ProofWe first establish the following symmetry inequality for pure strategies: for allh, c∈V, Payoff(h, c) + Payoff(c, h)≤1.(7) Fixh, c∈V

In particular, there exists a (possibly randomized) learner strategyp V overVsuch that for everyc∈V, Payoff(pV , c)≤ 1 2