Game Theory: Combinatorial

Combinatorial game theory studies games with a finite set of positions, perfect information, and no chance — e.g. chess, go, nim. The key idea: under certain conditions, the game has a determinate outcome (win, loss, or draw) and optimal strategies can be computed. It's less about negotiation and more about sequential moves and backward induction. For founders, the link is to any setting where moves are discrete, information is complete, and you can reason backward from the end state — auctions, some negotiations, or multi-stage competitions. When the structure is combinatorial, invest in working out the tree.

When the situation is finite, sequential, and deterministic, sketch the move tree. Work backward from terminal outcomes to find best responses. Use that to decide your first move or to spot when the other side has a winning strategy. If the game is too large to solve, use heuristics (e.g. control the center, limit options) borrowed from combinatorial games.

Combinatorial game theory: finite positions, perfect information, no chance. Solve by backward induction. Use when moves are sequential and known — negotiations, auctions, multi-stage competition. Map the tree and reason from the end.