2
3
4
β’
o π = {1,β¦ , π}
o π
o π β π π’π: ππ β β
j β π π π β π
π π’π(π 1, β¦ , π π)
β’
5
6
Selling ice cream at the beach. One day your cousin Ted shows up. His ice cream is identical!
You split the beach in half; you set up at 1/4. 50% of the customers buy from you. 50% buy from Teddy.
One day Teddy sets up at the 1/2 point! Now you serve only 37.5%!
β’ π’π π π , π π =
π π+π π
2, π π < π π
1 βπ π+π π
2, π π > π π
1
2, π π = π π
β’ π = 1,2
β’ π = [0,1]
β’
7
β’
β’
o
o
β’
8
9
β’
β’
β’
10
β’
o
o
β’
o
o
β’
o
o
11
12
13
β’
β’
π = π 1β¦ , π π β ππ
βπ β π, βπ πβ² β π, π’π π β₯ π’π(π π
β², π βπ)
14
β’
1. 0
2. 1
3. 2
4. 3
15
16
17
18
Day 3 of the ice cream wars⦠Teddy sets up south of you! You go south of Teddy.
Eventuallyβ¦
19
20
β’
β’ π β π π₯π
π₯π(π π) = Pr[π plays π π]
β’ π β π
π’π π₯1, β¦ , π₯π =
(π 1,β¦,π π)βππ
π’π π 1, β¦ , π π β ΰ·
π=1
π
π₯π (π π)
21
β’1
2,1
2, 0
0,1
2,1
2π’1
β’1
3,1
3,1
3
π’1
22
β’
1.1
2,1
2, 0 ,
1
2,1
2, 0
2.1
2,1
2, 0 ,
1
2, 0,
1
2
3.1
3,1
3,1
3,
1
3,1
3,1
3
4.1
3,2
3, 0 ,
2
3, 0,
1
3
23
β’
24
β’ {2, β¦ , 100}
β’
β’ π π‘ π < π‘π + 2
π β 2
β’
25
β’
o
o
o
β’
o
26