There is a society of six individuals, {1, 2, 3, 4,5,6), who are connected in a social network as below. If there is a link between two individuals, then that pair of individuals are friends. If there is no link between two individuals, then that pair are not friends. 6 3 4 2 5 All individuals like Netflix. Specifically, if someone views Netflix they get a benefit of 1. However, Netflix is costly which is bad. To purchase a Netflix account costs ce (0,1). Netflix allow multiple devices to stream simultaneously. This means that if some indi- vidual purchases a Netflix account, then he/she will share with all of his/her friends. Each individual has strategy set {0,1} where 1 means to purchase a Netflix account and O means to not purchase. The payoff to individual i depends directly on his/her own action and the actions of his/her friends. Writing s; for the strategy of person i, and 8_i for the vector of strategies of everyone other than i, the payoff to person i, 7($i,3_i) is 1, if some friend chose to purchase an account 0, if no friend chose to purchase an account Ti(1,s-i) =1-C, for all s_i S T: (0,8-1)={ = S- = Answer the following: (a) 5 marks Does any player have a dominant strategy (strictly or weakly)? (b) 5 marks Does any player have a dominated strategy (strictly or weakly)? (c) 5 marks Find all the pure strategy nash equilibria. (Either write out mathematically or depict graphically.) There is a society of six individuals, {1, 2, 3, 4,5,6), who are connected in a social network as below. If there is a link between two individuals, then that pair of individuals are friends. If there is no link between two individuals, then that pair are not friends. 6 3 4 2 5 All individuals like Netflix. Specifically, if someone views Netflix they get a benefit of 1. However, Netflix is costly which is bad. To purchase a Netflix account costs ce (0,1). Netflix allow multiple devices to stream simultaneously. This means that if some indi- vidual purchases a Netflix account, then he/she will share with all of his/her friends. Each individual has strategy set {0,1} where 1 means to purchase a Netflix account and O means to not purchase. The payoff to individual i depends directly on his/her own action and the actions of his/her friends. Writing s; for the strategy of person i, and 8_i for the vector of strategies of everyone other than i, the payoff to person i, 7($i,3_i) is 1, if some friend chose to purchase an account 0, if no friend chose to purchase an account Ti(1,s-i) =1-C, for all s_i S T: (0,8-1)={ = S- = Answer the following: (a) 5 marks Does any player have a dominant strategy (strictly or weakly)? (b) 5 marks Does any player have a dominated strategy (strictly or weakly)? (c) 5 marks Find all the pure strategy nash equilibria. (Either write out mathematically or depict graphically.)
