Consider the following n-player variant of the game of the Prisoners' Dilemma: Each player i chooses...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Consider the following n-player variant of the game of the Prisoners' Dilemma: Each player i chooses from a set of strate- gies A, = {C, D}. Payoffs are given as follows: . If i plays a, = C and k other players (0 ≤ k ≤ n - 1), j, play a, = D. then i receives 3 - (2). n . If i plays a play aj D and exactly k other players (0 ≤ k ≤n-1), j, D, then i receives frame The idea is that a defecting player gets a good deal if they are the only player providing the evidence, but that deal is not as good as more other players also give evidence to the police. Also, the quality of the evidence the Police have to convict players that choose C (or the chance that a Court will use this evidence) is increasing in the number of people that provide the evidence (i.e., the number that choose D). (You can verify that this game is identical to the two-player Prisoners' Dilemma when 7 = 2.) (a) (2 point) Show that the profile where all players cooperate (C..... C) is not a Nash equilibrium for all n. (b) (3 points) Show that the profile where all players defect (D...., D) is a Nash equilibrium for all n. (Hint: Apply the definition.) (e) (6 points) Using the definition of Nash equilibrium, write two inequalities (expressed in terms of k* and n) that are necessary and sufficient for a profile with exactly k (0 <k* <n) players playing D to be a Nash equilibrium. (Hint: Players that play D must not find it profitable to deviate to C; and the same for those playing D. You do not need to solve these inequalities for k* .) (d) (2 points) Based on your answer in part (e), are there Nash equi- 32 libria with only one (k = 1) player playing D when = When n25? Explain. Consider the following n-player variant of the game of the Prisoners' Dilemma: Each player i chooses from a set of strate- gies A, = {C, D}. Payoffs are given as follows: . If i plays a, = C and k other players (0 ≤ k ≤ n - 1), j, play a, = D. then i receives 3 - (2). n . If i plays a play aj D and exactly k other players (0 ≤ k ≤n-1), j, D, then i receives frame The idea is that a defecting player gets a good deal if they are the only player providing the evidence, but that deal is not as good as more other players also give evidence to the police. Also, the quality of the evidence the Police have to convict players that choose C (or the chance that a Court will use this evidence) is increasing in the number of people that provide the evidence (i.e., the number that choose D). (You can verify that this game is identical to the two-player Prisoners' Dilemma when 7 = 2.) (a) (2 point) Show that the profile where all players cooperate (C..... C) is not a Nash equilibrium for all n. (b) (3 points) Show that the profile where all players defect (D...., D) is a Nash equilibrium for all n. (Hint: Apply the definition.) (e) (6 points) Using the definition of Nash equilibrium, write two inequalities (expressed in terms of k* and n) that are necessary and sufficient for a profile with exactly k (0 <k* <n) players playing D to be a Nash equilibrium. (Hint: Players that play D must not find it profitable to deviate to C; and the same for those playing D. You do not need to solve these inequalities for k* .) (d) (2 points) Based on your answer in part (e), are there Nash equi- 32 libria with only one (k = 1) player playing D when = When n25? Explain.
Expert Answer:
Answer rating: 100% (QA)
aThe profile where all players cooperate is not a Nash equilibrium for all n because there is always ... View the full answer
Related Book For
Posted Date:
Students also viewed these economics questions
-
When you do not know how many items need to be sorted in a program, you can create an array that has _____. a. Variable-sized elements b. At least as many elements as the number you predict you will...
-
Consider the following game between two players. Each player i has an initial endowment of 5 cans of beer. This beer can hidden in their private account (xi) or put in a public account, the fridge...
-
Consider a simultaneous game in which player A chooses one of two actions (Up or Down), and B chooses one of two actions (Left or Right). The game has the following payoff matrix, where the first...
-
What are the three workflows in the revised SELECT Perspective (Apperly et al., 2003)?
-
A maintenance supervisor is comparing the standard version of an instructional booklet with one that has been claimed to be superior. An experiment is conducted in which 26 technicians are divided...
-
To what extent are the determinants and characteristics of audit quality similar to those of the audit expectations gap?
-
Spice Inc. issued bonds payable on December 31. Spice's bonds were dated July 31. Which statement is true of Spice's journal entry to record issuance of the bonds payable? a. Spice must pay one...
-
Describe briefly the legal rights and privileges of common stockholders. MINI CASE Sam Struthers and Shawna Tibbs are senior vice presidents of the Mutual of Seattle. They are co-directors of the...
-
Abigail is a beneficiary of a Reverse Q-Tip Marital Trust established under her late husband's Will, valued at $3.5 million. Abigail also has property in her name alone worth $12 million. During her...
-
Sparky's Amusement Park is an entertainment park run by recent college graduates. It caters to young people and others who are young at heart. The owners are very interested in applying what they...
-
You are a manager at Percolated Fiber, which is considering adding a new product line. Your boss said to you "We already owe these consultants $1.2 million, and all they estimated is Net Income....
-
Companies have codes of conduct, and with recent financial scandals, there are a few that have specific codes of conducts spelled out for their CFOs. Research three companies with specific codes of...
-
Identify the statistical population, sample, and variable of interest in each of the following situations: (a) Tensile strength is measured on 20 specimens of super strength thread made of the same...
-
The output of an instrument is often a waveform. With the goal of developing a numerical measure of closeness, scientists asked 11 experts to look at two waveforms on the same graph and give a number...
-
A factory experiencing a board-solder defect problem with an LED panel board product tested each board manufactured for LED failure. Data were collected on the area of the board on which LEDs were...
-
Show that \[\sum_{i=1}^{n}\left(x_{i}-\bar{x} ight)=0\] for any set of observations $x_{1}, x_{2}, \ldots, x_{n}$.
-
Marc's mutual funds have had yearly changes of -11.60%, -6.12%, and 3.78%. Calculate the annual average change in Marc's investment. Give your answer as a percent accurate to at least two decimal...
-
A sprinkler head malfunctions at midfield in an NFL football field. The puddle of water forms a circular pattern around the sprinkler head with a radius in yards that grows as a function of time, in...
-
Attaching structures end to end is called _____________. a. Nesting b. Untangling c. Building d. Stacking
-
When you use an IDE instead of a simple text editor to develop a program, ____________. a. The logic is more complicated b. The logic is simpler c. The syntax is different d. Some help is provided
-
Create the logic for a program that prompts a user for 12 numbers and stores them in an array. Pass the array to a method that reverses the order of the numbers. Display the reversed numbers in the...
-
True or False. Vibration can cause structural and mechanical failures.
-
A car moving on a rough road, in the form of a sinusoidal surface, is modeled as a springmass system, as shown in Fig. 9.41. The sinusoidal surface has a wave length of \(5 \mathrm{~m}\) and an...
-
Name some sources of industrial vibration.
Study smarter with the SolutionInn App