$TITLE: M4-2.GMS: Find all pure-strategy Nash equilibrium * with discrete strategy sets $ONTEXT two firms, one in country h and one in country f each firm chooses one of three strategies: don't enter: strategy 0 enter with a single plant and export to the other country: strategy 1 enter with plants in both countries (horizontal multinational) strategy 2 $OFFTEXT SETS R strategies for firm h /SH0, SH1, SH2/ C strategies for firm f /SF0, SF1, SF2/; ALIAS(R,RR) ALIAS(C,CC); PARAMETERS ROWMAX(R,C) maximum value over the rows for a given column C COLMAX(R,C) maximum value over the columns for a given row R NASHEQ(R,C) matrix of 0-1 where 1 is a Nash equilibrium PROFHNE(R,C) profit of firm h in Nash equilibrium PROFFNE(R,C) profit of firm f in Nash equilibrium; * small maintenance costs -0.1 when not entering, not needed TABLE PAYOFFH(*,*) SF0 SF1 SF2 SH0 -.1 -.1 -.1 SH1 10 6 3 SH2 12 5 2 ; TABLE PAYOFFF(*,*) SF0 SF1 SF2 SH0 -.1 10 12 SH1 -.1 6 5 SH2 -.1 3 2 ; DISPLAY PAYOFFH, PAYOFFF; ROWMAX(R,C) = 1$(PAYOFFH(R,C) EQ SMAX(RR, PAYOFFH(RR,C))); COLMAX(R,C) = 1$(PAYOFFF(R,C) EQ SMAX(CC, PAYOFFF(R,CC))); DISPLAY ROWMAX, COLMAX; NASHEQ(R,C) = ROWMAX(R,C)*COLMAX(R,C); DISPLAY NASHEQ; PROFHNE(R,C) = PAYOFFH(R,C)$NASHEQ(R,C); PROFFNE(R,C) = PAYOFFF(R,C)$NASHEQ(R,C); DISPLAY PROFHNE, PROFFNE; *CASE 2: MARKETS TOO SMALL FOR A FIRM TO ENTER AGAINST A TWO-PLANT RIVAL *subtract 4 from each payoff strategies 1 and 2 TABLE PAYOFFH2(*,*) SF0 SF1 SF2 SH0 -.1 -.1 -.1 SH1 6 2 -1 SH2 8 1 -2 ; TABLE PAYOFFF2(*,*) SF0 SF1 SF2 SH0 -.1 6 8 SH1 -.1 2 1 SH2 -.1 -1 -2 ; ROWMAX(R,C) = 1$(PAYOFFH2(R,C) EQ SMAX(RR, PAYOFFH2(RR,C))); COLMAX(R,C) = 1$(PAYOFFF2(R,C) EQ SMAX(CC, PAYOFFF2(R,CC))); NASHEQ(R,C) = ROWMAX(R,C)*COLMAX(R,C); DISPLAY NASHEQ; PROFHNE(R,C) = PAYOFFH2(R,C)$NASHEQ(R,C); PROFFNE(R,C) = PAYOFFF2(R,C)$NASHEQ(R,C); DISPLAY PROFHNE, PROFFNE; *CASE 3: LOWER FIRM FIXED COSTS, RAISE PLANT FIXED COSTS *makes two-plant production more profitable *add 2 when playing strategy 2 TABLE PAYOFFH3(*,*) SF0 SF1 SF2 SH0 -.1 -.1 -.1 SH1 10 6 3 SH2 14 7 4 ; TABLE PAYOFFF3(*,*) SF0 SF1 SF2 SH0 -.1 10 14 SH1 -.1 6 7 SH2 -.1 3 4 ; ROWMAX(R,C) = 1$(PAYOFFH3(R,C) EQ SMAX(RR, PAYOFFH3(RR,C))); COLMAX(R,C) = 1$(PAYOFFF3(R,C) EQ SMAX(CC, PAYOFFF3(R,CC))); NASHEQ(R,C) = ROWMAX(R,C)*COLMAX(R,C); DISPLAY NASHEQ; PROFHNE(R,C) = PAYOFFH3(R,C)$NASHEQ(R,C); PROFFNE(R,C) = PAYOFFF3(R,C)$NASHEQ(R,C); DISPLAY PROFHNE, PROFFNE;