Game theory explains why we have to sanction Putin -- even if it's costly

Let’s call this the Repeated Sanctions Game, which has two players. In each round of the game, Player 1 (i.e., an adversary such as Putin) chooses whether to transgress, then Player 2 (i.e., NATO) chooses whether to sanction. Transgressing benefits Player 1 (Putin would like to annex Ukraine) but costs Player 2 (NATO would prefer that Ukraine be free). As in real life, sanctioning is costly not just to Player 1 but also to Player 2, who might prefer not to, for example, suffer higher prices or lose revenue from Player 1’s products and businesses as a result. Then Player 2 plays the game again and again — perhaps with the same Player 1, perhaps with another (Putin now, maybe Xi next time).

For Player 2 to deter future transgressions in this game, she would have to threaten to sanction Player 1 whenever he transgresses. This threat has to be credible, otherwise Player 1 will simply call Player 2’s bluff. Player 2 must, if called upon, reliably follow through on her threat.

How can this be worth it for Player 2, given that, as already acknowledged, sanctioning is costly? To see, we must factor future expectations into the cost-benefit calculation. When a transgression isn’t met with sanctions, everyone would reasonably expect that future transgressions may also go unpunished. This is the norm collapsing. So long as Player 2 cares enough about the costs of all those future transgressions, she’ll prefer the collateral costs of punishing the transgressor today to increasing the likelihood of future transgressions. It’s not preventing or stopping the current transgression that’s motivating Player 2 to sanction, it’s the fact that without sanctions as a response, there will inevitably be more transgressions.