GAME THEORY

Problem 5. Al and Bob are engaged in a joint project. The amount of time Al and Bob can devote to the project is denoted A and B, respectively. This time can be spent either on the actual goals of the project (productive time, denoted a and b), or on non-productive tasks (a and ,8) that help win the favour of Al's and Bob's boss the person who decides about the way players are rewarded for their joint project output. Total payoH equals the sum of the productive time put in by both players, a + b. If neither player wastes time on nonproductive tasks (a = 6 = 0), each gets half of the total payoff; otherwise, Al gets the share \"A\" of the total payoH, and Bob receives the rest. Games and Decisions: Home Assignment Jan Zouhar a) Find the unique Nash equilibrium for the case A = B. Note: In your bestresponse analysis, you will have to investigate the comer strategies (e.g., a = 0 or a = A) and the interior strategies (0. E (0,A)) separately. For the interior strategies, use rst-order conditions, as in the Cournot oligopoly. 6 points b) Use the rst order conditions show that when A 7'5 B and the solution is still interior (non-zero a,oc, but?) both players get half of the total payoH. W'hich player allocates a greater share of his project time to productive tasks? 4 points