In a small town there are two pizza restaurants . If neither restaurant advertises, its revenue will not change. If only one firm advertises, the firm that advertises will double its revenue and the firm that doesn't advertise will see a decrease in its revenue, but if both firms advertise, their revenue will not change. What outcome would be predicted by game theory in this market? Both restaurants will advertise. Game theory would predict chat sometimes one restaurant would advertise, and the rest of the time both will advertise. ONeither restaurant will advertise Game theory is only a theory and cannot predict real-world events. One restaurant will advertise.
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- Game theory has a wide range of applicationsin business and economics. e.g. market coordination, pricing strategy, advertising decision etc. Now suppose that your firm competes against another firm for customers. You and your rivals know that your products will be obsolete at the end of the year and must simultaneously determine whether or not to advertise. In this type of business, the effect of advertising is not to entice customers to buy the product but to induce them to switch among the products of different firms. Given the following pay-off matrix; FIRM A Strategy FIRM B Advertise NOT Advertise Advertise P4,000 / P4,000 P20,000 / P1,000 Don’t Advertise P1,000 / P2,000 P10,000 / P10,000 Using a simultaneous move – one shot game routine, determine the following; • Dominant strategy • Nash equilibrium • Under the Nash equilibrium condition, what is the optimum…There are two firms in an industry, Firm A and Firm B. If firm A and firm B both advertise, they each will earn $5 million in profits. If neither firm advertises, they will each earn $10 million in profits. However, if one firm advertises and the other does not, the firm that advertises will earn $15 million and the non-advertising firm will earn $1 million. List all Nash equilibrium to this game. Both firms advertise Firm A advertises and Firm B does not Firm B advertises and Firm B does not Neither firm advertises No Nash equilbrium existsBarnes and Nobel and Amazon are the two largest online book retailers in the U.S.. The two companies compete in the online market for‘Harry Potter and the Sorcerer’s Stone’, a famous book by the English author J. K. Rawling. Both companies can buy copies of the bookfrom Scholastic at $8 per copy and have an additional average cost $1 per copy.Use game theoretical concepts to explain why, even if the two companies have significant market power, on most days they both sell the bookat $9 per copy.
- 7. Solving for dominant strategies and the Nash equilibrium Suppose Dmitri and Frances are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Dmitri chooses Right and Frances chooses Right, Dmitri will receive a payoff of 7 and Frances will receive a payoff of 6. Frances Left Right Left 4, 3 6, 4 Dmitri Right 6, 7 7, 6 to choose The only dominant strategy in this game is for and Frances chooses The outcome reflecting the unique Nash equilibrium in this game is as follows: Dmitri chooses vDairy King Advertise Doesn't Advertise Advertise 7,7 12, 3 Creamland Doesn't Advertise 3, 12 10, 10 For example, the upper right cell shows that if Creamland advertises and Dairy King doesn't advertise, Creamland will make a profit of $12 million, and Dairy King will make a profit of $3 million. Assume this is a simultaneous game and that Creamland and Dairy King are both profit-maximizing firms. If Creamland decides to advertise, it will earn a profit of not advertise. million if Dairy King advertises and a profit of million if Dairy King does If Creamland decides not to advertise, it will earn a profit of does not advertise. million if Dairy King advertises and a profit of million if Dairy King If Dairy King advertises, Creamland makes a higher profit if it chooses If Dairy King doesn't advertise, Creamland makes a higher profit if it chooses Suppose that both firms start off not advertising. If the firms act independently, what strategies will they end up choosing? ◇ Creamland will…Team 2 plays A Team 2 plays B Team 1 plays A 2, 1 0,0 Team 1 plays B 0,0 1, 2 Consider the game above. Which of the following is a Nash Equilibrium of the game? O Team 1 plays A two thirds of the time and plays the rest of the time, while team 2 plays A two thirds of the time and plays B the rest of the time. Team 1 plays A one quarter of the time and plays B the rest of the time, while team 2 plays A one quarter of the time and plays B the rest of the time. Team 1 plays A one quarter of the time and plays B the rest of the time, while team 2 plays A three quarters of the time and plays B the rest of the time. O None of the other answers are correct. Team 1 plays A two thirds of the time and plays B the rest of the time, while team 2 plays A one third of the time and plays B the rest of the time.
