The authors consider game (Israeli) style extension of swing options considered as multiple exercise derivatives. Peculiarities of multiple exercise options are due to restrictions such as an order of exercises and a delay time between them because without restrictions the claims or rights could be considered as separate options. In a binomial market model, assuming that the underlying security can be traded without restrictions, the authors derive a formula for valuation of multiple exercise options via classical hedging arguments. The notion of the shortfall risk for such option is also introduced and partial hedging leading to minimization of this risk is studied.