Game Theory Game 3 Your Value to a

Game Theory Game 3 Your Value to a Game

Your Value to a Game n You: Director of a commercial-free music video channel q Cable companies pay to carry you q You make a take-it-or-leave it offer q n Cable Companies: Each channel has $100 K in value q Cable companies have varying capacities (k) q Select the k best (lowest) offers q Market 1: 50, Market 2: 30, Market 3: 20 q 2

Your Value to a Game Your added value = the size of the pie when you are in the game minus the size of the pie when you are not 3

Unlimited Capacity (k=50) Unlimited Capacity What is your value to the game? n What is the total value of the game? n How much should you be paid to play? n 4

Class Results n Most requested 100 q Or n 99, or 99. 9 But…some LOVE the cable company q. A few requested less than 50 q One requested 2 5

Slightly Limited Capacity (k=30) Perception of Bargaining Power What is your value to the game? n What is your perceived value? n What is the total value of the game? n How much should you be paid to play? n 6

Limited Capacity (k=20) Perception of Bargaining Power What is your value to the game? n What is the total value of the game? n How much should you be paid to play? n 7

Payoff Summary k = 50 k = 30 k = 20 Average offer: 83 58 22 Accept offers below: 100 55 20 Average accepted offer: 83 48 11 My profit per channel: 17 52 89 x 39 My profit: = 663 x 30 = 1560 (+135%) 8 x 20 = 1780 (+168%)

Intuition n By reducing capacity q. I lower your added value q I gain bargaining power q I get a better price per channel q I gain higher profits overall n But: q The 9 value of the game is smaller

Best Score maximum profit = 100 + 55 + 20 = 175 10 n Tim 100 + 50 + 15 = 165 n Alex 100 + 50 + 15 = 165 n Xiaoying 99 + 45 + 18 = 162

Others n Swinging for the fences q Alexandra n Playing it safe q Carl q Paul 11 99. 9 + 74 + 45 = 100 + 20 + 5 = 125 100 + 35 + 1 = 136