23 a simultaneous game of airline alliances the

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Unformatted text preview: ine alliances. The foregoing analysis suggests that airline alliances are profitable only under some circumstances. Let us then propose the following two-stage game. In the first stage airlines 1 and 2 and airlines 3 and 4 decide simultaneously and independently whether to form an alliance. In stage two, given the inherited outcome from the first stage, airlines set fares. From our previous 8 The precise condition is > d(4b4 +9b2 d2 -3d4 ) 2(20b5 -23b3 d2 +5bd4 ) . The r.h.s. is increasing with d so that the higher value it can take is 10/4. Hence, it is sufficient that > 2.5 to have that consumers are better off with both alliances. 11 analysis the subgame perfect equilibrium amounts to characterizing the Nash equilibrium of the following normal-form game, where each cell shows profit per airline: Airlines 1 or 2// 3 or 4 Alliance No Alliance Alliance b(2b+d) 2(4b2 -d2 )2 2 , b(2b+d)2 b(3b+2d)2 , 4(3b2 -d2 )2 8(3b2 -d2 )2 b(2b+d) 2(4b2 -d2 )2 2 No Alliance b(3b+2d)2 b(2b+d)2 , 8(3b2 -d2 )2 4(3b2 -d2 )2 b(3b+2d)2 b(3b+2d)2 , (9b2 -4d2 )2 (9b2 -4d2 )2 We may use the above results to solve for the Nash equilibrium. Suppose that airlines 3 and 4 do not form an alliance. Then,...
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