Question 1

Consider a duopoly game in which two firms simultaneously and independently select prices that are greater than or equal to zero. Denote firm 1's price as $P_1$ and firm 2's price as $P_2$. After the prices are set, consumers demand $10 - P_1 + P_2$ units of the good that firm 1 produces, and they demand $10 - P_2 + P_1$ units of the good that firm 2 produces. Assume that each firm produces at zero cost, so firm $i$'s payoff (profit) is $(10 - P_i + P_j)P_i$, where $P_i$ is firm $i$'s price and $P_j$ is the other firm's price. Answer the given sub questions based on this information: Figure from the original question paper Consider a duopoly game in which two firms simultaneously and independently select prices that are greater than or equal to zero. Denote firm 1's price as $P_1$ and firm 2's price as $P_2$. After the prices are set, consumers demand $10 - P_1 + P_2$ units of the good that firm 1 produces, and they demand $10 - P_2 + P_1$ units of the good that firm 2 produces. Assume that each firm produces at zero cost, so firm $i$'s payoff (profit) is $(10 - P_i + P_j)P_i$, where $P_i$ is firm $i$'s price and $P_j$ is the other firm's price. Answer the given sub questions based on this information: Choose the incorrect statement **(Choosing a route)** Four people must drive from A to B at the same time. Two routes are available, one via X and one via Y (Refer to the left panel of following Figure). The roads from A to X, and from Y to B are both short and narrow; in each case, one car takes 6 minutes, and each additional car increases the travel time per car by 3 minutes. (If two cars drive from A to X, for example, each car takes 9 minutes.) The roads from A to Y, and from X to B are long and wide; on A to Y one car takes 20 minutes, and each additional car increases the travel time per car by 1 minute; on X to B one car takes 20 minutes, and each additional car increases the travel time per car by 0.9 minutes. Formulate this situation as a strategic game and answer the given subquestions. Road network diagrams from A to B via X and Y, original network and network with new road from X to Y, with travel times on each road Choose the correct alternative