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- If ExxonMobil invests in Venezuela's oil fields, it runs the risk that Venezuela will later partially nationalize the assets. The payoffs are represented in the game tree illustrated in the figure to the right Nationalize (24,96) Suppose that the parties could initially agree to a binding contract that Venezuela would pay ExxonMobil x dollars if it nationalizes the oil fields. How large does x have to be for ExxonMobil to invest in Venezuela? Government Venezuela (60,60) Don't nationalize ExxonMobil The value of x would have to be at least equal to $ for ExxonMobil to invest in Venezuela (Enter your response as a whole number) Elsewhere (30,0)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?The 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…
- A roulette wheel has 30 slots, consisting of 2 blues, 8 whites, and 20 red slots. You will receive P100 if the roulette stops spinning on a blue slot, you will receive P50 on a white slot, but you will be penalized P10 if the roulette stops spinning on a red slot. Let X be the amount you will recieve (or pay). The probaility of receiving P50 is 2/30 or 1/15, and of receiving P50 is 8/30 or 4/15. What is the probability of penalty of P10? 2/3 1/3 -2/3Consider the following Extended Form Game: O (2,3) (B,A') (A,A') A (B',B') (A',B') P1 A' (5,5) A' B (3,8) A P2 B' P2 B' Player 1 chooses the strategy (B,A). What is the best response of player 2? (1,9) P1 B (9,1)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)
- At a science fair, 4 different groups of students from a local school are showcasing their projects. The groups arrive with their advisors and each group has a different number of students (40, 33, 25, and 50, respectively). A participant is chosen randomly from the entire pool of students. Let’s use the variable X to represent the number of students in the group that the selected participant belongs to. Meanwhile, the event organizers decide to acknowledge the hard work of one of the advisors by ”randomly selecting” one of them for special recognition. Let’s use the variable Y to represent the number of students who came with the chosen advisor. (a) Before doing any computations, which of E(X) or E(Y) do you think is larger? Or are they the same? Why? (b) Compute E(X) and E(Y). Comment.Consider the four-player game with the followingcharacteristic function:v({1, 2, 3}) v({1, 2, 4}) v({1, 3, 4})v({2, 3, 4}) 75 v({1, 2, 3, 4}) 1001, 2, v({3, 4}) 60v(v(S) 0 for all other coalitionsShow that this game has an empty core.You are playing a single joint game with all your fellow students where you have to choose an integer from (0,1,2, .100}. A player's payoff depends on the distance of his answer to 2/3 of the average of all players' answers; the closer the better. Example: Your answer is 45. There are two other players whose answers are 25 and 56. Then, the average is (45+25+56)/3=42. 2/3 of the average is 28. Your distance to 2/3 of the average is 145-28|=17. All players will be ranked according to their answer's proximity to 2/3 of the average. The top 25% of the players get 2 points. The next 50% get 1 point. The bottom 25% get 0 points. (In case of ties, points will be distributed evenly in the enlarged classes.) Please give your answer as a single integer from (0,1,2,3,.100}. A valid submission would look like this: 45
- The following graph is an interaction plot between factors A and B in a 2* factorial experiment. B+ 60 50 B- 40 B+ 30 20 10 B- Factor A There is a weak interaction between factors A and B Select one: O True O False ResponseThe following game has no saddle point and is fair, find the possible values of 2, and 2,. -9 4 -7The standard Tower of Hanoi game is with three pegs andn disks of different sizes that are stacked one on top of the other, with the largest at the bottom. The goal of the game is to be able to re-stack the disks in the target peg with the condition that one can only move one disk at a time and that a larger disk cannot be placed on top of a smaller one If T(n) denotes the minimum number of moves in the game, which is the recurrence relation that corresponds to the said game? A TIn) = 2 T(n-1) + 1, T(1) = 1 TIn) = 2 T(n- 1) + 1, 7(0) = 1 © T(n) = 2T(n- 1) + 1, 7(0) = 2 T(n) = 2 T(n- 1) + 1, T(1) = 2
