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(20 marks) Consider two firms that are choosing their sizes. Each firm can choose a large or small size. If both of them choose large each makes a profit of GHc192; if both choose small, each makes a profit of GHc200. If one chooses large and the other chooses small the large firm makes a profit of GHc216 and the small firm makes GHc180. Assume a simultaneous move game and answer the questions below: (3 marks) Draw the extensive form of the game. How many subgames are there? (5 marks) Show the strategic form of the game and find the Nash equilibrium (7 marks) Now assume the game is played twice. Draw the extensive form of the game assuming a discount rate of r (5 marks) Show that a cooperative equilibrium (small, small) is not a subgame perfect Nash equilibrium. a. b. c. 0.1 d.
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Sn2 R-1 brn 소 | Small |、200,100+ 1 80,216 al In the tig1 al the ditevent Rames possible are shown twough the diagom Ye when hom 1 Chooses smau the tom 2 uuu yo tor loyse becaure 216 7200 Sumlaly uhen thom 1 choos es Lavge the tam 2 ul aaun choose Lorge Theretove urespechve of what tom 1 Choice is the hom2 wit Choose Large This s the game als o going ty avgethoughー f-the. make a-. Coopera hve decision-otDoducing gmo i ema they wwi end up makin hen lorg e , large but shiu they ul end up ot is the Nath eqii ulimum n the gome Both the fioms are choosing larpe imespechive of the o the, hims choice Theretore, boin of them wll end up at lage laure 192,192] C)一Now, discount reue 0.1 - cft mahnx Gome is played one mare bme Large 192 +1a2Co 192 + 19.2 21 2 二 220Smalu lange all, lanpe 180+ 18g0, 216 + 216 C 180-t 18, 216+21-6 198,-239b pe 232 9211.2 211 is is the extensive tt om 어 the game.一Again the Nash equ bnum (s lar sel latce : No coope Yahon them fako deesiins depending upem the decsmon ot the other hrmm Tt hom 4 Chooses smau, tom 2 uuu choose larse hecaiut 220<237 . 6 and 198<211-2, Sim larly m fo hm 2 Nash equil boud

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