Question 4 (8 points) The manufacturers Pharmax and Medix are currently the only providers of vaccines against the COVOD-19 virus. Both strive for maximum total profit. Pharmax is considering the development of an entirely new vaccine. Pharmax can choose from three types of an existing vaccine, each effective against one particular aspect of the virus. The required investments in research are specifically aimed at one type of vaccine and can therefore be regarded as sunk costs. Due to competitive considerations, Pharmax wants to keep secret which type of vaccine it will develop until the moment of the market launch. Pharmax assumes that Medix faces the same choice with regard to the development of a certain type of vaccine. Arrangements between producers about the split of the market are not allowed by the country's Market Authority. The situation between Pharmax and Medix can be regarded as a static simultaneous game with the following expected profits in millions of euros over the patent period of 10 years. Medix decision to opt for Type I Type II Type II Pharmex Type I A -200; -200 B 250; 300 C 200; 400 decision to Type II D 300: 250 E-400; -400 F 250; 300 opt for Type III G 400; 200 H 300; 250 I-300; -300 4a Choose from the matrix the letter (s) of the cell (s) where there a Nash equilibrium exists. Explain your answer (2 points). A consultant believes that secrecy is not wise: "It is best for Pharmax to immediately disclose its choice for a type of vaccine, so that Medix will be forced to take that choice of Pharmax into account." The resulting sequential game is shown in the game tree in Figure 1, with expected winnings in millions of euros over the 10-year patent period. -200 ; -200 Medix 250 ; 300 200 : 400 + 300 ; 250 Pharmax Medix -400 : -400 III III 250 : 300 400 ; 200 *Medix 1I 300 ; 250 -300 : -300 Figure 1: game tree in choosing the type of vaccine to be developedb. Based on the data in the game tree, what type of vaccine will Pharmax choose? Explain your choice (1 point)- The consultant does, however, make a comment: "In order for this sequential game to develop, it is essential that Pharmax makes its first choice so convincing that Medix can no longer be in any doubt about it. Pharmax can achieve this by immediately announcing that large specific investments have been made in the development of the chosen type of vaccine." C. Explain which steps Pharmex will have to take and what the consequences will be (2 points). d. Explain why these steps are necessary for Medix to convincingly believe Pharmex's intentions (1 point). e. Give an advantage and a disadvantage for the patients in case a division of the market is achieved whereby both manufacturers market a different type of vaccine (2 points)