Problem Set VI The solutions to the following questions are due in your portfolio. The final solutions must be highlighted or circled. The questions are hypothetical and are not meant to represent reality. 1. This is a game between a data storage company and a customer. The company can be one of two types: safe, meaning the company uses extra precautions to protect its customers' data, or unsafe, meaning the company uses very few precautions. Nature moves first and selects the safe company with probability p and the unsafe company with probability 1-p. Nature then moves again and sends a noisy signal to the customer about past data breaches. The company knows its type. The customer does not observe the type of the company, but he does know the prior probabilities and he observes the signal from past data breaches. The probability of a data breach if the company is safe is 1/2. The probability of a data breach it the company is unsafe is 3/4. (a) Use Bayes' Rule to find the posterior probability (after receiving the signal about past data breaches) that the company is unsafe following no data breach. [1 point (b) Use Bayes' Rule to find the posterior probability (after receiving the signal about past data breaches) that the company is unsafe following a data breach. [1 point] Now assume that after getting the signal, the customer decides whether to use this storage company or not. If not, both the customer and the company get a payoff of 0. If the customer uses the storage company's service, the company decides whether to share the customer's data with third parties (making it less secure). The customer gets a benefit of 6 from using the company's services and pays a cost of d if the company shares his data. The safe company gets a payoff of O from sharing the data and a payoff of r from not sharing, where r > 0. The unsafe company gets a payoff of II from sharing the data and a payoff of 0 from not sharing, where II >0. (c) What critical value of b, call it b', makes the customer indifferent between using the storage company and not using the storage company after he observes no breach? Hint: Set the customer's payoff from using the company equal to the payoff for not using the company and solve for b. [1 point) (d) Now assume that b> be and the customer observes no breach. Describe the strategies played by the company and the customer, as well as the beliefs of the customer, in a Perfect Bayesian equilibrium. [1 point) Problem Set VI The solutions to the following questions are due in your portfolio. The final solutions must be highlighted or circled. The questions are hypothetical and are not meant to represent reality. 1. This is a game between a data storage company and a customer. The company can be one of two types: safe, meaning the company uses extra precautions to protect its customers' data, or unsafe, meaning the company uses very few precautions. Nature moves first and selects the safe company with probability p and the unsafe company with probability 1-p. Nature then moves again and sends a noisy signal to the customer about past data breaches. The company knows its type. The customer does not observe the type of the company, but he does know the prior probabilities and he observes the signal from past data breaches. The probability of a data breach if the company is safe is 1/2. The probability of a data breach it the company is unsafe is 3/4. (a) Use Bayes' Rule to find the posterior probability (after receiving the signal about past data breaches) that the company is unsafe following no data breach. [1 point (b) Use Bayes' Rule to find the posterior probability (after receiving the signal about past data breaches) that the company is unsafe following a data breach. [1 point] Now assume that after getting the signal, the customer decides whether to use this storage company or not. If not, both the customer and the company get a payoff of 0. If the customer uses the storage company's service, the company decides whether to share the customer's data with third parties (making it less secure). The customer gets a benefit of 6 from using the company's services and pays a cost of d if the company shares his data. The safe company gets a payoff of O from sharing the data and a payoff of r from not sharing, where r > 0. The unsafe company gets a payoff of II from sharing the data and a payoff of 0 from not sharing, where II >0. (c) What critical value of b, call it b', makes the customer indifferent between using the storage company and not using the storage company after he observes no breach? Hint: Set the customer's payoff from using the company equal to the payoff for not using the company and solve for b. [1 point) (d) Now assume that b> be and the customer observes no breach. Describe the strategies played by the company and the customer, as well as the beliefs of the customer, in a Perfect Bayesian equilibrium. [1 point)
