Suppose rules of the scenario change such that Village1 and Village2 are having a conflict on the ownership of this stream of nearby river. If both villages decide not to battle against each other, V1 will receive a monetary gain of 20S while V2 will receive a monetary gain of 50$. However, if both decide to battle, there is no monetary gain for both. If V1 decides to attach V2 but V2 stays neutral, V1 receives a gain of 80$ while V2 gets 60S. V2 will get 80S if it attacks V1 and in return V1 does not attack. In this scenario, Vl's monetary gain would be just 10s. You are required to construct the pay-off matrix of this scenario.
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- There are a kicker and a goalie who confront each other in a penalty kick that willdetermine the outcome of the game. The kicker can kick the ball left or right, while the goaliecan choose to jump left or right. Because of the speed of the kick, the decisions need to bemade simultaneously. If the goalie jumps in the same direction as the kick, then the goalie winsand the kicker loses. If the goalie jumps in the opposite direction of the kick then the kickerwins and the goalie loses. Model this as a strategic form game and write down the matrix thatrepresents the game you modeled. Find the Nash equilibrium.First Player can invest $1.00 with Second Player. Second Player chooses whether tc cooperate and make the promised investment, or appropriate and keep First Player'a $1.00. Based on the payoff matrix shown below (first player payoffs on bottom left of cell, second player payoffa on upper right of cell), what will be First Player's payoff if contracis are not enforceable? Second Player Cooperate Appropriate Invest 1.5 1.0 First Player 1.5 -1.0 Don't InvestQuestion 1 Saue Answe Consider a 2-player game with strategy sets S1-(a,b}for player 1 and Sz =(c,d) for player 2. Which statement is true if player 1 has no dominant strategy? O Strategy b guaranteos playor 1 the best possible payaff, no matter what strategy player 2 choosos. O Depending on what strategy player 2 chooses, sometimes strategy a leads to a (weakly) higher payoff for player 1 than strategy b, and sometimes strategy b leads to a (weakiy) higher payoff for player 1 than strategy a. O We cannot say whether any of the other 3 alternatives is true. O Strategy a guarantees player 1 the best possible payoff, no matter whhat strategy player 2 chooses.
- Consider an extensive game. First, a firm from City 1 (Player2) makes Betty (Player 1) a job offer. The offer promises an income y1. ThenBetty decides whether to accept the offer. If the o§er is accepted, the payffsto Betty and the firm are (y1 - x1; 1- y1), where x1 is the house price inCity 1. While Betty is contemplating over this o§er, she receives another joboffer from a firm in City 2. This outside option promises an income of y2and a house price x2. If Betty rejects Player 2ís offer and accepts the outsideoption, the payoffs to the two players are (y2 - x2; 0). If Betty rejects bothoffers, then the payo§s are (0; 0). Assume y1 > x1, y2 > x2, 0 < y1 < 1and y2 - x2 + x1 <=1 .assume that Betty will accept an offer if she isindifferent from accepting and rejecting it. Do the following: (a) Draw thegame tree. (b) Find the subgame perfect equilibrium (SPE) by specifyingstrategies used. (c) What is Bettyís payoff in the SPE? How does this payoffchange respectively with…The next 3 questions involve the following game. There are two players, a husband and wife. They can either be selfish (S) or selfless (U) in their marriage. If they choose to be selfish, then there is a negative ʻguilt’ payoff of g. The payoff matrix is below. Figure 1: The Marriage Game Wife S U S 10-g, 10-g 15-g, 2 U 2, 15-g 12, 12 Number left (right) of comma refers to H's (W's) payoff. 23. Suppose that g = 0. What is the Nash equilibrium (or equilibria)? (A) (S, S). (B) (U, S) and (S, U). (C) (S, S) and (U, U) (D) (U, U). 24. Suppose that g= 5. What is the Nash equilibrium (or equilibria)? (A) (S, S). (B) (U, S) and (S, U). (C) (S, S) and (U, U) (D) (U, U). 25. Suppose that g = 10. What is the Nash equilibrium (or equilibria)? (A) (S, S). (B) (U, S) and (S, U). (C) (S, S) and (U, U) (D) (U, U). HusbandQuestion 4. Zeynep and Mehmet will eventually play the following game. Mehmet L R U 3,1 0,0 Zeynep D 0,3 1,3 In a preliminary stage, Zeynep has already asked Mehmet to allow her to move first and proposed to pay him 1 unit of her own payoff in exchange. So Mehmet has to options: • If he accepts Zeynep's offer: they will play the sequential move version of the above game in which Zeynep moves first. Mehmet will receive 1 unit of utility more, and Zeynep will receive 1 unit of utility less (in any outcome of the game) compared to the payoffs given in the bimatrix. 2 • If he rejects Zeynep's offer: they will play the simultaneous move game. a. Represent this strategic interaction in a game tree. b. How many information sets does each player have? c. Characterize the set of pure strategies for both players. d. Present this game as a normal-form game, and characterize the set of pure strategy Nash equi- libria.
