On fingerprinting capacity games for arbitrary alphabets and their asymptotics

Fingerprinting capacity has recently been derived as the value of a two-person zero-sum game. In this work, we study fingerprinting capacity games with k pirates under the combined digit model proposed by Škorić et al. For small k, capacities along with optimal strategies for both players of the game are obtained explicitly. For large k, we extend our earlier asymptotic analysis for the binary alphabet to this general model and show that capacity is asymptotic to A/k² where the constant A is identified. Saddle-point solutions to the functional maximin game are obtained using methods of variational calculus.