Joshua LetchfordJoshua Letchford - Duke University
嚜澧PS 296.1
LP and IP in Game theory
(Normal-form Games, Nash Equilibria
and Stackelberg Games)
Joshua Letchford
Rock-paper-scissors 每 Seinfeld variant
MICKEY: All right, rock beats paper!
(Mickey smacks Kramer's hand for losing)
KRAMER: I thought
h
h paper coveredd rock.
k
MICKEY: Nah, rock flies right through paper.
KRAMER: What beats rock?
MICKEY: (looks at hand) Nothing beats rock
rock.
0 0 1,
0,
1 -1
1 1,
1 -1
1
-1,
1 1 0,
0 0 -1,
1 1
-1, 1 1, -1 0, 0
Dominance
? Player i*s strategy si strictly dominates si* iff
每 for any s-ii, ui(si , s-ii) > ui(si*, s-ii)
? si weakly dominates si* if
-i = ※the player(s) other
than i§
每 for any s-ii, ui(si , s-ii) ≡ ui(si*, s-ii); and
每 for some s-i, ui(si , s-i) > ui(si*, s-i)
strict dominance
weak dominance
0 0 1,
0,
1 -1
1 1,
1 -1
1
-1,
1 1 0,
0 0 -1,
1 1
-1, 1 1, -1 0, 0
Mixed strategies
? Mixed strategy for player i = probability
distribution over player i*s (pure) strategies
? E.g.,1/3
E g 1/3
, 1/3
, 1/3
? Example
p of dominance by
y a mixed strategy:
gy
1/2
1/2
3, 0 0, 0
0, 0 3, 0
1 0 1,
1,
1 0
Usage:
考i denotes a mixed
strategy,
si denotes a pure
strategy
Checking for dominance by mixed strategies
? Linear program for checking whether strategy si* is
strictly dominated by a mixed strategy:
? maximize 汍
? such that:
每 for any s-i, 曳si psi ui(si, s-i) ≡ ui(si*, s-i) + 汍
每 曳si psi = 1
? Li
Linear program ffor checking
h ki whether
h th strategy
t t
si* is
i
weakly dominated by a mixed strategy:
? maximize
i i 曳s-i[(曳si psi ui(s
( i, s-i)) - ui(s
( i*,
* s-i)]
? such that:
每 for any s-i, 曳si psi ui(si, s-i) ≡ ui(si*, s-i)
每 曳si psi = 1
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related download
- joshua d kershaw elementary school cps ciwp chicago public schools
- state of iowa vs joshua daniel fleming defendant appellant
- joshua d kershaw elementary school
- tournament winners history team double all events national deaf mixed
- joshua daniel m d
- information for release 8 24 2010 date of the notification to cps near
- daniel c beard elementary school cps ciwp chicago public schools
- information for release 9 12 2013 date of the notification to cps joshua
- posture discourse joshua daniel
- case 3 20 bk 03138 doc 431 filed 11 16 20 entered 11 16 20 18 stretto
Related searches
- duke university nonprofit certificate program
- duke university nonprofit management program
- duke university certificate in nonprofit
- is duke university a 501c3
- duke university executive leadership program
- duke university nonprofit leadership
- duke university ein number
- duke university hospital leadership
- duke university directions
- duke university certificate program online
- duke university graduate certificate programs
- duke university undergraduate application