Game theory and strategic interactions

Identify a real-world situation in which you see game theory/strategic behavior in action. Explain the game: Who are the players ? What are the strategies they have at their disposal? How are payoffs determined? What, if any, is the Nash equilibrium? Note, this article from Up Journey might help you come up with an example: https://upjourney.com/game-theory-examples-in-real-life

Game Theory and Strategic Choices - End of Chapter Problem Your instructor challenges you to solve this classic economics thought experiment called the stag hunt: Suppose you and a hunting partner are hunting for food to feed your families in a post-apocalyptic world with no stores, farms, or trade. You lay a trap for a deer that will provide a large number of calories for your two families to continue to survive. While waiting, you both spot a hare running through the trap. If you chase after the hare, you'll catch it but you will scare any wildlife in the area and you won't catch the deer you were waiting for. The hare only provides a small amount of calories for your own family and none for your partner's family. Use the payoff matrix to answer the question. You hunt the deer You hunt the hare Your friend hunts the deer Your payoff is 5 Your friend's payoff is 5 Your payoff is 2 Your friend's payoff is A Your friend hunts the hare Your payoff is A Your friend's payoff is 2 Your…

Question 1 (1 point) In the following game, what is the Nash equilibrium? For each cell, the first number is the payoff for firm A, and the second number is the payoff for firm B. Firm A High Low Firm B High Low 2,2 6,0 0,6 4, 4 Firm A chooses low; Firm B chooses high Firm A chooses high; Firm B chooses high Firm A chooses low; Firm B chooses low Firm A chooses high; Firm B chooses low

Nash Equilibrium (NE) A: Period 1 B: A A: 4 A: 2 B: 1 B: 2 Period 2 Nash Equilibrium (NE) Nash Equilibrium (NE) A: A: B: B: A: 6 A: 4 A: 7 A: 5 A: 4 A: 2 A:5 A: 3 B: 6 B: 7 B: 4 B: 5 B: 7 B: 8 B:5 B: 6 d. Solve the game by the Rollback method. Identify the dominant strategies and circle the Nash Equilibrium for each subgame and write it above its starting node. е. How has the penalty changed the firm's behavior?

8) Consider the following game: There are 10 players. Each player is asked to write a number between 0 and 100. The player whose choice is closest to half of the average is the winner. Describe the game and discuss what would you expect to be the average number if the game were played in class with your colleagues. Do you expect them to play the Nash equilibrium strategy? Explain.

QUESTION 3 Up Down In the game above, what is/are the sub-game perfect Nash equilibrium? Ⓒ (up,up) (up,down) Player 1 (down, up) (down, down) No equilibrium exists Up Down Up Down Player 2 P1 gets $25 P2 gets $25 P1 gets $7 P2 gets $30 P1 gets $13 P2 gets $9 P1 gets $8 P2 gets $6

Question: Which of the following best describes a Nash equilibrium in game theory? A) A situation where one player dominates the other player B) A situation where players cooperate to achieve the best possible outcome C) A situation where no player has an incentive to unilaterally change their strategy D) A situation where players collude to maximize their joint payoffs

Game theory can capture strategic situations where your outcome depends not only upon your own choice but also upon the choice of another. Present a coordination game of your choice where you and another player each have two choices or strategies. Explain in words the Nash Equilibrium concept, and identify the Nash equilibrium or Nash equilibria for your game. Explain why the outcomes that are not Nash equilibria are not.

Game theory terminology Select the term that best describes each definition listed in the following table. Definition Nash Equilibrium Dominant Strategy Collusion Tit-for-tat Strategy Payoff Matrix Prisoners' Dilemma Game A strategy in which a player cooperates until the other player defects and then defects until the other player cooperates again               The event that occurs when agents in a game form an agreement about which strategies to implement               A player's best choice, if it exists, regardless of his or her opponent's strategy               A case in which individually rational behavior leads to a jointly inefficient outcome

