Reference no: EM131252245
Consider a game that has a continuum of players. In particular, the players are uniformly distributed on the interval [0, 1]. (See Appendix A for the definition of uniform distribution.) Each x ∈ [0, 1] represents an individual player; that is, we can identify a player by her location on the interval [0, 1]. In the game, the players simultaneously and independently select either F or G.
The story is that each player is choosing a type of music software to buy, where F and G are the competing brands. The players have different values of the two brands; they also have a preference for buying what other people are buying (either because they want to be in fashion or they find it easier to exchange music with others who use the same software).
The following payoff function represents these preferences. If player x selects G, then her payoff is the constant g. If player x selects F, then her payoff is 2m - cx, where c is a constant and m is the fraction of players who select F. Note that m is between 0 and 1
(a) Consider the case in which g = 1 and c = 0. What are the rationalizable strategies for the players? Is there a symmetric Nash equilibrium, in which all of the players play the same strategy? If so, describe such an equilibrium.
(b) Next, consider the case in which g = 1 and c = 2. Calculate the rationalizable strategy profiles and show your steps. (Hint: Let m denote an upper bound on the fraction of players who rationally select F. Use this variable in your analysis.)
c) Describe the rationalizable strategy profiles for the case in which g = -1 and c = 4.
|
What theorem of number theory does this prove
: How many ways are there to do the same if we do not consider two paint jobs different if one can be obtained from the other by rotation?
|
|
Initialization vector iv for running
: Assume that the initialization vector IV for running the considered block cipher in CBC mode is known. How many plaintexts and ciphertexts are now needed to break the cipher by performing an exhaustive key search? How many steps need now maximally..
|
|
Create your own hypothesis about the world of work
: One hypothesis might read: Manufacturing jobs are decreasing in the United States because more manufacturing work is being done overseas. Create your own hypothesis about the world of work. Then, brainstorm ways you would find data to prove your h..
|
|
Description of the procedural steps
: Describe the steps you took to use each function. Explain when each function would be useful. Submit a copy of original document and amended document you created together with your description of the procedural steps you took (saved as one file).
|
|
What are the rationalizable strategies for the players
: What are the rationalizable strategies for the players? - Is there a symmetric Nash equilibrium, in which all of the players play the same strategy?
|
|
Describe what you think are the top three social problems
: Write an essay (750-1,000 words) in which you define and describe what you think are the top three social problems in the United States at the present time. Explain why these issues are important. Also, explain what conditions led to the emergence..
|
|
Analyze essential attributes in coordinating integrated unit
: Analyze the essential attributes and flaws in coordinating integrated units in multiage classrooms. Determine at least four conceptual lenses that will affect the coordination of the integrated units.
|
|
Types of traffic flow discussed in the lectures
: Does cloud computing fit into the types of traffic flow discussed in the lectures (terminal/host, client/server, peer-to-peer, server/server, etc) or is it a new type of traffic flow? Why?
|
|
What are the nash equilibria under the assumption
: What are the Nash equilibria under the assumption that the police do not ticket anyone? - What are the Nash equilibria under the assumption that the police ticket everyone who travels more than 70?
|