Transcript THE COACH’S DILEMMA by Daniele & Gianfranco Gambarelli Group D FIRST DAY: June 14th Costa Rica Italy Uruguay England 3-1 2-1 Group D COSTA RICA ITALY ENGLAND URUGUAY NEXT MATCH Italy Costa Rica vs Costa Rica Italy Cesare Prandelli Jorge Luis Pinto THE FORECASTS THE FORECASTS % ITA win. % draw ,

THE COACH’S
DILEMMA
by Daniele & Gianfranco Gambarelli
Group D
FIRST DAY: June 14th
Costa Rica
Italy
Uruguay
England
3-1
2-1
Group D
COSTA RICA
3
ITALY
3
ENGLAND
0
URUGUAY
0
NEXT MATCH
Italy
Costa Rica
vs
Costa
Rica
Italy
Cesare Prandelli
Jorge Luis Pinto
THE FORECASTS
THE FORECASTS
%
ITA
win.
%
draw
, ,
%
C.R.
win.
DEFENSE
DEFENSE
ATTACK
56, 34, 10
76, 19, 05
61, 24, 15
ATTACK
66, 09, 25
66, 14, 20
THE PAYOFFS
DEFENSE - DEFENSE
ITA
Payoff
C.R.
Payoff
0.56 x 3 + 0.34 x 1 =
2.02
0.10 x 3 + 0.34 x 1 =
0.64
THE STRATEGIES
PAYOFFS
ITA
Payoff
,
C.R.
Payoff
DEFENSE
ATTACK
DEFENSE
2.02 , 0.64
2.47 , 0.34
ATTACK
2.07 , 0.84
2.12 , 0.74
THE SOLUTION
ATTACK
DEFENSE
NO DOMINANCE?
Nash (1950)
Having called
qAD = % defense of A
qAO = % attack of A
h = (aOD - aOO) / (aDO + aOD - aDD - aOO),
it is:
qAD = h if 0  h  1.
Elsewhere

0
if min (aDD, aDO) < min (aOD, aOO)
qAD = 
1
if min (aDD, aDO) > min (aOD, aOO)
 x: 0 < x < 1 otherwise
qAO = 1 - qAD.
+10%
THE STABILITY
-10%
DEFENSE
ATTACK
DEFENSE
61, 65, 15
56, 31,
34, 08
10
20,
20, 24, 15
76,
73, 19,
65, 05
03
ATTACK
71,
65, 15
66, 09,
25
20, 08, 21
68,
66, 17,
14, 15
20
20, 65, 15
AN OPEN PROBLEM:
- Discrete  Continuum
CONCLUSIONS:
- To Game-Theorists:
Discrete  Continuum
- To Coaches:
Before the match  No stone unturned
- To Curious:
…
What happened?
but …