- Suppose that two firms, firm A and firm B, are competing in the market. Assume that each firm has two strategies available: “no promotion” and “extensive promotion”. If both firms choose “no promotion”, each firm will get a payoff of 8000. If both firms choose “extensive promotion”, each firm will get a payoff of 5000. If one firm chooses “no promotion” and the other firm chooses “extensive promotion”, the firm that chooses “no promotion” will get a payoff of 4000 and the firm that chooses “extensive promotion” will get a payoff of 10000.a. Assume the game is a 2-players one-shot simultaneous game, please develop the normal form of this game by showing the players, the strategies and the payoffs. b. Follow part (a), determine the dominant strategy of firm A. c. Follow part (a), determine the dominant strategy of firm B. d. Follow part (a), determine the equilibrium of this game. e. If the game becomes an infinitely repeated game, what do you expect to happen?Firm A Strategy Advertise Don't Advertise Firm B Advertise 0,0 -1,40 Don't Advertise 40, -1 10, 10 Two cigarette manufacturers play the following simultaneous-move billboard advertising game. Profit payoffs for both companies are shown in the normal form game below. There is a 20 percent chance that the government will ban cigarette sales in any given year. If they collude and Firm A cheats, how much will Firm A earn in period 1? (Enter a numerical value as your answer with no decimal points. For example, if your answer is "one hundred" you need to type in "100"). What is the probability that the game will end? (Enter a numerical value as your answer with no decimal points. For example, if your answer is "one hundred percent" you need to type in "100"). If they collude and Firm A cheats, what will be the profit for Firm A for all periods? (Enter a numerical value as your answer with no decimal points. For example, if your answer is "one hundred" you need to type in "100"). If they…7. Solving for dominant strategies and the Nash equilibrium Suppose Andrew and Beth are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Andrew chooses Right and Beth chooses Right, Andrew will receive a payoff of 6 and Beth will receive a payoff of 5. Andrew Left Right Left 8,4 5,4 Beth Right 4,5 6,5 The only dominant strategy in this game is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Andrew chooses and Beth chooses
- 5 Suppose two players play one of the two normal-form games shown in Figure 1. L U 0,-1 D 2,4 R 2,0 6,0 L U | 4,-1 D 2,-2 R 2,0Now suppose that Player 2 knows which game is being played, but Player 1 does not. Find the pure strategy Bayesian Nash equilibrium of this game.PLAYER B LEFT RIGHT UP 5 FOR A, 30 FOR B 10 FOR A, 12 FOR B PLAYER A DOWN -2 FOR A, 10 FOR B 8 FOR A, 15 FOR B In the above game, the players are seeking to maximize the number they recieve. They choose at the same time. What is the Nash equillibrium? Player A will choose UP and player B will choose LEFT Player A will UP and player B will choose RIGHT Player A will choose DOWN and player B will choose LEFT Player A will choose DOWN and player B will choose RIGHT Player A will choose LEFT and player B will choose UP Player A will choose LEFT and player B will choose DOWN Player A will choose RIGHT and player B will choose UP Player A will choose RIGHT and player B will choose DOWN4. Using a payoff matrix to determine the equilibrium outcome Suppose that Flashfry and Warmbreeze are the only two firms in a hypothetical market that produce and sell air fryers. The following payoff matrix gives profit scenarios for each company (in millions of dollars), depending on whether it chooses to set a high or low price for fryers. Flashfry Pricing High Low Warmbreeze Pricing High Low 11, 11 2,13 13, 2 10, 10 For example, the lower-left cell shows that if Flashfry prices low and Warmbreeze prices high, Flashfry will earn a profit of $13 million, and Warmbreeze will earn a profit of $2 million. Assume this is a simultaneous game and that Flashfry and Warmbreeze are both profit-maximizing firms. price, and if Flashfry prices low, Warmbreeze will make more profit if it If Flashfry prices high, Warmbreeze will make more profit if it chooses a chooses a price. If Warmbreeze prices high, Flashfry will make more profit if it chooses a chooses a price. Considering all of the…