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Politecnico di Milano Facoltà di Ingegneria dell’Informazione AUTONOMOUS AGENTS AND MULTIAGENT SYSTEMS September 10th, 2010 LAST NAME AND FIRST NAME ROW COLUMN ID NUMBER (MATRICOLA) x The exam is composed of three stapled sheets printed on both sides. x This front page must be filled with last name, first name, ID number, position (row and column communicated by the instructor), and signature. x Exams without a completely filled front page or with missing sheets will not be considered. x Answers can be written only on these sheets. If you need more space, please write on the last page. x Exam is closed books (i.e., no books, notebooks, notes, … are allowed). Cell phones, bags, cases, and wallets are not allowed on the desk during the exam. x All the answers must be justified. SIGNATURE Question 1 (8 points). Consider the two following strategic games in normal form (Ga and Gb) between two agents, 1 (row agent) and 2 (column agent): 2, 2 0, 00, 1 1, 0U D L R Ga 0, 0 2, 2-1, 0 0, 1U D L R Gb 1) Find the pure strategy Nash equilibria of each game. 2) Find the mixed strategy Nash equilibria of each game. 3) Now assume that agent 1 knows which of the two games is played and that agent 2 does not ; assume also that this fact is common knowledge betwee n the agents. However, it is also common knowledge between the agents that game G a is played with probability 0.7 and that game G b is played with probability 0.3. What are the rational pure strategies that the agents should play in this case? Justify your answer. 1) For Ga: (U, L). For Gb: (D, R). 2) It is easy to see that there are not mixed strategy Nash equilibria (other than those found in 1)). 3) Agents are uncertain between (U, L) and (D, R), which are the rational pure strategies in the two games. The expected playoff…