  We study the problem of super-replication for game options under proportional
transaction costs. We consider a multidimensional continuous time model, in
which the discounted stock price process satisfies the conditional full support
property. We show that the super-replication price is the cheapest cost of a
trivial super-replication strategy. This result is an extension of previous
papers (see [3] and [7]) which considered only European options. In these
papers the authors showed that with the presence of proportional transaction
costs the super--replication price of a European option is given in terms of
the concave envelope of the payoff function. In the present work we prove that
for game options the super-replication price is given by a game variant analog
of the standard concave envelope term. The treatment of game options is more
complicated and requires additional tools. We combine the theory of consistent
price systems together with the theory of extended weak convergence which was
developed in [1]. The second theory is essential in dealing with hedging which
involves stopping times, like in the case of game options.
