Analytical Politics Task (A) In both problems, let variable ???? be equal to the day in your birth date. (For example, if you were born on February 19, 1997, then ????=19.) Write down ???? with your name at the top of your answer. A strategic interaction between two players, Voter and Politician, is described as follows. Voter moves first, deciding whether or not the Politician must report on his actions. Transparency (“must report”) costs ???? to Voters regardless of other decisions. Then, Politician moves, either exerting high effort or low effort. If Voter decided previously that Politician must report, Voter knows the Politician’s effort. If Voter decided that Politician must not report, Voter does not know the Politician’s effort. Finally, Voter moves again, either re-electing Politician for the next term, or not. The payoffs The payoffs are as follows. If Politician exerted high effort and was not re-elected, Voter gets ????, Politician 0. If Politician exerted high effort and was re-elected, Voter gets ????+5, Politician 7. If Politician exerted low effort and was re-elected, Voter gets 3, Politician 10. If Politician exerted low effort and was not re-elected, Voter gets 4, Politician 3. (a) Draw the game tree, labeling each action, marking information sets, and indicating payoffs at the terminal nodes. (b) List all strategies for each of two players in the extensive form game. How many strategies each of the two players has? (c) Find a subgame-perfect Nash equilibrium in pure strategies. Write down the equilibrium strategy profile and players’ payoff in the equilibrium. (d) List other Nash equilibria of this game if there are any. Task (B) Importantly, this is an exercise in analytical politics, not in creative writing or philosophy. Your grade will take into an account the quality of your model as a tool for analyzing the episode and telling the story, yet the main emphasis will be on the game-theoretic properties of the model and the correctness of your solution. In other words, it is better to write down and correctly solve a less realistic model, rather than provide a partial or incorrect analysis of a more realistic one. The task: Choose on an electoral campaign in any country around the world that happened in 2020-2022. It might be a national race (a presidential campaign) or a local race (senator, governor, etc.). You will need to tell a story that features strategic interaction, uncertainty, and consequences of an external shock. Construct a game, find equilibria, and analyze comparative statics. The game you constructed should correspond to the story that you tell. Comparative statics analysis will correspond to “would be” scenarios in your story. Your paper should include: • An Introduction, no longer than 1 page (1,700 characters with spaces), describing, in plain words, what is done in the rest of the paper. In particular, it should describe the story that you are telling. • A brief section (not longer than 0.5 pages) that provides background information about the episode you analyze. • A section with the model that has, as subsections, Setup and Analysis. The Setup should contain full description of your game (set of players, a game tree if needed, information structure, sets of strategies, payoffs, equilibrium concepts). The Analysis should contain results on equilibria (existence, full characterization) and comparative statics. Relegate all proof details to the Appendix. • A section Discussion, not longer than 1 page, that should relate the results of Analysis and the real facts of the episode you describe. If the match is imperfect, then briefly explain why you think this happened. • Appendix with proofs detailed as you see fit. You do not need to provide a lot of details. Still, proofs should be full and correct. If your story requires using more than one model, then all setups should be grouped in the Setup subsection, and all the analyses in the Analysis subsection. Yet better stick to one model. When you make formal statements, be careful about qualifies. For example, one equilibrium might be a unique Nash equilibrium in pure strategies, but not “a unique Nash equilibrium” as a Nash equilibrium might be in mixed strategies.