cooperative versus non-cooperative games

When several parties stand to gain by working together, two very different questions arise. The first: can they actually make a binding promise — a contract someone will enforce — to stick to a joint plan? The second, if they can't: what will each do when everyone acts only in self-interest? Game theory splits into two branches along exactly this line. Non-cooperative game theory studies what happens when players cannot enforce agreements and each looks out for themselves; cooperative game theory studies what happens when binding agreements are possible and asks how the gains from teamwork should be divided.

The key dividing line is enforceability, not friendliness. In a non-cooperative game, any promise is just talk unless it is in a player's own interest to keep it — so the central tool is the Nash equilibrium, where each acts in self-defense. In a cooperative game, players can form coalitions and commit to share the spoils, so the questions become which groups will band together and what split is fair or stable. Cooperative theory has its own famous tools, like the Shapley value, which divides a joint payoff according to each member's average contribution. Example: three towns can build a shared water pipeline far more cheaply than three separate ones; cooperative theory asks how to split the savings so no town would rather go it alone.

The distinction matters because it tells you what kind of institution a problem needs. If a situation is non-cooperative and the self-interested outcome is bad (a prisoner's dilemma), the fix is usually external — laws, courts, regulators, or repeated dealings — that make promises enforceable and convert the game into a cooperative one. Much of contract law, antitrust, and international treaty-making is precisely the effort to turn destructive non-cooperative games into productive cooperative ones.