, we are looking at a situation similar to the Oligopoly version of the Prisoner's Dilemma.
A duopoly exists here, with both companies being aware of each other's payoff matrix. The question is about determining the dominant strategies for each company and identifying any potential Nash equilibrium.
By examining the payoff matrix, we can deduce the strategies. If Eurorail adds a train, their best response is contingent upon Swissrail's action.
They earn $4,000 if Swissrail also adds a train, and $7,500 if Swissrail does not. If Eurorail does not add a train, they earn $2,000 if Swissrail adds, and $3,000 if Swissrail does not. For Eurorail, there is no dominant strategy as their best response depends on Swissrail's actions.
Conversely, for Swissrail, adding a train earns them $4,000 or $1,500, compared to not adding, which earns them $2,000 or $3,000. Swissrail's highest payoff comes from adding the train, irrespective of Eurorail's decision, making it their dominant strategy.
Concerning the existence of a Nash equilibrium, it occurs when both players choose the actions that give them the highest payoff, given the other player's action.
In this case, the Nash equilibrium exists in the upper right quadrant of the payoff matrix, where Eurorail adds a train, and Swissrail does not add a train, resulting in payoffs of $7,500 and $2,000, respectively.
Both companies choose the best possible strategy in response to the other's action, so neither has an incentive to deviate, fulfilling the Nash equilibrium condition.