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THE COACH’S DILEMMA

THE COACH’S DILEMMA. by Daniele & Gianfranco Gambarelli. Group D FIRST DAY: June 14th. Group D. NEXT MATCH. vs. ATTACK OR DEFENSE?. Costa Rica. Italy. Cesare Prandelli Jorge Luis Pinto. THE FORECASTS. THE FORECASTS. , ,. % ITA win. % C.R. win. % draw.

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THE COACH’S DILEMMA

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

  2. Group D FIRST DAY: June 14th

  3. Group D

  4. NEXT MATCH vs

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

  6. THE FORECASTS

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

  8. THE PAYOFFS THE STRATEGIES , ITA Payoff C.R. Payoff < 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 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% -10% 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

  11. AN OPEN PROBLEM: • Discrete  Continuum

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

  13. What happened?

  14. but …

  15. ITALIA 0 – COSTA RICA 1

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