Contributed Session Thu.3.MA 043

Thursday, 15:15 - 16:45 h, Room: MA 043

Cluster 8: Game theory [...]

Software piracy and mastermind


Chair: Carola Winzen



Thursday, 15:15 - 15:40 h, Room: MA 043, Talk 1

Yael Perlman
Software piracy prevention and price determination

Coauthors: Konstantin Kogan, Yaacov Ozinci


We consider a monopolistic producer offering software that is updated periodically, but, by the end of one period, a pirated version is available at a transaction cost. This presents the heterogeneous consumer with possible strategies for either buying a new product or pirating it. We address pricing and protection investment strategies to regain the profits affected by the piracy. In particular, we find that even when the transaction cost is exogenous, the producer does not necessarily want to fully price out the piracy. The decisive factor in such a case is the level of product newness relative to the transaction cost. If the producer is able to achieve high newness for the updated product relative to the transaction cost, then a high retail price ensures that he will gain the largest profit possible even though some of the demand will be lost due to piracy. On the other hand, when the transaction cost is endogenous, the producer may have two alternatives: pricing the software out or investing heavily in software protection. As newness levels rise, the option of pricing out the piracy becomes increasingly preferable.



Thursday, 15:45 - 16:10 h, Room: MA 043, Talk 2

Carola Winzen
Playing mastermind with many colors

Coauthors: Benjamin Doerr, Reto Spoehel, Henning Thomas


We consider the black-peg version of Mastermind with n holes and k ≤ n colors. For the most interesting case k = n, by combining previous approaches of Chvátal (Combinatorica 3 (1983), 325-329) and Goodrich (Information Processing Letters 109 (2009), 675-678), we show that there exists a deterministic winning strategy that allows the codebreaker to find the secret code with O(n log1/2 n) guesses.
This improves the previously best known bounds of Chvátal, Goodrich, and others, which are all of order n log n; both for the black-peg version of Mastermind and the original game with both black and white answer-pegs.
More generally, one of the key arguments, the success probability of random sampling, can be applied to the Mastermind game with any number k ≤ n e-log^{1/2 n} of colors, and it yields a winning strategy using O(n log k/log(n/k)) guesses.


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