|
related topics |
{error, code, errors} |
{let, theorem, proof} |
{states, state, optimal} |
{group, space, representation} |
{theory, mechanics, state} |
{measurement, state, measurements} |
{classical, space, random} |
{operator, operators, space} |
{equation, function, exp} |
{time, decoherence, evolution} |
{state, states, entangled} |
|
A new mathematical representation of Game Theory II
Jinshan Wu
abstract: In another paper with the same name\cite{frame}, we proposed a new
representation of Game Theory, but most results are given by specific examples
and argument. In this paper, we try to prove the conclusions as far as we can,
including a proof of equivalence between the new representation and the
traditional Game Theory, and a proof of Classical Nash Theorem in the new
representation. And it also gives manipulation definition of quantum game and a
proof of the equivalence between this definition and the general abstract
representation. A Quantum Nash Proposition is proposed but without a general
proof. Then, some comparison between Nash Equilibrium (NE) and the
pseudo-dynamical equilibrium (PDE) is discussed. At last, we investigate the
possibility that whether such representation leads to truly Quantum Game, and
whether such a new representation is helpful to Classical Game, as an answer to
the questions in \cite{enk}. Some discussion on continuous-strategy games are
also included.
- oai_identifier:
- oai:arXiv.org:quant-ph/0405183
- categories:
- quant-ph
- comments:
- 15 pages, a mathematical version of exemplified quant-ph/0404159, in
the style of definition, theorem and proof, a few of new points
- arxiv_id:
- quant-ph/0405183
- created:
- 2004-05-30
Full article ▸
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