practice question

Question 2: Andrea and Brett are two medical researchers who need to decide whether to join forces. On their own Andrea and Brett are, respectively, able to develop new cough medication. Either player gets a utility of 1 if they both pursue this solo-project. If they join forces, Andrea and Brett will tackle the big problem of finding a cure of long Covid. If both work on the cure for long Covid, each of the two researchers gets a utility of 3. If only one devotes his or her energy to long Covid, nothing will come of it: the researcher committed to long Covid receives a utility of 0, but the other one researching cough medicine receives a utility of 2 because he or she does receive full credit for it . a) Assume both researchers decide at the same time. Draw a matrix to represent this two-player game. (2 Marks) b) Solve the game for all Nash equilibria in pure and mixed strategies. (4 Marks) c) What type of game (cooperation game, social dilemma or coordination game)is this and why? (4 Marks) d) Now consider a sequential version of the game. Draw a game tree where Brett decides before Andrea and Andrea is not aware of Brett's decision. (2 Marks) e) Find the subgame-perfect Nash-equilibrium in the sequential game if Andrea is aware of Brett's decision. Are there any non-subgame perfect Nash-equilibria? (4 Marks)