P.PORTO Tipo de Prova Practical Work 1 Curso: Master in Business Decision Support Methods Unidade Curricular Game Theory Ano Letivo Data 08-12-2021 2021/2022 Hora Durao DESCRIPTION: Practical Work 1 (PW1) carried out of class, consists on the resolution of a problem on the topic C2-Static Games with Complete Information These problems must be solved manually, with AMPL and discussed EVALUATION AND GROUP CONSTITUTION: PW1hasa weight of 50% of the final classification of the UC, a minimum score of 75 values andis mandatory This is an individual work REPORT PREPARATION: The manual resolutions of the problems should digitalized and a single pdf file must be upload in moodle. Print the pages with and questions and write manually your answer. Fill your name on each page Digitalize your answers and upload a single PDF file in moodle. DELIVERY AND FOLLOW-UP: The PW must be submitted in moodle until January 9th The discussion takes place on January 13th 14:00 on zoom and take 20 minutes Doubts can be clarified on Thursdays from 14:00 to 1500 via zoom at https://videoconf-colibri.zoom.us/1/82462370356 1 2 4 1. Two companies share the bulk of the market for a particular kind of product Each is now planning its newmarketing plans for the next year in an attempt to wrest some sales away from the other company (The total sales for the product are relatively fixed, so one company can increase its sales only by win- ning them away from the other) Each company is considering three possibilities: (1) better packaging of the product (2) increased advertising, and (3) a slight reduction in price The costs of erna- tives are quite comparable and sufficiently large that each company will select just one. The estimated effect of each combination of alternatives on the increased percentage of the sales for company is as follows Player 2 2 3 12 Player 1 2 1 3 3 -2 -1 Each company must make its selection before learning the decision of the other company (a) Without eliminating dominated strategies, use the minimax (or maximin) criterion to determine the best strategy for each company (b) Now identify and eliminate dominated strategies as far as possible. Make a list of the dominated strategies, showing the order in which you were able to eliminate them Then show the resulting reduced payoff table with no remaining dominated strategies. 2. Consider the game having the following payoff table. Player 2 1 2 3 Player 1 - 2 2-1 Use the graphical procedure described in Sec 14.4 to determine the value of the game and the optimal mixed strategy for each player according to the minimax criterion Check your answer for player 2 by constructing his payoff table and applying the graphical procedure directly to this table ESG-PRUS MOVE Paginal de A 1 1. Two companies share the bulk of the market for a particular kind of product Each is now planning its new marketing plans for the next year in an attempt to wrest some sales away from the other company. (The total sales for the product are relatively fixed, so one company can increase its sales only by win- ning them away from the other.) Each company is considering three possibilities: (1) better packaging of the product, (2) increased advertising, and (3) a slight reduction in price. The costs of the three alterna- tives are quite comparable and sufficiently large that each company will select just one. The estimated effect of each combination of alternatives on the increased percentage of the sales for company 1 is as follows: Player 2. 2 3 1 2. 3 1 Player 1 2 1 3 3 -2 -1 Each company must make its selection before learning the decision of the other company. (a) Without eliminating dominated strategies, use the minimax (or maximin) criterion to determine the best strategy for each company. (b) Now identify and eliminate dominated strategies as far as possible. Make a list of the dominated strategies, showing the order in which you were able to eliminate them. Then show the resulting reduced payoff table with no remaining dominated strategies. 4 0