Two workers at the Meta Headquarters in Menlo Park, California need to work closely on a project. Each worker i = 1,2 chooses simultaneously (and independently) an amount of effort ei >= 0 (measured in hours of work per day) to invest on the project. The effort is costly, but there are synergies between the two workers. The value to each worker from effort levels (e1, e2) is e1 + 2e2 + e1e2. Worker 1’s cost of effort is 51 e21 and worker 2’s cost of effort is 2e2.
(a) Write down the normal form of this game.
(b) What is the best response correspondence of each worker?