1. Consider the following sequential game where there are two players move sequentially. The payoffs are listed in the following extensive form game. Find all the Nash Equilibria of the game. Show all your work. b. Find the Subgame Game Perfect Equilibrium of the game. Show all your work. а. 1 A B 2,0 1 0,0 a 0,1 -1,-2
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- 2.)A jar contains 2 red, 3 green, and 6 blue marbles. In a game a player closes their eyes, reaches into the jar and randomly chooses two marbles. The player wins the game if at least one of their marbles is red. Suppose it costs $1 to play the game and the winning prize is $3. Mathematically analyze this game and determine if it is in your financial interest to play the game.Consider the following normal form of a game. A B C OC OA OD OB (-3,-4) (-1,0) What is the maximin strategy of the row player? D (-2,-5) (-4,-3)Consider the following normal form of a game. K L M D O (LE) O (D.L) (1,3) O (L,D) (3,4) (2,5) no dominant strategy equilibrium (2,1) What is the dominant strategy equilibrium of this game? (5,2) (3,4) F (3,2) (4,3) (2,3)
- Two players, A and B, are playing an asymmetrical game. There are n points on the game board. Each turn player A targets a pair of points and player B says whether those two points are connected or unconnected. A can target each pair only once and the game ends when all pairs have been targeted. Player B wins iff a point is connected with all other points on the very last turn, while player A wins if any point is connected with all other points on any turn but the very last one OR if no point is connected to all other points after the last turn. For what values of n does either player have a winning strategy?Consider the game described by the following table. What is the best response for the column player if s/he knows that the row player will make the Y move? B OA O C ROW PLAYER O There is no definitive answer. X Y COLUMN PLAYER A 4, -1 3, -1 B -1,0 -2,4 C 2,1 0,2In two player’s dynamic games the player who moves second gets the advantage because we solve the game backwards. Explain why or why not?
- 3. Consider this game in an extensive form (there are 2 players, A and B): right left B B (2, 3) (4, 2) (6, 6) (1, 9) (1, 9) (7, 7) (5, 3) a. Find the subgame-perfect equilibrium. (1) b. Explain why the players cannot reach the outcome with the payoffs circled in orange (which they both would prefer to the equilibrium outcome). (1) gauche milieu gauche milieu gauche milieu droit13. (i) Reduce the following game by dominance and find the game value. Player B Player A I II III IIXO IV I 3 3 4 0 II 2 4 2 4 III 4240 IV 0 4 000 8The point spread in sports betting is essentially a handicap towards the underdog, for example the point spread of the game this weekend between Cincinnati Bengals and Kansas City Chief in Cincinnati +3 or Kansas city is -3. If you place a bet on the bengals, Kansas city must win by less than 3 points for your bet to wim. If Kansas city wins by exactly 3 points then the bet is a push and your stake is returned. Now suppose you placed a bet of 100 dollars on the bengals on a website where they charge 10% commission (if you win $90) when line was CIncinati +3 or Kansas City -3 According to previous studies the final margin of victory for NFL team in a given game can be approximated as a normal variable with a mean of points spread line and a standard deviation of 12, however suppose the bengals just announced that their star receiver Chase would return this weekend which adds two points in favour of the bengals. In other words, we suppose that the winning margin now for Kansas City this…
- Let's consider the following game: Player 1 chooses a (potentially negative) number x, and player 2 chooses a (potentially negative) number y. The payoff for player 1 is given by U1 = 100x - x2 - 2xy. The payoff for player 2 is given by U2 = 130y - 2y2 - 2xy. Solve for the Nash equilibrium in pure strategies. What is Player 1's payoff in the equilibrium? Enter a numerical answer below. You may round to the second decimal if necessary.Consider the game having the following normal form. In applying IESDS, which of the following strategies of the row player will be eliminated? COLUMN PLAYER A 6, 5 -5, 11 7,9 ROW PLAYER Y 10, 6 7, 10 11, 9 11, 7 -4, 11 8, 4 W 11, 3 -1, 10 8, 8 X.Model the situation as a strategic game assuming that both ‘James’ and ‘Robert’ are altruistic, ranking outcomes according to the other person’s comfort and, out of politeness, prefer to stand than to sit if the other person stands. Model the situation as a strategic game and find any Nash equilibrium (equilibria) if it exists. Does a dominant strategy exist for either ‘James’ or ‘Robert’ with these preferences? Show all steps and working in support of the answerContext:The London Metro Bus is crowded for travel during peak hours. During such travel hours two daily passengers ‘James’ and ‘Robert’ enter the Metro. Luckily, two adjacent seats are free in the bus. Each of them must decide whether to sit or stand. For both, sitting alone is more comfortable than sitting next to the other person, which in turn is more comfortable than standing. consider james as "Row Player" and Robert as "Column Player"