01746nas a2200241   4500000000100000000000100001008004100002260001200043653002100055653003700076653001200113653001400125653001600139100002500155700003400180700001800214245005100232856008100283300000800364490001300372520110500385022001401490       9998                            d  c09/202310aNash Equilibrium10aPolynomial Time Quantum Problems10aQuantum10aComputing10aGame Theory1 aRaquel Pérez-Antón1 aJosé Ignacio López Sánchez1 aAlberto Corbi00aThe Game Theory in Quantum Computers: A Review  uhttps://www.ijimai.org/journal/sites/default/files/2023-09/ip2023_09_001.pdf  a1-90 vIn Press3 aGame theory has been studied extensively in recent centuries as a set of formal mathematical strategies for optimal decision making. This discipline improved its efficiency with the arrival, in the 20th century, of digital computer science. However, the computational limitations related to exponential time type problems in digital processors, triggered the search for more efficient alternatives. One of these choices is quantum computing. Certainly, quantum processors seem to be able to solve some of these complex problems, at least in theory. For this reason, in recent times, many research works have emerged related to the field of quantum game theory. In this paper we review the main studies about the subject, including operational requirements and implementation details. In addition, we describe various quantum games, their design strategy, and the used supporting tools. We also present the still open debate linked to the interpretation of the transformations of classical algorithms in fundamental game theory to their quantum version, with special attention to the Nash equilibrium.  a1989-1660