If we have r chemical reaction independent leading to r equilibrium how the gibbs phase rule will

subgame perfect Nash equilibrium? Question 3: In which situations should we need the mixed extension of a game? Question 4: Find, if any, all Nash equilibria of the following famous matrix game: L R U (2,0) (3,3) D (3,4) (1,2) Question 5: What is the difference between a separating equilibrium and a pooling equilibrium in Bayesian games? Question 6: Give another name for, if it exists, the intersection of the players’ best-response « functions » in a game? Question 7: assuming we only deal with pure strategies, the Prisoner’s Dilemma is a situation with: No Nash equilibrium One sub-optimal Nash equilibrium One sub-optimal dominant profile No dominant profile Question 8: If it exists, a pure Nash equilibrium is always a profile of dominant strategies: True False Question 9: All games have at least one pure strategy Nash equilibrium: True False Question 10: If a tree game has a backward induction equilibrium then it must also be a Nash equilibrium of all of its subgames: Tr 2/2 Question 11: The mixed Nash equilibrium payoffs are always strictly smaller than the pure Nash equilibrium payoffs: True False Question 12: Which of the following statements about dominant/dominated strategies is/are true? I. A dominant strategy dominates a dominated strategy in 2x2 games. II. A dominated strategy must be dominated by a dominant strategy in all games. III. A profile of dominant strategies must be a pure strategy Nash equilibrium. IV. A dominated strategy must be dominated by a dominant strategy in 2x2 games. I, II and IV only I, II and III only II and III only I and IV only I, III and IV only I and II only Question 13: A pure strategy Nash equilibrium is a special case of a mixed strategy Nash equilibrium: True False Question 14: Consider the following 2x2 matrix game: L R U (3,2) (2,4) D (-1,4) (4,3) The number of pure and mixed Nash equilibria in the above game is: 0 1 2 3 Exercise (corresponding to questions 15 to 20 below): assume a medical doctor (M) prescribes either drug A or drug B to a patient (P), who complies (C) or not (NC) with each of this treatment. In case of compliance, controlled by an authority in charge of health services quality, the physician is rewarded at a level of 1 for drug A and 2 for drug B. In case of noncompliance, the physician is « punished » at -1 level for non-compliance of the patient with drug A and at -2 level for non-compliance with drug B. As for the compliant patient, drug A should give him back 2 years of life saved and drug B, only 1 year of life saved. When noncompliant with drug A, the same patient wins 3 years of life (due to avoiding unexpected allergic shock for instance), and when non-compliant with drug B, the patient loses 3 years of life. Question 15: You will draw the corresponding matrix of the simultaneous doctor-patient game. Question 16: Find, if any, the profile(s) of dominant strategies of this game. Question 17: Find, if any, the pure strategy Nash equilibrium/equilibria of this game. Question 18: Find, if any, the mixed strategy Nash equilibrium/equilibria of this game. Questions 19 and 20: Now the doctor prescribes first, then the patient complies or not: draw the corresponding extensive-form game (= question 19) AND find the subgame perfect Nash equilibrium/equilibria (=

he efficacy of this spending is therefore relatively important. When it comes to contagious diseases, there are generally two strategies that can be adopted. The first involves prevention, which includes vaccinations to lower or eliminate the risk of contracting a disease. The second involves treatment of those unfortunate enough to get sick, treatment typically requires some form of a drug. Since pharmaceutical companies can produce both vaccines and drugs, we would like to understand the incentives they have to develop each type of medicine. To explore this question, consider a population of 100 consumers, 90 of whom have a low disease risk, say 10%. The remaining ten have a high risk – to make things simple, assume they are certain to contract the disease. In addition, suppose the disease generates personal harm equal to the loss of $100 for each individual when they are infected. Suppose also that pharmaceuticals of either form (vaccines or drugs) are costless to produce (once R & D has occurred) and are perfectly effective Question 2. What price would a profit maximising monopolist charge for a vaccine? What are the monopoly profits on the vaccine? What is the efficient outcome (i.e. SMB = SMC)? What is the welfare under the monopoly and at the efficient allocation? Question 3.Now consider the demand for the drug (assume that the vaccine is not available). Construct the demand function for the drug and plot it on a diagram. What price would a profit maximising monopolist charge for the drug? What are the monopoly profits from the drug? What is the efficient outcome? What is the welfare under the monopoly and at the efficient allocation? Question 4. If the R&D costs of the vaccine and drug are the same, what will the pharmaceutical company do? Explain your answer in terms of the variation in the willingness to pay and the size of the R& D costs. What would a social planner do? Question 5. What are the R&D cost for the vaccine and the R&D cost for the vaccine drug that would make a pharmaceutical company indifferent between developing the vaccine and the drug? Is the social planner indifferent in this case? Explain any difference.