TWO TO TANGO © 2011 John Vrooman Vanderbilt University USA

Competitive balance In pro sports leagues © 2011 John Vrooman Vanderbilt University USA

John vrooman Vanderbilt university, usa © 2011 John Vrooman Vanderbilt University USA

$M/w 2 $M/w 1 COMPETITIVE PROFIT-MAX EQUILIBRIUM A cT MR 2 cT MR 1 w1w1 © 2011 John Vrooman Vanderbilt University USA

COOPERATIVE PROFIT MAX EQUILIBRIUM $M/w 2 $M/w 1 A cT MR 2 cT MR 1 MR 1 ′ MR 2 ′ w1w1 A’ © 2011 John Vrooman Vanderbilt University USA

PAYROLL CAP $M/w 2 $M/w 1 A cT MR 2 cT MR 1 w1w1 CAP 1 C’T B © 2011 John Vrooman Vanderbilt University USA

$M/w 2 $M/w 1 REVENUE SHARING & Payroll CAP A cT MR 2 cT MR 1 MR 1 ′ w1w1 CAP 1 B C’T C’’T MR 2 ′ © 2011 John Vrooman Vanderbilt University USA A’A’

$M/w 2 $M/w 1 REVENUE SHARING & Payroll MINIMUM A cT MR 1 MR 1 ′ w1w1 CAP 1 B C MIN 2 C’T C’’T B’ MR 2 ′ © 2011 John Vrooman Vanderbilt University USA A’A’ MR 2

AR 1 MR 2 A cT AR 2 MR 1 $M/w 2 $M/w 1 SPORTSMAN WIN-MAX LEAGUE B cT © 2011 John Vrooman Vanderbilt University USA

AR 1 AR 2 ’ A AR 1 ’ $M/w 2 $M/w 1 Win-Max REVENUE SHARING cT AR 2 P1P1 P0P0 P2P2 © 2011 John Vrooman Vanderbilt University USA B

AR 1 A C’T AR 2 $M/w 2 $M/w 1 Win-Max PAYROLL CAP P2P2 CAP 2 CAP 1 B P1P1 © 2011 John Vrooman Vanderbilt University USA

AR 1 AR 2 ’ A cT AR 2 AR 1 ’ $M/w 2 $M/w 1 PAYROLL CAP & REVENUE SHARING B cT CAP 2 CAP 1 C’T P2P2 C P1P1 © 2011 John Vrooman Vanderbilt University USA

w t = w t -1 w t = a + b w t-1 + e t w t =.500 Win t Win t -1 b = 0 b = 1 a a = 0 a =.500 Beta Balance © 2011 John Vrooman Vanderbilt University USA

National Football League © 2011 John Vrooman Vanderbilt University USA

Major League Baseball © 2011 John Vrooman Vanderbilt University USA

National Basketball Association © 2011 John Vrooman Vanderbilt University USA

English Premier League © 2011 John Vrooman Vanderbilt University USA

fin © 2011 John Vrooman Vanderbilt University USA