QUESTION 2 In the game above, what is/are the sub-game perfect Nash equilibrium? (up, up) (up, down) ( down, up) (down, down) No equilibrium exists QUESTION 2 Up Down Player 1 No equilibrium exists Up In the game above, what is/are the sub-game perfect Nash equilibrium? (up,up) (up,down) (down, up) □ (down, down) Down Up Down Player 2 P1 gets $45 P2 gets $155 P1 gets $100 P2 gets $10 P1 gets $85 P2 gets $85 P1 gets $95 P2 gets $95

Class Exercise Chapter 13: Game Theory Two firms are in the chocolate market. Each can choose to go for the high end of the market (high quality) or the low end (low quality). Resulting profits are given by the following payoff matrix: Firm 2 Low -20, -30 High 100, 800 Firm Low 1 High 900, 600 50, 50 a. What outcomes, if any, are Nash equilibria? b. If the managers of both firms are conservative and each follows a maximin strategy, what will be the outcome? c. What is the cooperative outcome? d. Which firm benefits most from the cooperative outcome? How much would that firm need to offer the other to persuade it to collude?

QUESTION 4 Suppose there are 2 players in a non- cooperative game theory situation. Player A can move Up or Down while Player B can choose Left or Right. The following matrix contains the payoffs that each player receives under 4 scenarios. The first number in each cell refers to the payoffs for Player A. Player A Up Down A. B. C. 10, 60 D. 20, 80 Player B Suppose Player A moves first and Player B moves second. There is one equilibrium, Up, Left Left There is one equilibrium: Down, Right. 50, 90 40, 50 There are two equilibria, (Down, Left) and (Up, Right) Right There is one equilibrium in this game, Up Right

3. The following is an interpretation of the rivalry between the United States (USA) and the Soviet Ünion (USSR) during the cold war. Each side has the choice of two strategies: Aggressive and Restrained. The payoff table is given as follows: USSR Restrained Aggressiveness Restrained 4,3 1,4 USA Aggressiveness 3,1 2,2 a) Consider this game when the two countries move simultaneously. Find all pure strategy Nash equilibria. b) Next consider three alternative ways in which the game could be played with sequential moves: (i) The USA moves first and the USSR moves second. (i) the USSR moves first and the USA moves second. (i) The USSR moves first, and the USA moves second, but the USSR has a further move after the USA moves. For each case, draw the game tree and find the subgame-perfect Nash equilibrium. c) What are the key strategic issues (commitment, credibility and so on) for the two countries. (Note: Be concise. Your answer should not exceed 300 words].

6) The following is a static game D 2,2 0,3 D 3,0 1,1 a) Convert this game into dynamic form game b) Find the Nash equilibrium and subgame perfect Nash equilibrium of this game. c) If you consider this game as dynamic then what kind of dynamic game is this.

Player 2 Strategy A Strategy B Strategy 1 (1,4) (2,3) Player 1 Strategy 2 (6,5) (5,4) Consider the game depicted in the table above. The payout for player 1 is given first in parenthesis, with Player 2's payout second. What is the Nash equilibrium in this game? Strategy 1 and Strategy A Strategy 2 and Strategy A Strategy 2 and Strategy B This game does not have a Nash equilibrium

QUESTION 6 Up Down Player 1 equilibrium exists Up Down Up In the game above, what is/are the EFFICIENT sub-game perfect Nash equilibrium? (up.up) (up.down) (down, up) (down, down) No Down Player 2 P1 gets $45 P2 gets $150 P1 gets $100 P2 gets $100 P1 gets $95 P2 gets $95 P1 gets $15 P2 gets $25

3) Recently, a major question in the news is why the Afghan army collapsed so quickly and unexpectedly in the face of the Taliban offensive. To help understand the situation, consider the following simplified model of the situation. Assume that there are two Afghan soldiers in the same unit. Each can stay and fight the Taliban or desert. If both stay and fight, they will win any battle against the Taliban, which each values at 100 utility. If either soldier deserts, the Taliban wins, which they each values at 0 utility. In addition, if only one soldier stays, that soldier will be killed by the Taliban, which he values at -1000 utility. In addition, the Taliban is offering a bounty to any soldier that deserts. ne soldier does not care about this, and would not take the bounty, while the other values the bounty at 50 utility. a. Draw the game based on this scenario. b. Find all pure strategy Nash equilibria c. Find the mixed strategy Nash equilibrium d. What does this game and the…

