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 …