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Politecnico di Milano Facoltà di Ingegneria dell’Informazione AUTONOMOUS AGENTS AND MULTIAGENT SYSTEMS February 27th, 2013 LAST NAME AND FIRST NAME ROW COLUMN ID NUMBER (MATRICOLA) • The exam is composed of three stapled sheets printed on both sides. • This front page must be filled with last name, first name, ID number, position (row and column communicated by the instructor), and signature. • Exams without a completely filled front page or with missing sheets will not be considered. • Answers can be written only on these sheets. If you need more space, please write on the last page. • 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. • All the answers must be justified. SIGNATURE Question 1 (8 points). Consider the following situation with four agents, A, B, C, and D : The agents are wearing hats (which can be black or w hite). Each agent does not know the color of its own hat, but it can look forward and see the color of t he hats of the agents it sees. For example, agent D can see the color of the hats of agents B and C. T he agents cannot see through the wall. For example, agent A cannot see the color of the hats of other agents. It is common knowledge that there are four agents, that the hats are eithe r black or white, that the agents are positioned as shown in figure (wall includ ed), and that two hats are black and two hats are white . 1) Write the set S of the possible states of the world. 2) Write the partitions A℘ , B℘ , C℘ , and D℘ induced on S by the perception functions of the four agents, respectively. 3) Now let assume that an external supervisor asks ag ent D if it knows the color of its hat. What is the answer of agent D and why? 4) After all…