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- Game Theory Question A non-profit firm is on a local community online donation platform for a community event it wants to hold (only community members can donate via the website). The event will be held only if the non-profit firm collects $20,000 total from members of the community. Each member values the event at $500. Suppose that there are 100 community members. Community members can only donate by purchasing a lottery ticket from the firm. Each ticket costs $200 and only one ticket can be purchased per member. The proceeds will be collected by the firm. The lottery winner gets a premier meal at a local restaurant that's worth $100. Remember, the firm keeps all the donated money. If the amount of donations is less than $20,000, then the firm returns the donated money to the community members (since there'll be no event held but the lottery winner still gets to eat that fancy meal). If the donations sum up to $20,000, the community event will take place. What are the Nash…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 $6Aedri Quick Lesson in Game Theory A Nash Equilibrium is an outcome in which neither player is better off by changing their strategy. 2.7 Is a Dominant Strategy equilibrium also a Nash equilibrium? a) Yes b) No esc The Ice Cream Guys $3.99 $4.99 + Chucky's Chunky CCT: $20,000 $3.99 ICG: $20,000 CCT: $60,000 ICG: $10,000 tab Treats CCT: $10,000 $4.99 ICG: $60,000 CCT: $40,000 ICG: $40,000 The table above is the payoff matrix for the annual profit of the only two ice-cream-truck firms operating in Beach City. They are deciding the price of an ice cream cone. %3D caps lo 2.8 What is Chucky's dominant strategy? a) $3.99 b) $4.99 c) Not enough information hift 2.9 What is the dominant strategy equilibrium in this situation? a) Both charge $3.99 b) Both charge $4.99 c) CCT charges $3.99 and ICG charges $4.99 d) CCT charges $4.99 and ICG charges $3.99 2.10 Suppose these two firms engaged in collusion (which, of course, totally doesn't happen because it is against the law). Which outcome would…
- 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 $25Game theory Consider a simultaneous move game with two players. Player 1 has three possible actions (A, B, or C) and Player 2 has two possible actions (D or E.) In the payoff matrix below, each cell contains the payoff for Player 1 followed by the payoff for Player 2. Player 2 7. Player 1 A B C D -3, -3 0, -11 -4, 3 -11, E 0 -7, -7 -12, 0 (a) Identify any dominated strategies in this game. If there are none, state this clearly. (b) Identify any pure strategy Nash Equilibria in this game. If there are none, state this clearlyUp ооооо Down Player 1 Up No EFFICIENT equilibrium exists Down Up Down Player 2 P1 gets $120 P2 gets $5 P1 gets $100 P2 gets $10 P1 gets $95 P2 gets $95 In the game above, what is/are the EFFICIENT sub-game perfect Nash equilibrium? (up,up) (up,down) (down, up) (down, down) P1 gets $15 P2 gets $25
- Player 1 оооо Up (up, left) (up, right) (down, left) (down, right) None Down Player 2 Left P1: $15 P2: $15 In the game shown above, list all of the Nash Equilibrium (please check ALL that apply) P1: $12 P2: $18 Right P1:$11 P2: $16 P1: $13 P2: $13Game theory Consider a simultaneous move game with two players. Player 1 has three possible actions (A, B, or C) and Player 2 has two possible actions (D or E.) In the payoff matrix below, each cell contains the payoff for Player 1 followed by the payoff for Player 2. Player 2 7. Player 1 ہے A B C D -3, -3 0, -11 -4, 3 -11, E 0 -7, -7 -12, 0 (a) Identify any dominated strategies in this game. If there are none, state this clearly. (b) Identify any pure strategy Nash Equilibria in this game. If there are none, state this clearly.1. Each of two players simultaneously announces either Rock, Paper, or Scissors. Paper beats Rock, Rock beats Scissors, and Scissors beats Paper. The player who names the winning object receives $1 from her opponent. If both players make the same choice, no payment is made. Each players's preferences are represented by by the expected amount of money she receives. a) Formulate the situation as a strategic game and find all its mixed strategy equilibria. Make sure that you consider all different supports. b) Find all the mixed strategy equilibria of the modified game in which player 2 is prohibited from announcing Rock.
- 5. The following problem was first considered by John von Neumann and is a fundamentalresult game theory.A and B play the following game:A writes down either number 1 or number 2, and B must guess which one.If the number that A has written down is i and B has guessed correctly, B receives i units from A.If B makes a wrong guess, B pays 4/5 of a unit to A.First we consider the expected gain of player B.Suppose B guesses 1 with probability p and 2 with probability 1 −p.Let X1 denote B’s gain (or loss) in a game where A has written down 1.Let 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 ASuppose that A writes down 1 with probability q and 2 with probability 1 −q.Let Y1 be A’s loss (or gain) if B chooses number 1.Let Y2 be A’s loss (or gain) if B…Up ооооо Down Player 1 Up Down Up Down Player 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 P1 gets $100 P2 gets $100 P1 gets $10 P2 gets $110 P1 gets $15 P2 gets $15 P1 gets $65 P2 gets $10Up Down Player 1 in the game above, what is/are the sub-game perfect Nash equilibrium? (up,up) (up,down) (down, up) (down, down) No equilibrium exists Up Down Up Down Player 2 P1 gets $100 P2 gets $100 P1 gets $10 P2 gets $10 P1 gets $15 P2 gets $5 P1 gets $110 P2 gets $10