  In Gapeev and K\"uhn (2005), the stochastic game corresponding to perpetual
convertible bonds was considered when driven by a Brownian motion and a
compound Poisson process with exponential jumps. We consider the same
stochastic game but driven by a spectrally positive L\'evy process. We
establish a complete solution to the game indicating four principle parameter
regimes as well as characterizing the occurence of continuous and smooth fit.
In Gapeev and K\"uhn (2005), the method of proof was mainly based on solving a
free boundary value problem. In this paper, we instead use fluctuation theory
and an auxiliary optimal stopping problem to find a solution to the game.
