- Econ 3115 Problem Set 5 April 12 Due April 19 Player 2 Tt1 1 Play Moderate Fish The First Time You Meet M If T 1 (45.7 KiB) Viewed 18 times
ECON 3115 Problem set 5 April 12 - Due April 19 Player 2: TT1. (1) Play "Moderate fish the first time you meet. (m) If the other player played "moderate" in the previous period, play moderate" this period. Otherwise, play "high" TT2. Always play "high" Two fishing companies use the same inshore fishery. Each month, the combined sustainable catch depends on the combined time they spend fishing and decreases if the total time is too high as they deplete the breeding stock. The following "game" shows how the number of toones of fish each company catches varies with the amount of fishing done by each company. The number on the left of each square is the catch for company 1; the number on the right is the catch for company 2 Calculate the retums from playing the repeat super strategy game. Show the minimum probability and interest rate necessary to necessary to support (SS1, TTI) 29 equilibrium is 1+1-13 T Player 2 => TTI TT2 Company - Low fishing Company 1! activity Moderate fishing High fishing activity activity Player 11 (25, 35) (25, 65) (20,75) SSI Low fishing activity Moderate fishing activity High fishing activity (45, 35) (40, 60) (32,48) SS2 (55, 30) , (48, 32) (35, 35) Note: because the game is asymmetric, you need to calculate two conditions for the Nash equilibrium. The condition above is the highest of the two conditions. 1. What is the Nash equilibrium pair of strategies for the two companies? Are these socially optimal strategies? [2 marks] Part 2 [3 marks] This question explores the above game in circumstances discussed in the notes where players have a discount rate and a probability of encountering each other in the future. This means players discount the value of future rewards at a combined rate? .r is the annual interest rate 1+1 1., The two players adopt a repeat game strategy. They wish to support "moderate, moderate fishing by cooperating, with the threat of reverting to the high fish, high fish" equilibrium if someone defects. They adopt the following super strategies: Player 1: SS1. Play "Moderate fish" the first time you meet. (ii) If the other player played "moderate" in the previous period, play "moderate this period. Otherwise, play "high" SS2. Always play "high"