1. THE COACH’S DILEMMA
by Daniele & Gianfranco Gambarelli

2. Group D
FIRST DAY: June 14th
Costa Rica
Uruguay
3-1
Italy
England
2-1

3. Group D
COSTA RICA 3
ITALY
ENGLAND
URUGUAY

4. NEXT MATCH
Italy
Costa Rica vs

5. Cesare Prandelli Jorge Luis Pinto
ATTACK OR DEFENSE?
Costa Rica
Italy
Cesare Prandelli Jorge Luis Pinto

6. THE FORECASTS

7. , , THE FORECASTS THE PAYOFFS 0.56 x 3 + 0.34 x 1 = 2.02
DEFENSE
ATTACK
, , %
ITA
win.
draw
C.R.
56, 34, 10
76, 19, 05
61, 24, 15
66, 09, 25
66, 14, 20
THE PAYOFFS
DEFENSE - DEFENSE
ITA Payoff
0.56 x x 1 =
2.02
C.R. Payoff
0.10 x x 1 =
0.64

8. , THE STRATEGIES THE PAYOFFS THE SOLUTION < < < <
ITA Payoff
C.R. Payoff
DEFENSE
ATTACK
<
2.02 , 0.64
2.47 , 0.34
<
<
<
2.07 , 0.84
2.12 , 0.74
THE SOLUTION
ATTACK
DEFENSE

9. 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
 if min (aDD, aDO) < min (aOD, aOO)
qAD =  if min (aDD, aDO) > min (aOD, aOO)
 x: 0 < x < 1 otherwise
qAO = 1 - qAD.

10. THE STABILITY +10% -10% DEFENSE ATTACK 61, 65, 15 20, 31, 08
61, 65, 15
20, 31, 08
20, 24, 15
73, 65, 03
56, 34, 10
76, 19, 05
71, 65, 15
20, 08, 21
68, 17, 15
20, 65, 15
66, 09, 25
66, 14, 20

12. AN OPEN PROBLEM:
Discrete  Continuum

13. CONCLUSIONS: … To Game-Theorists: To Coaches: To Curious:
Discrete  Continuum
To Coaches:
Before the match  No stone unturned
To Curious: …

14. What happened?

15. but …

17. ITALIA 0 – COSTA RICA 1