What is the difference between collusion and competition?   Group of answer choices   1-Competition is when firms operate independently. Collusion is when firms in the oligopoly market structure try to invite new entrants into the market to make it more competitive.   2-Collusion is when firms act together in ways to reduce output, keep prices high, and divide up markets. Competition is when firms operate independently.   3-Competition firms follow the price changes and product changes of the dominant firm in an oligopolistic market. Collusion is when firms operate independently.   4-Collusion is when firms follow the price changes and product changes of the dominant firm in an oligopolistic market.Competition is when firms operate independently.

Player 2 Middle Left P1: $45 P1: $70 Up P2: $45 P2: $50 Player 1 P1: $50 P1: $60 Middle P2: $50 P2: $60 P1: $60 P1: $50 Down P2: $60 P2: $70 In the game shown above, list all of the Nash Equilibrium (please check ALL that apply) (up, left) (up, middle) (up, right) (middle, left) (middle, middle) (middle, right) (down, left) (down, middle) (down, right) No equilibrium Right P1: $45 P2: $60 P1: $50 P2: $70 P1: $60 P2: $60

Up Down Player 1 In the game above, what is/are the sub-game perfect Nash equilibrium? □ (up,up) Ⓒ (up,down) ☐ (down, up) O (down, down) No equilibrium exists Up Down Up Down Player 2 P1 gets $45 P2 gets $155 P1 gets $100 P2 gets $10 P1 gets $85 P2 gets $85 P1 gets $95 P2 gets $95

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…

4. Game theory: An example of the prisoner's dilemma in the real world is when two competitors are battling it out in the marketplace. Often, many sectors of the economy have two main rivals. There can be rivalry such as between du and Etisalat in Telecommunications services, Coca-Cola and Pepsi-Cola in soft drinks. Suppose du plans to cut its price. Etisalat will likely follow suit to retain its market share. This may end up with low profits for both companies. A price drop by either company may thus be construed as defecting since it breaks an implicit agreement to keep prices high and maximize profits. Thus, if du drops its price but Etisalat continues to keep prices high, du is defecting, while Etisalat is cooperating (by sticking to the spirit of the implicit agreement). In this scenario, du may win market share and earn incremental profits by selling more. Assume that the incremental profits that accrue to du and Etisalat are as follows: o If both keep prices high (Cooperate),…

3. Two individuals are planning to start a business. The earnings from a grocery store business would be $30,000 for each, but the business requires two people (one to watch over the stock and the other to act as a cashier). Each individual could instead start an mpesa business. The take from mpesa business is only $3000 but can be done with one person acting alone. i) Write down the payoff matrix for this game ( ii) Solve the Nash equilibrium

Question 7 Discuss i) the social dilemma we may observe in the process of the vaccination roll-out and ii) how it can be understood by game theory. To help your discussion, consider individuals who are to choose between two strategies: i) to get vaccinated now and ii) to wait and see. Your discussion must refer to the following: social dilemma prisoner’s dilemma public goods game Nash equilibrium   Question 8  Provide a potential solution to the social dilemma you discussed in Question 7. You must cite at least one reputable source from your own research. Use the source(s) to support your argument; do not simply quote the source. Include the full reference at the end of your answer, which will not count towards the word limit. Use a standard referencing system (e.g. Harvard style).   Question 9 Evaluate whether your proposed solution is ethically acceptable by using either a consequentialist or a deontological framework. Your discussion must include: the definition of your chosen…

QUESTION 12 This is a HOT SPOT question. You will need to evaluate the picture of the game below, and answer the question by clicking on a specific area (the hot spot) of the picture. Question: Are there any dominant strategies in this game? If there are, click on the box that corresponds to that dominant strategy (either UP, DOWN, LEFT, or RIGHT). If there aren't any anywhere outside of these boxes. If there are dominant strategies for both players, clicking on only one of them will suffice. Player 1 Player 2 Selected Coordinates Clear UP DOWN LEFT 45, 80 70, 100 RIGHT 50, 150 60, 60

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…