Finite Automata Capturing Winning Sequences for All Possible Variants of the PQ Penny Flip Game

Theodore Andronikos, Alla Sirokofskich, Kalliopi Kastampolidou, Magdalini Varvouzou, Konstantinos Giannakis and Alexander Singh
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Theodore Andronikos: Department of Informatics, Ionian University, 7 Tsirigoti Square, Corfu 49100, Greece
Alla Sirokofskich: Department of History and Philosophy of Sciences, National and Kapodistrian University of Athens, Athens 15771, Greece
Kalliopi Kastampolidou: Department of Informatics, Ionian University, 7 Tsirigoti Square, Corfu 49100, Greece
Magdalini Varvouzou: Department of Informatics, Ionian University, 7 Tsirigoti Square, Corfu 49100, Greece
Konstantinos Giannakis: Department of Informatics, Ionian University, 7 Tsirigoti Square, Corfu 49100, Greece
Alexander Singh: Department of Informatics, Ionian University, 7 Tsirigoti Square, Corfu 49100, Greece

Mathematics, 2018, vol. 6, issue 2, 1-26

Abstract: The meticulous study of finite automata has produced many important and useful results. Automata are simple yet efficient finite state machines that can be utilized in a plethora of situations. It comes, therefore, as no surprise that they have been used in classic game theory in order to model players and their actions. Game theory has recently been influenced by ideas from the field of quantum computation. As a result, quantum versions of classic games have already been introduced and studied. The P Q penny flip game is a famous quantum game introduced by Meyer in 1999. In this paper, we investigate all possible finite games that can be played between the two players Q and Picard of the original P Q game. For this purpose, we establish a rigorous connection between finite automata and the P Q game along with all its possible variations. Starting from the automaton that corresponds to the original game, we construct more elaborate automata for certain extensions of the game, before finally presenting a semiautomaton that captures the intrinsic behavior of all possible variants of the P Q game. What this means is that, from the semiautomaton in question, by setting appropriate initial and accepting states, one can construct deterministic automata able to capture every possible finite game that can be played between the two players Q and Picard. Moreover, we introduce the new concepts of a winning automaton and complete automaton for either player.

Keywords: finite automata; games; PQ penny flip game; game variants; winning sequences (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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