Question

Subgame-perfect Nash Equilibria
Consider the situation where the journalist J can either write a nice or a harsh article about a politician Z. Further suppose that the politician Z has managed to implement a
so-called media tribunal according to which he can decide to punish or not to punish J whenever J writes harshly about him. J would really love to write harshly about Z as long as he can get away without any punishment. However, J would rather write a nice article about Z than being punished. Z would really love to read a nice article about himself. However, in the situation where an harsh article had been written he would rather refrain from punishing J in order to avoid international criticism about him restricting the freedom of the press.

• Describe the above strategic situation as a game in extensive form (i.e., draw a game tree and attach for both players utilities to all possible outcomes).
• Identify all Nash equilibria.
• Identify all subgame-perfect Nash equilibria.

Answer 1

Figure-1 in the document attached below illustrates the extensive for the game in this instance through a game tree. Journalist J has initially two strategies at his or her disposal which is to either write a nice article about political Z or a harsh article about him or her. Now, if J writes a nice article about Z then let's assume that the utility or payoff for J would be 100 as mentioned or indicated in figure-1 and in this case, the respective payoff or utility of Z has been denoted as GR or Good Reputation in figure-1. On the other hand, if J initially decides to write a haarhs article about J then J would have two strategies to implement in this instance which are either punish J or not punish J. As implied in figure-1, if Z decides to punish J then the respective payoff or utilities of both J and Z assumably becomes 0 and BR or Bad Reputation for Z for suppressing the freedom of speech by public media and if Z decides not to punish J then the respective payoffs for J and Z would assumably become 100 and GR assuming that Z would be successfully able to avoid international criticisms for curbing freedom of speech of public media and manage to maintain a good reputation somehow.

Now, in this particular strategical game, considering that J would prefer to write a harsh article about Z initially, he or she would choose to write harsh article in this instance at the beginning of the game in which case, Z would expectedly respond by not punishing him or her as he or she would like to maintain a good reputation by avoiding international criticisms for suppressing the freedom of speech by press and public media as opposed to being negatively criticized and having bad reputation. Therefore, a possible Subgame Nash equilibrium of this game could be that J choosing to write harsh article and Z responding by not punishing J in order to maintain his or her good reputation with a respective payoff or utility of both J and Z as (100,GR).

From a general standpoint, J could also choose to write nice article about Z to ensure a better payoff or utility of 100 instead of extending the game and inducing a probability of 0 payoff or utility by writing a harsh article, considering the possibility that Z responds to J's strategy by punishing him or her. Therefore, if J decides to choose to write a nice article about Z initially, the game ends instantly with a respective payoff of J and Z as (100,GR). On the other hand, as J chooses to write harsh article about Z initially, it would be in the best interest of Z to respond by not punishing him or her in order to receive or maintain a good reputation by avoiding international criticisms of suppressing the freedom of speech which would subsequently end up with a respective payoff of J and Z of (100,GR). Hence, the possible Nash equilibria of this game could be J choosing strategy of writing a nice article about Z with a respective payoffs or utilities of J and Z as (100,GR) nd writing a harsh article about Z and Z ending up not punishing J with a subsequent payoffs for J and Z of (100,GR) respectively.