Show that the game has a mixed strategy nash equilibrium

Reference no: EM13907076

(Choosing numbers) Players 1 and 2 each choose a positive integer up to K. If the players choose the same number then player 2 pays $1 to player 1; otherwise no payment is made. Each player's preferences are represented by her expected monetary payoff.

a. Show that the game has a mixed strategy Nash equilibrium in which each player chooses each positive integer up to K with probability 1/K.

b. (More difficult.) Show that the game has no other mixed strategy Nash equi- libria. (Deduce from the fact that player 1 assigns positive probability to some action k that player 2 must do so; then look at the implied restriction on player 1's equilibrium strategy.)

Reference no: EM13907076

Questions Cloud

Show that game has no nash equilibrium in pure strategies : Show that the game has no Nash equilibrium in pure strategies, and that the pair of mixed strategies in which each player chooses 1, 2, and 5 each with probability 1 is a mixed strategy Nash equilibrium.

What is your estimate of the stocks current price : A company currently pays a dividend of $2.75 per share (D0 = $2.75). It is estimated that the company's dividend will grow at a rate of 25% per year for the next 2 years, and then at a constant rate of 6% thereafter. The company's stock has a beta of..

Explain what course of action is recommended : Explain what course of action is recommended

Identify which ethical principles apply to these decisions : Generate at least two ideas for ways that medical errors could be reduced and identify which ethical principles apply to these decisions, the individuals involved, the organization, and the community. Be sure to focus on the ethics part and NOT th..

Show that the game has a mixed strategy nash equilibrium : Show that the game has a mixed strategy Nash equilibrium in which each player chooses each positive integer up to K with probability 1/K.

Find the crossover rate for projects : Consider the following cash flows for projects A and B.-$1000 900 700 500 -200 200 The cost of capital for both projects is 10% a. Find the NPV and MIRR of projects A and B. If projects A and B are mutually exclusive, which project would you select?

Calculate the commission owing for that record : Construct an algorithm that will read a record on the file, calculate the commission owing for that record, and print the retail price, commission and employee number

Represents an extract from the business accounting records : The Balance Sheet of the book wholesaler " Read More Books" owned by John Read, reported assets of $215,500 and liabilities of $93500 as at 1 July 2014. You are presented with the following extract from the business accounts at 30 June 2015. Note tha..

Find the mixed strategy nash equilibria of the game : Find the mixed strategy Nash equilibria of the game (depending on c and Π). Does the existence of a friend make it more or less likely that you decide to go swimming on the first day?

User Account

All Pages