We show that quantum game theory offers an interesting solution to the famous Newcomb's paradox (free-will problem). Divine foreknowledge is not necessary for a successful completion of the game because quantum theory offers a way to discern human intentions in such a way that the human retain her/his free-will but cannot profit from changing decision. Possible interpretation in terms of quantum market games is proposed.
We show that quantum game theory offers an interesting solution to the famous Newcomb's paradox (free-will problem). Divine foreknowledge is not necessary for a successful completion of the game because quantum theory offers a way to discern human intentions in such a way that the human retain her/his free-will but cannot profit from changing decision. Possible interpretation in terms of quantum market games is proposed.
Humans do not always make the most rational decisions. As studies have shown, even when logic and reasoning point in one direction, sometimes humans “walk” to the opposite route, motivated by personal bias or simply wishful thinking. This paradoxical human behavior has resisted explanation by classical decision theory for over a decade. Scientists have shown that a quantum probability model can provide a simple explanation for human decision-making. In military, decision-making process is considered to be the most neuralgic one. With the recent interest in quantum computing and quantum information theory, there has been an effort to recast classical game theory using quantum probability amplitudes, and hence study the effect of quantum superposition, interference and entanglement on the agents’ optimal strategies. Apart from unsolved problems in quantum information theory, quantum game theory and decision –making, may be useful in studying quantum communication since that can be considered as a game where the objective is to maximize effective communication. This paper discusses the idea of using quantum theory to decision making. 1 HellemicArmy 14, Kanigos Str., Piraeus 18534, Greece.
Newcomb’s problem is a game between two players, one of who has an ability to predict the future: let Bob have an ability to predict Alice’s will. Now, Bob prepares two boxes, Box1 and Box2, and Alice can select either Box2 or both boxes. Box1 contains $1. Box2 contains $1,000 only if Alice selects only Box2; otherwise Box2 is empty($0). Which is better for Alice? Since Alice cannot decide which one is better in general, this problem is called Newcomb’s paradox. In this paper, we propose quantum strategies for this paradox by Bob having quantum ability. Many other results including quantum strategies put emphasis on finding out equilibrium points. On the other hand, our results put emphasis on whether a player can predict another player’s will. Then, we show some positive solutions for this problem.
I apply some of the lessons from quantum theory, in particular from Bell’s theorem, to a debate on the foundations of decision theory and causation. By tracing a formal analogy between the basic assumptions of causal decision theory (CDT)—which was developed partly in response to Newcomb’s problem— and those of a local hidden variable theory in the context of quantum mechanics, I show that an agent who acts according to CDT and gives any nonzero credence to some possible causal interpretations underlying quantum phenomena should bet against quantum mechanics in some feasible game scenarios involving entangled systems, no matter what evidence they acquire. As a consequence, either the most accepted version of decision theory is wrong, or it provides a practical distinction, in terms of the prescribed behaviour of rational agents, between some metaphysical hypotheses regarding the causal structure underlying quantum mechanics. 1. Introduction 2. Newcomb’s Probleme 3. Causal Decision Theory 3.1 Regions of causal influence 3.2 Evidential and effective probabilities 4. The parallel with Bell’s theorem 4.1 Consequences of the analogy 4.1.1 The marble boxes game 4.1.2 Mechanism underlying the marble boxes game 4.1.3 The causalist’s decision 4.1.4 The Bell game 5. Communicated versus Non-communicated Predictions 6. Summary and Conclusion
We reason about possible future development of quantum game theory and its impact on information processing and the emerging information society. Two of the authors have recently proposed a quantum description of financial market in terms of quantum game theory. These "new games" cannot by themselves create extraordinary profits or multiplication of goods, but they may cause the dynamism of transaction which would result in more effective markets and capital flow into hands of the most efficient traders. We focus upon the problem of universality of measurement in quantum market games. Quantum-like approach to market description proves to be an important theoretical tool for investigation of computability problems in economics or game theory even if never implemented in real markets.
Game theory is a mathematical methodology for analyzing calculated circumstances, such as it happens in games, where a person’s success is based upon the choices of others. More formally, it is the study ofmathematical models of conflict and cooperation between intelligent rational decision-makers [1]. Another way of describing this is interactive decision theory [2]. Game theory is mainly used in economics, political science, psychology, logic, and biology. The subject first addressed is called zero-sum games, such that one person’s gains exactly equal net losses of the other participant(s). In our days game theory applies to a wide range of class relations, and has developed into an umbrella term for the logical side of science, including both human and non-humans (computers). Classic uses include a sense of balance in numerous games, where each participant develops a tactic that cannot successfully better his/her results.
Quantum games have proposed a new point of view for the solution of the classical problems and dilemmas in game theory. Certain quantization relationships can be proposed with the objective that a game can be generalized into a quantum domain where the linear superposition of actions is allowed. This quantization let us describe and solution problems originated by conflicting or cooperative behaviors among the members of a system from the point of view of quantum mechanical interactions. This leads us to interesting aspects which only can be observed through the quantization of a game like the possibility of the entanglement between players, the definition of a socioeconomical temperature in a system, the collective welfare principle,the analysis of a game through elements of quantum information theory and the globalization process. The relationships between quantum mechanics and game theory are also studied and its shown how although both systems analyzed are described through two theories apparently different (quantum mechanics and game theory) both are analogous and thus exactly equivalents.