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 ...