Explain why a subgame does not split up information sets.Explain what a subgame-perfect Nash equilibrium is.

PurposeThis assignment is designed to provide you with the opportunity to communicate about technical and abstract material in a clear and straightforward manner. You will spend some time each week writing up a response to a question/prompt, and then posting that on a discussion board that your peers will review. By doing this each week, you’ll get practice writing about technical matters. DirectionsHere is the prompt. In 500 words, write an answer to the following question:Discussion PromptConsider a scenario with the following game tree: U +——-> (x1) 2, 6 | Y | +——-> (x5) 2, 0 | B | 1—+ (x0) +——-> 2—+ (x3) | | . | | | . +——-> (x6) 2, 1 | | . X +——-> 1—+ (x2) . D | . Y | . +——-> (x7) 1, 4 | . | +——-> 2—+(x4) 5, 2 A | +——-> (x8) 3, 4 XThis is an ascii-art version of an extensive-form game. The players are labeled 1 and 2, the nodes are labeled x0, x1, and so on through x8, the strategies are U, D, A, B, X, and Y, and they are written by each branch. The payoffs are listed at each leaf node. There is a dotted line for Player 2 connecting their move at x3 and x4. Player 1 can choose U or D at x0, then A or B at x2. Player 2 does not know if they are at x3 or x4 (as indicated by the dotted line), so they can choose only X or Y.What are the subgame-perfect Nash equilibria for this game?In your answer, be sure to complete the following tasks:Explain why backward induction does not work for games of imperfect information.Explain what a subgame is.Explain why a subgame does not split up information sets.Explain what a subgame-perfect Nash equilibrium is.Explain the procedure for finding subgame-perfect Nash equilibria.Use that procedure to find the subgame-perfect Nash equilibria for the above game, and explain how you did it (i.e., explain/show your work).Next week, you will review each other’s answers to this question. To review the assignment, you will basically check that your peer completed each of the tasks — (a) through (f) — listed above, and you will assign 1 point for each completed task. To make this explicit, you will use the rubric below to assign points.Click the Reply button below to post your response. SubmissionThe deadline for your initial response posting is Sunday 11:59 p.m. Peer reviews will begin in next week’s module and be due the next Sunday 11:59 p.m. See the next Module for more detailed instructions. GradingIn next week’s module, one of your tasks will be to go back and review what your peers wrote. The rubric that you will use to review each other’s answers is as follows. You can also click on the Options icon at the top right corner of this forum (three dots) and select the Show Rubric button. TaskPointsCriteria a 1Did the author explain why backward induction does not work for games of imperfect information, and did their explanation match the lectures/handouts/textbook? b 1Did the author explain what a subgame is, and did their explanation match the lectures/handouts/textbook? c 1Did the author explain why a subgame does not split up information sets, and did their explanation match the lectures/handouts/textbook? d 1Did the author explain what a subgame-perfect Nash equilibrium is, and did their explanation match the lectures/handouts/textbook? e 1Did the author explain the procedure for finding subgame-perfect Nash equilibria, and did their explanation match the lectures/handouts/textbook? f1Did the author use that procedure to find the subgame-perfect Nash equilibria for the provided game, and did they explain how they did it (i.e., did they show your work), and are they correct?So, you will be awarded 1 point for completing each of the tasks (a)–(f), to earn a total of 6 points. To ensure that you get all 6 points, make sure to write clearly and concisely, and make it very obvious to your reader that you have in fact answered each of (a)–(f).Be straightforward and honest, and write in as simple a way as possible. We don’t care for fancy words and flourish in the math and/or business world.