- Consider the following game: Player 2 In Out Player 1 In -2,-2 2, 0 Out 0, 2 0, 0 (a) What is the Nash equilibrium of this game, or what are the Nash equilibriaof this game? (b) Does either firm have a dominate strategy (a strategy that is always abest response)? Which? (c) Suppose Player 1 could move before Player 2 and Player 2 could observe Player 1’s move. What do you think would happen?2. Consider a game that game theory people refer to as the “ultimatum game.”We will refer to our two players as the “offerer” and the “decider”. How the gameworks is that the offerer proposes a way to split $1000 between the two players.While this could be done in a variety of ways, we will assume that the offerersonly has two possible proposals: Either a 50-50 split, or she offers the decider$50 and keeps the rest. The decider can either accept or reject the offer. If the offer is accepted, the money is split as proposed. If the offer is rejected, themoney spontaneously combusts and nobody gets anything. a) List the strategies for each player and write an extensive form version of thegame with payouts. b) List all the Nash equilibria of this game. c) Explain which, if any of the Nash equilibrium are not sub-game perfect. d) Write the game out in normal form and find the pure strategy Nashequilibrium. Explain how this matches with your answers to (b) and (c) . Alsoexplain why there…In game theory, a dominant strategy is the best strategy to pick, no matter which moves are chosen by the other player. O to make the exact same move that was made by the other player. the choice that causes the payoff for the other player to be minimized, regardless of the payoff it earns the best strategy to pick, assuming the other player makes his or her best possible choice. to allocate all personnel resources towards defensive talent in order to dominate opposing offenses. 46°F
- 4. Consider a two player game with Fred and Barney, who tal turns removing matchsticks from a pile. They start with 33 matchsticks, and Fred goes first. On each turn, ecach player may remove either one, two, three, four, or five matchsticks. The player to remove the last matchstick wins the game. What are the optimal strategies for each player? Who will win? b. Suppose now that they can remove up to six matchsticks, how will the optimal strategies change for- each player? a.Two farmers, Ali and Hasan, graze their animals on a common land. They canchoose to use the common resource lightly or heavily and the resulting strategic interactionmay be described as a strategic form game. The payoff matrix is the following: (The table is attached on iamges part) Suppose that the game is repeated infinitely. If both players play a Grim-Trigger strategy, findthe discount factor δ such that (Light,Light) be a Nash equilibriumHal and Nick are racing to develop a new brand of coconut milk that they both believe will be the next big soft drink. The payoff matrix shows the economic profit in millions of dollars for the game that Hal and Nick play. O A. Hal and Nick will never cooperate in this research. OB. Hal and Nick will cooperate in this research every time they play the game. Q Search OC. It is possible for cooperation in this research and development game if the game is played repeatedly and cheating on the agreement is punished using a tit-for-tat strategy OD. Hal and Nick will cooperate in this research only if a threat exists that a third firm will enter the coconut milk market Pat's strategies (blue squares) Develop Not develop 0 Hal's strategies (red squares) Develop -1.0 2.5 2.5 1.0 Not develop Next -1.0 1.0