Question

eurorail and swissrail 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 eurorail's payoffs for each outcome are listed first in each cell. assume that both companies have complete knowledge of the other's payoff matrix. swissrail add train do not add train eurorail add train $4,000, $1,500 $7,500, $2,000 do not add train $2,000, $4,000 $3,000, $3,000 select the answer that best describes the strategies in this game. neither company has a dominant strategy. eurorail's dominant strategy is to not add the train, whereas swissrail's dominant strategy is to add the train. both companies dominant strategy is to add the train. eurorail's dominant strategy is to add the train, whereas swissrail does not have a dominant strategy. does a nash equilibrium exist in this game? yes, it exists in the upper right quadrant. yes, it exists in the lower left quadrant. yes, it exists in the upper left quadrant. no, it does not exist.

Answer 1

In the given duopoly scenario of Eurorail and Swissrail, Swissrail's dominant strategy is to add the train, while Eurorail has no dominant strategy. The Nash equilibrium occurs at the lower left quadrant of the payoff matrix, where Eurorail does not add a train and Swissrail adds a train.

Step-by-step explanation:

The scenario presented is an example of an oligopoly situation, where two companies, Eurorail and Swissrail, operate in a duopoly and face a Prisoner's Dilemma. The decision whether to add an extra train on the route connecting Zurich and Munich can be analyzed using game theory. A dominant strategy is one that is the best choice for a player, no matter what the other player decides to do. According to the payoff matrix provided, if we compare the payoffs for Eurorail and Swissrail for both strategies (to add or not to add an extra train), we can identify the Nash equilibrium and dominant strategies.

Eurorail has no dominant strategy because the best decision depends on Swissrail's action. On the other hand, Swissrail's dominant strategy would be to add the train because it gives better payoffs ($4,000 vs. $3,000 if Eurorail adds a train, and $2,000 vs. $3,000 if Eurorail doesn't). The Nash equilibrium is the situation where both firms choose the best possible strategy, given the other firm's strategy, and in this scenario, it exists in the lower left quadrant where Eurorail does not add a train and Swissrail does, resulting in payoffs of $2,000 and $4,000 respectively.

Answer 2

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.