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## Main Question or Discussion Point

In the applied mathematics of Game Theory, dimensions are considered alternative strategies.

I have been reading a classic from the Society of Industrial and Applied Mathematics [SIAM]: Tamer Basar and Geert Jan Olsder. 'Dynamic Noncooperative Game Theory', revised 1999 from 1982. The authors refer to this as a type of representation theory.

Game theory appears to be formulated to allow sets, probability and topology to be viewed as sub-categories.

Since this is mathematics, the language is similar, but not identical to representation theory used in physics.

Some differences include using C* for cost-to-come and G* for cost-to-go,

Similarities include index sets, infinite topological structured sets, mappings and functionals in discrete time.

There is substitution for some of these items in continuous time such as time intervals, Borel sets, trajectory, action and informational topological spaces.

Tme appears to be treated as a duality.

There may or not be stochastic influences.

The Isaacs condition for the Hamiltonian is used.

Types of such games include:

for discrete time -

OL - open loop

CLPS - closed loop perfect state information

CLIS - CL imperfect state

FB - feedback perfect

FIS - feedback imperfect

1DCLPS - one-step delayed CLPS

1DOS - one-step delayed obsevation sharing

for continuous time -

OL

CLPS

eta-DCLPS - eta-delayed DCLPS

MPS - memoryless perfect state

FB

If players are allowed to be entities capable of exchanging enegy quanta or longevity then this might considered enegy economics?

The stochastic game may be consitent with the probablistic nature of QM.

Is phyisics failing to use a valluable tool of representation theory from applied mathematics?

I have been reading a classic from the Society of Industrial and Applied Mathematics [SIAM]: Tamer Basar and Geert Jan Olsder. 'Dynamic Noncooperative Game Theory', revised 1999 from 1982. The authors refer to this as a type of representation theory.

Game theory appears to be formulated to allow sets, probability and topology to be viewed as sub-categories.

Since this is mathematics, the language is similar, but not identical to representation theory used in physics.

Some differences include using C* for cost-to-come and G* for cost-to-go,

Similarities include index sets, infinite topological structured sets, mappings and functionals in discrete time.

There is substitution for some of these items in continuous time such as time intervals, Borel sets, trajectory, action and informational topological spaces.

Tme appears to be treated as a duality.

There may or not be stochastic influences.

The Isaacs condition for the Hamiltonian is used.

Types of such games include:

for discrete time -

OL - open loop

CLPS - closed loop perfect state information

CLIS - CL imperfect state

FB - feedback perfect

FIS - feedback imperfect

1DCLPS - one-step delayed CLPS

1DOS - one-step delayed obsevation sharing

for continuous time -

OL

CLPS

eta-DCLPS - eta-delayed DCLPS

MPS - memoryless perfect state

FB

If players are allowed to be entities capable of exchanging enegy quanta or longevity then this might considered enegy economics?

The stochastic game may be consitent with the probablistic nature of QM.

Is phyisics failing to use a valluable tool of representation theory from applied mathematics?