- Motivations from two aspects
- Operator Representation
- From the manipulative to the abstract definition, a general scheme to quantize Classical Games
- A series of classical games and quantum games
- A general proof of the existence of NE
- General algorithm searching for NE
- Let a quantum entangle system to be the game object
- Could the state of players be an entangle state? From Classical Coalitional Game to Quantum Coalitional Game
- Quantum Game from Quantum Communication/Quantum Computation

Our question is how about we replace the two-side coin here with a ½-quantum spin? What's the effect of this on Game Theory? It's still a game-theory question. Players can still choose strategies to act on the spin, although they have much more choices now. Compared with Non-flip and Flip , in Quantum Mechanics, any unitary 2×2 matrices can be used as operators, and I, X, Y, Z are the four typical matrices of them. Now the Game Theory must answer how to define the strategy state for this game, how to define NE, and the existence of NE. At last, we have to ask whether such game can be studied within the framework of Traditional Game Theory (TGT), or should we develop a new framework but still with the same spirit of Game Theory? In this work, we will construct a new framework, which can be used both TGT and the game on quantum objects, named Quantum Game Theory (QGT).

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