Dear colleague,

your question is interesting but without specifying information accessible to respective players it cannot be answered: the payoff function you are discussing does not suffice. Please, complete the game specification as the optimization task (I expect that 2-players case will suffice). Your sincerely M. Karny  

Hello Miroslav: I do not follow really your comment. Surely once the payoff function is defined, the game is defined? You say "specifying the information accessible to respective players": I guess this means, do the players know the payoff function (all its values), i.e. the "rules of the game"? In that case the answer is yes.

OK - I have added a little more to the file asking the problem/question (attached).....

Dear Michael,

I mean that admissible moves and knowledge available for them for respective players are the significant  parts of the game rules. While it is intuitively obvious in prisoner's dilema, it is not true generally and itroduces additional constraints relevant to your problem ...  

Dear Prof. Mc Gettrick,

                                       I think what you have in mind by asking this question is an information theoretic answer which is programmable for which I do not have a direct answer except to draw your attention to some of my research papers like the one on Haag Theorem resolution of Dynamic Genetic Quantum Mechanical Stock Markets which can by using my developed DBranes String Resolution of Complex TimexSpace scalable information and energy flows preserving Arrow of Time Genetically Quantum Actions can be resolved into algorithms which are genetic and preserve Higgs-Englert-Bosonic Meanfield Stocks and Flows. Since Games which involve some degree of complexity can only be resolved nonlinearly hence it takes some physical reduction methods before one can subdivide them into "simpler "subgames. Of course if the strategic form description of the game is available it is possible to apply subgame perfection techniques for equilibrium refinements. You can refer to any advanced Game Theory book like the one by Shubik. Earl Chair Prof. Dr. SKM QC EPS Fellow (In) MRES MES MAICTE