I have seen many 2 Player Game problems while solving problems on codeforces, and these problems don't follow a specific methodology for solving them. Is there any method or way to go about thinking/modeling these problems in general?
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I found a resource once, maybe it helps.
Game theory starts at 147/167 of https://algo.is/aflv16/aflv_10_mathematics.pdf
Personally I draw a graph showing the various outcomes, and I try to find some strategy or pattern. Sometimes there might be a greedy way, or it mist be solved using DP. Sometimes it's unrelated to these at all.
I am not very clever. So for these problems I sometimes print a winner/SG table for small numbers using bruteforce.