How to solv a multistage optimization (repeated nash game)

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Hello everybody, my issue is kind of related to the dataset function of mathlab.
What my goal is to create a multi stage interaction optimisation. it's a nash game where at each stage the players interact and optimize sequentially their profit function. at each step other may wish to enter and according to their potential profit they will join. now i need to make an optimization at each step that is sequential. then create a database with the outputs. On the basics of the new output I perform a new optimization and accordingly create a new dataset. Repeat the process untill a equlibrium is found. The potential amount of entrants is unlimited.
There is just one variable X e(0,1) that can be modified by each player to maximise their output. So we have N plaers, so N optimisations ( Nt is dependent on N t-1) and N different X(the variable) that will be adjusted at each stage. Also the outputs are cumulative, so thats the reason, I think, creating a new dataset each turn would be a good solution.
thank you for your support. this is going to be on my masterthesis and I will put everybody,if he desires, on the references to give him the rightfull credits he deserves.
thanl you all
max

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