T gy Q1: Take it or Leave it (1 point) Consider the following game. At t=0 Uh-Oh Insurance Company makes a one-time take-it-or-leave-it employment offer to a prospective hire. The offer promises to pay a first year salary of 8 > 0 regardless of effort. The prospective hire can either accept the salary and begin working or reject it and seek employment elsewhere. Currently the prospective hire has no other offers, so assume their reservation salary (the minimum offer needed to incentivize work) is zero. At t=1 the employee, if they have accepted the salary offer, will begin work. They will provide a quality of work w > 0 that will lead to firm profits for Uh-Oh Insurance Company. Those profits accrue for the firm according to the function mp = Aw 8 and income accrues to the employee according to the function My = 8 axzw\" . Assume that A > Q0 and a > 0. This is a one-shot game where firms and employees match for a single negotiation, then must move on in the next period (regardless of whether the offer is accepted or rejected). A. Solve for the selfish sub-game perfect equilibrium (wage offer and effort level) of this game where the worker only cares about their income and the firm only cares about their profits. (1/2 point) . Solve for the socially efficient wage offer and effort level. By socially efficient we mean the wage and effort levels that maximize the joint profits of the firm and their prospective hire. Describe and explain how this answer compares to what you found in part (A). (1/2 point) A. Draw the payoff matrix for the game rock=paper-scissors. Assume that a win results in a positive payoff of 1 util, a tie generates no change in utility, and a loss results in the loss of 1 util. . Calculate the expected payoff one would receive from playing a pure 'rock' strategy. . Calculate the expected payoff one would receive from playing a pure 'paper' strategy. . Calculate the expected payoff one would receive from playing a pure 'scissors' strategy. . How many Nash equilibria does this game have? What are[is] theyl[it]? . What is the expected payoff to each player if both are playing an equilibrium strategy? O mOOw . Suppose you observe an RPS tournament at the Memorial Union. After an hour of play a single champion emerges. While accepting their prize in front of hundreds of spectators the winner attributes their success to a secret 'can't miss strategy' Does this make sense? Why or why not? H. How might a deft RPS player potentially take advantage of their opponent's cognitive bias(es)? Be creative in identifying a potential behavioral response that can be capitalized upon. I. Suppose you just won a round of RPS (scissors cut paper). Your opponent immediately challenges you to a rematch. You know they are twice as likely to throw a different gesture after a loss, but they are equally likely to choose rock or scissors if they do change their gesture. Repeat items a-e for the rematch