Quantum Information Processing (2019) 18:10 https://doi.org/10.1007/s11128-018-2113-5 Quantization and experimental realization of the Colonel Blotto game A. C. Maioli 1,3 · M. H. M. Passos 1,3 · W. F. Balthazar 2 · C. E. R. Souza 3,4 · J. A. O. Huguenin 1,3 · A. G. M. Schmidt 1,3 Received: 26 July 2018 / Accepted: 7 November 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract We present a quantum mechanical version of the Colonel Blotto game, where two players, Blotto and Enemy, collocate their soldiers (resources) sequentially in a finite number of territories. We analyse the representative classical cases of this game as well as the trivial case—which on its turn has no interest at all in the point of view of classical game theory—where, surprisingly, a player that could control a single parameter can win the game even if he/she is greatly outnumbered by his/her opponent. Besides the theoretical study we present an experimental realization of classical game by using linear optics circuits as well as a proposal of an experimental investigation of the quantized game. Finally, in order to check our quantization scheme we also present computer simulation results. Keywords Quantum games · Optical circuits · Transverse modes · Polarization modes 1 Introduction Game theory plays a very important role in the analysis of decision-making; it serves to model mathematically situations where agents, or players, are in some conflict situation. The paradigm of cooperation is the well-known prisoner’s dilemma—in fact, despite it is the most studied game, recently Dyson and Press [1] uncovered new B A. G. M. Schmidt agmschmidt@gmail.com 1 Instituto de Ciências Exatas, Universidade Federal Fluminense, CEP 27213-145 Volta Redonda - RJ, Brazil 2 Instituto Federal do Rio de Janeiro, CEP 27215-350 Volta Redonda - RJ, Brazil 3 Programa de Pós Graduação em Física Instituto de Física, Universidade Federal Fluminense, CEP 24210-346 Niterói - RJ, Brazil 4 Instituto de Física, Universidade Federal Fluminense, CEP 24210-346 Niterói - RJ, Brazil 0123456789().: V,-vol 123