Acme's Advertising Strategy Ajax's Advertising Strategy Large Budget Small Budget A B Large Budget $800 $800 $600 $1200 Small Budget C D $1200 $1000 $600 $1000 Refer to the game theory matrix, where the numerical data show the profits resulting from alternative combinations of advertising strategies for Ajax and Acme. Ajax's profits are shown in the upper right part of each cell; Acme's profits are shown in the lower left. With collusion and no cheating, the outcome of the game is cell Multiple Choice О О B. A.

See page 561 02 Question John and Daniel greatly enjoy each other's company but have different tastes regarding the best form of entertainment. John prefers the lowbrow entertainment of professional wrestling that disgusts Daniel. Meanwhile, Daniel likes highbrow opera, which bores John. However, each finds it preferable to spend the evening together rather than disagree about what to do and end up staying home angry. This interaction is modeled in the normal-form game below: Evening Entertainment John Part 1 Wrestling Opera Choose one or more: Daniel Wrestling 12.00, 4.00 0,0 Identify any pure strategy equilibria of this game. A. (wrestling, wrestling) B. (wrestling, opera) OC. (opera, wrestling) Part 2 Opera 0,0 6.00, 18.00 D. (opera, opera) DE. There are no pure strategy equilibria. Find the mixed strategy Nash equilibrium of this game. In it, John will choose wrestling with probability choose wrestling with probability (Give your answers to two decimal points.) See H See Hir ,and…

II.2 Companies A and B can compete on advertising or R&D. The profits (in millions of $ million) of the two firms are given in the table below assumig that they play a one-shot simultancous mov game (the profit or firm A is listed first in every cell of the matrix, followed by the profit of firm B): Advertising R&D 50, 25 10, 70 20, 40 60, 35 1. Find the mixed strategy equilibrium. A\B Advertising R&D 2. What are the expected profits for both firms in this equilibrium?

fnan421 WWord Gozden Geç r Gorunum Varc m Ne yaomak steci gnz soy evn 1) Two firms, X and Y, are planning to market their new products. Each firm can develop either TV or Laptop. Market research indicates that the resulting profits to each firm for the alternative strategies are given by the following payoff matrix: FIRM Y TV LAPTOP FIRM X TV 30, 30 50, 35 LAPTOP 40,70 20, 20 A) If both firms make their decisions at the same time and follow maximin (low-risk) strategies, what will the outcome be? B) Suppose both firms try to maximize profits, but Firm X has a head start in planning, and can commit first. Now what will the outcome be? What will the outcome be if Firm Y has a head start in planning and can commit first? I

Previous research suggests that many firms ‘over - invest’ in advertising - meaning spend beyond a point where advertising positively affects a firm’s bottom line (if interested see here: Advertising Effectiveness). Game Theory can explain some of this, but not all. What else can explain why many firms over invest in advertising? Are there are any reasons for firms to advertise beyond wanting to increase profits? Note: two recent Freakonomics on this topic can be found here: https://freakonomics.com/podcast/advertising-part-1 and https://freakonomics.com/podcast/advertising-part-2

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E.  Game theory   Two firms in Ithaca both making sandwiches have two strategies available:   charge a low price and charge a high price.    In each cell (box) the first entry is the profit to Angie’s Sandwiches (AS) and the second entry is the profit per week for James Jems. (JJ)   JJ charges low price JJ charges high price AS charges low price $20,000, $20,000 $45,000, $50,000 AS charges high price $50,000, $35,000 $30,000, $30,000   1.   Is there a Nash Equilibrium?   Where is it?   Explain.   2.   In which cell will the total profit be a maximum?

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5. The following problem was first considered by John von Neumann and is a fundamentalresult game theory.A and B play the following game:ˆA writes down either number 1 or number 2, and B must guess which one.ˆIf the number that A has written down is i and B has guessed correctly, B receives i units from A.ˆIf B makes a wrong guess, B pays 4/5 of a unit to A.First we consider the expected gain of player B.ˆSuppose B guesses 1 with probability p and 2 with probability 1 −p.ˆLet X1 denote B’s gain (or loss) in a game where A has written down 1.ˆLet X2 denote B’s gain (or loss) in a game where A has written down 2.(a)  Find the pmf of X1 and X2(b)  Find B’s expected gain for these two cases, E[X1] and E[X2].(c)  What value of p maximizes the minimum possible value of B’s expected gain?Now consider the expected loss of player AˆSuppose that A writes down 1 with probability q and 2 with probability 1 −q.ˆLet Y1 be A’s loss (or gain) if B chooses number 1.ˆLet Y2 be A’s loss (or gain) if B…