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There are two players in a simultaneous contest game. Each player i exerts an effort level of e; ( [0, co). Player 1 wins the

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There are two players in a simultaneous contest game. Each player i exerts an effort level of e; ( [0, co). Player 1 wins the contest with probability e1 e1 + e2 and Player 2 becomes the winner with the remaining probability. If both players exert zero effort, each would have 50% chance of winning the contest. The winner gets 205, while the loser gets nothing. Exerting one unit of effort has a cost of 1$. Assume further that this game will be repeated infinitely many times. Future payoffs are discounted by a common discount factor of = 0.8 for each player . Find an equilibrium in the form of a grim-trigger strategy. Show and explain your work! Hint: A contest game is a rent-seeking model in which exerting effort is inefficient.2. [20 marks] Consider a contest by two risk-neutral players, 1 and 2. They compete over a single prize that is worth V > 0 to each player. That is, if a player wins the contest, he gets a prize (benefit) worth V. The loser gets nothing. Each contestant puts in effort, et, that has a cost of C(ei) = eni = 1,2. Cost and benefit are in the same units (e.g., dollars). The players put in effort before knowing the outcome (win or loss) of the contest. Let player 1's probability of winning the contest be p1 = e1 and he loses the contest with probability, 1 - p1. Similarly, player 2's probability of winning is P2 = 1 - p1 = ez and he loses the contest with e 1 tez probability, 1 - P2. Player I's win is player 2's loss and vice versa. (i) Write down the expected payoff function of each player. (ii) Find the symmetric Nash equilibrium {el, ez} of this game. [You may need the following result: a e1 1 e1 = de1 e,tez e1tez - ( entez ) 21p17403805 - Rov. Sep 2018 WCLN.ca" 8. Now, using kinematics combined with your answer above, determine the initial velocity of the car based on the length of the skid marks. State any assumptions made as clearly as possible, Calculate Initial velocity, ve. of car. 19 Given information and assumptions V = 0 be it as to Vr Vo +2ad Come to a stop V.

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