  This paper examines the valuation of a generalized American-style option
known as a Game-style call option in an infinite time horizon setting. The
specifications of this contract allow the writer to terminate the call option
at any point in time for a fixed penalty amount paid directly to the holder.
Valuation of a perpetual Game-style put option was addressed by Kyprianou
(2004) in a Black-Scholes setting on a non-dividend paying asset. Here, we
undertake a similar analysis for the perpetual call option in the presence of
dividends and find qualitatively different explicit representations for the
value function depending on the relationship between the interest rate and
dividend yield. Specifically, we find that the value function is not convex
when $r>d$. Numerical results show the impact this phenomenon has upon the vega
of the option.

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