# Game Theory Course Master In Economics 2015 16 Universidad De Granada February 1

some exercise of game theory!!urgent!!!!

Question 1 (2 points): L M RT 2,5 2,1 0,1C 3,2 4,4 1,1B 4,0 4,1 2,2Answer the following question regarding the game above (reason all your answers):a) Strategy M weakly dominates strategy L. True or False?b) Find a mixed strategy that dominates action T.Question 2 (2 points):Find the all Nash equilibria (in pure and mixed strategies) of the following game (byrepresenting graphically the best response functions):L RT 10, 2 1, 1B 3, 3 2, 7Question 3 (3 points):Consider the following centipede game:a) Define each player strategies.b) Find the subgame perfect equilibria of this game.Game Theory CourseMaster in Economics 2015/16Universidad de GranadaTEST II:GAME THEORYHand in not later than Friday 05, 2016February 1, 2016Question 4 (2 points):Consider two firms competing for the same market. Firm 1 has been operating in the marketfor years and the technology it uses is known. Firm 2 is new in the market and it has notannounced yet the technology that it will use. Suppose that with a 40% of probability this firmwill use a new more efficient technology, instead of the old technology used by firm 1. Thetechnology that it uses is only known by firm 2. These two firms have two possibilities: Put alow price (L)E or put a high price (H). The payoffs for each of the firm are determined in thefollowing table:a) Define the states of the game and for each player the signals it may receive and thesignal functionb) Determine the best response functions for each of the players.c) Obtain the Nash equilibria of the game.Question 5 (1 points):In an infinitely repeated Prisoner’s Dilemma a version of what is known as a “tit for tat”strategy of a player I is described as follows:• There are two “statuses” that player i might be in during any period: “normal” and“revenge”;• In a normal status player i cooperates;• In a revenge status player i defects• From a normal status, player i switches to the revenge status in the next period only ifthe other player defects in this period;• From the revenge status, player i automatically switches back to the normal status inthe next period regardless of the other player’s action in this period.Notice that this tit-for-tat strategy is slightly different from the one that appears in yournotes.In the following infinitely repeated gameIf both players play Tit for Tat strategy (starting in a normal status), can (C,C) be hold as a Nashequilibrium? Justify your answer with calculus. Firm 2 (old technology) (new technology) H L H LFirm 1H 10, 10 0, 15 Firm 1 H 10, 30 5, 20L 15, 0 1, 1 L 15, 0 1, 1C DC 2,2 0,3D 3,0 1,1