Game Theory Exam June 2017: Nash Equilibria and Voting Games - Prof. Olaya, Ejercicios de Contabilidad Financiera

¡Descarga Game Theory Exam June 2017: Nash Equilibria and Voting Games - Prof. Olaya y más Ejercicios en PDF de Contabilidad Financiera solo en Docsity! Game Theory Exam June 2017 Name: Group: Grades: I II.1 II.2 II.3 II.4 Total You have two and a half hours to complete the exam. I. Short questions (5 points each) I.1 When a player chooses a mixed strategy in a Nash equilibrium, the pure strategies that are part of it may have different expected payoffs. Explain whether this statement is true or false. I.2 Provide an example of a dynamic game that shows the following fact: if one player sees one of her strategies eliminated, her utility in equilibrium increases. I.3 There are 3 players and they vote (one round only) for A, B or C. Their preferences are: Player 1: A better than B, B better than C, Player 2: B better than A, A better than C, Player 3: A better than C, C better than B. The alternative with most votes gets selected. In case of a tie between the three options, no one gets selected, which is regarded as the worst outcome for all players. Is there any Nash equilibrium in non-weakly dominated strategies in which B is elected? I.4. In the calculation of payoffs in an infinitely repeated game, show that discounting payoffs using the rule of the discount rate is equivalent to consider that the game is repeated with some probability. I.1 False. If they have different payoff, the one that has the highest will be a better reply than the mixed strategy. Then the mixed strategy cannot be part of a NE. I.2 1BA 1 2DC0 32