Game Theory and Strategy Quiz 1: 13 July 2025 (May 2025 term)

**(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

Based on the above data, answer the given subquestions.

Choose the correct alternative .

**(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

Based on the above data, answer the given subquestions.

Now suppose that a relatively short, wide road is built from X to Y, giving each person four options for travel from A to B: A–X–B, A–Y–B, A–X–Y–B, and A–Y– X–B (As shown in the right panel of the given figure). Assume that a person who takes A–X–Y–B travels the A–X portion at the same time as someone who takes A–X–B, and the Y–B portion at the same time as someone who takes A–Y–B. (Think of there being constant flows of traffic.) On the road between X and Y, one car takes 7 minutes and each additional car increases the travel time per car by 1 minute. Find the Nash equilibrium in this new situation
Choose the correct alternative

Determined to crack down on the drug trade, a city mayor puts more officers out on patrol to disrupt the business of drug dealers. A drug dealer in a neighborhood can work his trade either on a street corner or in the park. Each day, he decides where to set up shop, knowing that word about his location will travel among users. Because a good snitch is lacking, word does not travel to the police. The police officer on the beat then needs to decide whether she will patrol the park or the street corner, while not knowing where the drug dealer is hanging out that day. The decision of the officer and the dealer determine the extent of drug trades that day. Let suppose the total number of potential trades in the market is 500. A dealer's payoff is determined by the number of trades he consummates, while the officer’s payoff is based on the number of trades she disrupts. The table below illustrates the payoffs for both parties according to their respective strategies in the game.

Based on the above data, answer the given subquestions.

Choose the correct statement