Game Theory and Other Unconventional Approaches to Biological Systems

Abstract

This paper introduces a new quantum game called Quantum Tapsilou that is inspired from the classical traditional Greek coin tossing game tapsilou. The new quantum game, despite its increased complexity and scope, retains the crucial characteristic of the traditional game, namely that of fairness. In the classical game, both players have 1 4 probability to win. In its quantum version, both players have equal chances to win too, but now the probability to win varies considerably, depending on previous choices. The two most important novelties of Quantum Tapsilou can be attributed to its implementation of entanglement via the use of rotation gates instead of Hadamard gates, which generates Bell-like states with unequal probability amplitudes, and the integral use of groups. In Quantum Tapsilou both players agree on a specific cyclic rotation group of order 𝑛, for some sufficiently large 𝑛, which is the group upon which the game will be based, in the sense both players will pick rotations from this group to realize their actions using the corresponding 𝑅 𝑦 rotation gates. This fact is in accordance with a previous result in the literature showing that symmetric quantum games, where both players draw their moves from the same group, are fair.

A symmetric extensible protocol for quantum secret sharing

“…Striving to outperform traditional methods when dealing with problems and games, motivated researchers to also turn to the biological domain. Many classical games, including the Prisoners' Dilemma, have also been examined under the prism of biological notions [32,33,34,35]. Unsurprisingly, computation can be conducted in the context of biological and bio-inspired processes [36,37], even including computer viruses [38].…”