What does it mean for a strategy to weakly dominate

Assignment Help Mathematics

Reference no: EM13978388

1. Definitions-

Problem 1-(a) In a game, what does it mean for X to be common knowledge?

(b) What does it mean for a strategy s_i to weakly dominate another strategy s_i' ?

(d) What is an Nash equilibrium?

2. Application-

Problem 1- Recall Matching Pennies version 2, where player 2 observes what side of the coin player 1 has chosen before he chooses.
(a) Player 1, sensing this is quite unfair for her, demand that they revise the rule of the game. Player 2 agreed, but he demanded that he still be able to observe player 1's choice before he chooses. What can be changed about and/or added to the game so that the game is just as fair as when player 2 does not observe player 1's choice? Anything about the game can be changed except that 1) player 1 moves first then player 2 moves; 2) player 1 and 2 only may choose head or tail at each of his/her information sets; and 3) that player 2 observe player 1's choice. Represent the modified game in extensive form
(b) Represent the game in normal form. Is there a Nash equilibrium where both players play pure strategies?

Problem 2- Recall the Cournot competition discussed in class. Show that when firm 1 knows that firm 2 is rational and that firm 2 knows his profit function, 0 ≤ q1 < 2 is strictly dominated for firm 1 by q1 = 2 and also show that 2 < q1 ≤ 4 is not strictly dominated.

Problem 3- Represent the Hide-and-Seek game where there are only two cups and two players in normal form. If you hide a coin under a cup and seek where you hid, you do not get any payoff (unless your opponent happens to hide where you seek (and hide) as well). Is there any Nash equilibrium where both players play a pure strategy?

Problem 4- Recall the Bertrand competition, but now players can choose any price, not just the integer price. The market demand function is p = 8-q and only the firm that offers lowest price gets to earn revenue. When both firms offer the same price, say p, then they each sell the quantity 8-p/2 at the price of p (so of course firms will not want to charge a price p > 8) For simplicity, let the marginal cost be equal to zero for both firms. Show that

(a) both firms offering difference prices, both of which are greater than 0, is not a Nash equilibrium;
(b) both firms offering the same price higher than zero is not a Nash equilibrium; and
(c) both firms offering the price of zero is a Nash equilibrium.

Reference no: EM13978388

Questions Cloud

What are two arguments against productivity growth : What are two arguments against productivity growth as an explanation of the large U.S. current account deficits.

In an effort to control cost a quality control manager : In an effort to control cost, a quality control manager is interested in whether the mean number of ounces of sauce dispensed by bottle filling machines differs from 16 ounces

Determine an expression of the acceleration of each block : Determine an expression of the acceleration of each block for case when the blocks have different masses, but the heavier block 1 (mass m1) is positioned higher than the light one.

Income onmusic track downloads : John has a monthly allowance of $40. He spends all of this income onmusic track downloads and "other goods". Draw an indifference curvediagram with music downloads on the horizontal axis and "dollars spent onother goods" on the vertical axis. When th..

What does it mean for a strategy to weakly dominate : In a game, what does it mean for X to be common knowledge? What does it mean for a strategy si to weakly dominate another strategy si'? What does it mean for a strategy si to be never a best response

Will you provide toms parents with a copy of the clinic note : Tom is an employed, married 16-year-old male. He has recently been ill and saw his physician at the Rasmussen Clinic. Naturally his parents are concerned and have asked for a copy of the clinic visit.

What is the new capacitance of the capacitor : Consider two parallel-plate capacitors identical in shape, one aligned so that the plates are horizontal (Figure 1) , and the other with the plates vertical (Figure 2) . The horizontal capacitor is filled halfway with a material that has dielectri..

Explain how does the fact that a number of counties : Explain how does the fact that a number of counties and cities also have their own income taxes affect the top marginal tax rate for some higher earners.

The producer of a snack food claims that each package : Find and interpret the p value for testing that the mean weight of the snack food is less than 175 grams.

User Account

All Pages