Game theory and sharing

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What sort of mathematical knowledge is required for applying game theory specifically in relation to evaluating fairness in a shared resource environment?

One of the things I'd like to explore in my evaluation is the relation between fairness and efficiency. What is the impact of compromising a bit of fairness in order to achieve overall efficiency? Some sort of mathematical analysis to determine when it might be beneficial (and by how much) to co-operate or defect?

Could you please also suggest resources for self study in this regard?

I have referred to information presented here Game theory - self study

Thanks

NCB