BA 4129 STRATEGIC GAMES FOR MANAGER

1
BA 4129 STRATEGIC GAMES FOR MANAGER

• Delta vs. THY
• Prepared by Atay Kizilaslan

2
Conditions 1990

• Compete against each other on the route between
  Istanbul New York
• Decide on the number of discount seats offered on
  this route

3
Conditions 1990

• The number discount of seats offered by THY is ST
• The number of discount seats offered by Delta is
  SD
• The market-determined discount price (P) depends
  on the total number of seats offered by both
  airlines ST SD according to the equation
  P200-0.10(ST SD )
• Marginal cots are MCT 100
  MCD 50

4
Solution

• When we solve it according to cournot duopoly
• Profit(Si,Sj)PSi - MCi Si i,jT,D i?j where
  P200-0.10(ST SD )
• max Si(200-0.10(Si Sj ))Sj - MCi Si
• FONC
• Si (200-0.1 Sj MCi )/0.2

5
Solution

• ST (200-0.1SD-100)/0.2
• SD(200-0.1ST-50)/0.2
• ST 200-0.1((200-0.1ST-50)/0.2)-100/0.2
• ST500/3 SD2000/3
• Total Quantity2500/3 P350/3
• Profit of THY25000/3
• Profit of Delta400000/3
• Total Duopoly Profit 425000/3

6
Today

• Due to Economic Crisis in Turkey, both airlines
  reevaluate the profitability of the line
• They discover that both have the same marginal
  cost which is equal to 75

7
Solution

• According to this new cournot calculations
• max Si (200-0.10(Si Sj ))Sj - 75Si
• FONC
• 200-0.20Sj-0.10Sj-750
• Si(125-0.1 Si)/0.2

8
Solution

• New best response functions are
• ST (125-0.1SD)/0.2
• SD (125-0.1ST)/0.2
• When we solve them
• ST 1250/3 SD1250/3
• Total Quantity 2500/3
• P350/3
• Profit of THY Profit of Delta 156250/9

9
What will happen if the cournot duopoly collude?

• THY executives ask for more profit than they can
  get from cournot duopoly(deviation from cournot
  duopoly)
• They assume that they will play this game
  infinitely.
• They make calculations and find their own tirgger
  strategy
• Trigger Strategy Offer Sm/2 in period 1.In
  period t, offer Sm/2 if the outcome in all t-1
  preceeding periods was (Sm/2,Sm/2), and play ST
  otherwise

10
What will happen if the cournot duopoly collude?

• Cournot outputs are calculated before(ST
  1250/3,P350/3,?C156250/9)
• Their monopoly output (Sm/2) is equal to 312.5
  and Price is equal to 137.5 (?m/219531.25)
• Maximum number of seats they can offer,when Delta
  offers monopoly output (Sm/2),is 468.75 and price
  is equal to 121.875 (?D21972.65625)

11
What will happen if the cournot duopoly collude?

• Trigger strategy is SPE if
• ?m/21/1-dgt?D?C d/1-d
• d gt 0.529