4. Netix with constrained sharing Now suppose that Netix change their sharing policy. The purchaser of a Netix account is now only allowed to share with a xed number of others. Specically, each Netix account may only be viewed by the account purchaser and n: other people. If an account holder has (strictly) more than a friends then they must choose exactly it to share with. If an account holder has less than a friends then they may share with all of them. Suppose that the social network is unchanged. That is, it remains like this: Answer the following: (a) (b) (C) (d) 5 marks Write out the strategy set for player 1 for a = 1, 2, and 3. (There is no single correct way to do this. Just be clear what your notation means.) 15 marks 5 marks Write out the strategy set for player 3 for a = 1, 2, and 3. (There is no single correct way to do this. Just be clear what your notation means.) Find all the pure strategy nash equilibria for s. = 1, 2, and 3. (Either write out mathematically or depict graphically. Be as precise as possible.) 5 marks What value for a is optimal for Netix? 3. Netix with unlimited sharing Netix is an American mediaservices provider and production company headquartered in Los Gatos, California. The company's primary business is its subscriptionbased streaming service which offers online streaming of a library of lms and tv programs. 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. All individuals like Netix. Specically, if someone views Netix they get a benet of 1. However, Netix is costly which is bad. To purchase a Netix account costs 6 E (0, 1). Netix allow multiple devices to stream simultaneously. This means that if some indi vidual purchases a Netix account, then they will share with all of their friends. Each individual has strategy set {0, 1} where 1 means to purchase a Netix account and 0 means to not purchase. The payo to individual 1', depends directly on their own action and the actions of their friends. Writing .3,- for the strategy of person 1', and s_,- for the vector of strategies of everyone other than i, the payo to person i, 7r(s,-, s_,-) is 7710 s ) _ 1, if some friend chose to purchase an account 2 ' _ 0, if no friend chose to purchase an account 7r,(1,s_,-) : 1 7 c, for all s_