Prisoner's Dilemma vs Coordination Game
Prisoner's Dilemma and Coordination Game are related concepts in AP Economics that students often mix up. The prisoner's dilemma is a game theory scenario where two rational individuals acting in their own self-interest do not produce the optimal outcome for either. A coordination game is one where players do best by making the same choice, so it has two or more Nash equilibria and the problem is agreeing on one. Here is how they compare side by side.
In oligopoly, it explains why firms may fail to collude even when mutual cooperation would lead to higher joint profits, because each has an incentive to cheat on the agreement to gain a short-term advantage.
Interests here are mostly aligned: both players want to match, and mismatching hurts them both. That produces several Nash equilibria instead of one, which makes the question not what is best but which outcome the players will settle on. Because any of them is stable once expectations point that way, conventions, past practice, and focal points do the real work; drivers keeping to one side of the road is the everyday case. Some coordination games have equilibria that are not equally good, so a group can be stuck in a worse one that nobody can escape alone. That is the difference from a prisoner's dilemma, where there is a single equilibrium and it is bad because the players' incentives genuinely conflict.
Prisoner's Dilemma vs Coordination Game: One Bad Equilibrium or Several Good Ones
| Prisoner's Dilemma | Coordination Game | |
|---|---|---|
| What the players want | Different things, each is tempted to cheat on the other | The same thing, both want to end up matching |
| Dominant strategy | Both players have one, and it is to defect | Neither player has one |
| Number of equilibria in pure strategies | Exactly one | Two or more |
| Is the equilibrium the best outcome | No, both players prefer mutual cooperation | It can be the worse of two, yet still hold |
| What stands in the way | Trust, since any agreement is worth breaking | Expectations, since any agreed option is worth keeping |
| Does a promise with no penalty help | No, each side still gains by breaking it | Yes, it can settle which equilibrium happens |
| Textbook illustration | Two firms deciding whether to hold a cartel price | Two firms choosing which technical standard to build |
Run the deviation test on each grid and the two structures separate immediately
Payoffs are written as (row player, column player). In the dilemma, mutual cooperation pays (10, 10), defecting on a cooperator pays the defector 15 and leaves the other with 2, and mutual defection pays (5, 5). Check Row. Against a cooperator, defecting pays 15 against 10. Against a defector, defecting pays 5 against 2. Defecting wins both times, so it is a /glossary/dominant-strategy, and the same holds for Column. Mutual defection at (5, 5) is the equilibrium, and switching alone drops a player to 2, so it holds even though (10, 10) is better for both. Now the coordination grid. Two firms pick standard A or standard B, matching on A pays (3, 3), matching on B pays (2, 2), and any mismatch pays (0, 0). Row's best reply to A is A and its best reply to B is B, so there is no dominant strategy at all. Both matching cells are equilibria, since deviating alone pays 0 in each. That is the structural split. One game has a single equilibrium nobody likes, and the other has several nobody wants to leave.
The fix that works on one game does nothing to the other
Because the obstacles differ, so do the remedies, and exams test exactly that. In the coordination game a conversation is enough. If the two firms agree on standard A, then each expects the other at A, and A is the best reply to A, so the agreement enforces itself with no penalty attached. Notice that the worse equilibrium at (2, 2) is stable in the same way, so a pair of firms can be stuck on the weaker standard with each knowing the other one is better and neither able to move alone. In the dilemma the same conversation achieves nothing. Both firms can promise to hold the high price, and both still earn 15 by cutting it, so the promise is broken the moment it is tested. What changes the dilemma is a change in payoffs or a change in the game, through a binding contract, a regulator, or repetition that makes punishment possible later. This is why collusion in /micro/oligopoly is described as unstable while a shared industry standard is not, and why cartels need enforcement while standards mostly need an announcement.
Frequently asked questions
What is the difference between a prisoner's dilemma and a coordination game?
In a prisoner's dilemma each player has a dominant strategy to defect, producing one equilibrium that both players dislike, while in a coordination game there is no dominant strategy and two or more equilibria that both players are content to sit in. The dilemma is a problem of trust and the coordination game is a problem of agreeing which outcome to aim at. Checking whether a dominant strategy exists separates them in one step.
Can communication solve a prisoner's dilemma?
Not on its own, because talking does not change any payoff in the grid, and defecting still pays more than cooperating whatever the other player has promised. Agreements only bite when something enforces them, such as a contract, a regulator, or the threat of punishment in later rounds. In a coordination game the same conversation does work, since once both sides expect the agreed option neither wants to move away from it.
Does a coordination game always reach the best outcome?
No, players can settle on the worse equilibrium and stay there, because no single player gains by switching alone. If two firms are matched on a standard paying 2 each while a standard paying 3 each exists, whichever one moves first ends up mismatched and earns nothing. Escaping needs both to move together, which is why announcements, deadlines and industry bodies matter in these markets.
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