Sequential Game vs Coordination Game
Sequential Game and Coordination Game are two Game Theory & Information concepts in AP Economics that students often mix up. A sequential game is one where players move in turns and later movers see what came before, so it is drawn as a game tree and solved backward from the end. 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.
Because the second player observes the first player's move before choosing, a sequential game is drawn as a tree of decision nodes rather than a table. You solve it by backward induction: start at the last decision, pick the move that pays that player most, cross out the branches they would never take, then step back one node and repeat with those later choices treated as settled. The result is a path through the tree that no player wants to leave, which is why order of play can change the outcome completely. This is the difference from a simultaneous game shown in a payoff matrix, where neither side knows the other's move; here the first mover can act on the knowledge that their choice will be seen.
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.
Sequential vs Coordination Games: Timing Against Payoffs
| What you are comparing | Sequential Game | Coordination Game |
|---|---|---|
| What the label classifies | The order in which players move | The shape of the payoffs |
| Usual diagram | A tree with a branch at every decision node | A payoff matrix with both choices set side by side |
| Solution method | Backward induction, starting from the final move | List every Nash equilibrium, then ask which one players land on |
| How many outcomes the model points to | One surviving path in most textbook trees | Two or more, and the equilibrium concept alone picks none of them, even when one pays better than the other |
| What players want from each other | Anything at all, since timing says nothing about whose interests align | The same choice as the other player, whichever choice that turns out to be |
| The interesting problem | Whether a threat or promise made early is believable later | Agreeing on which equilibrium to play |
| Standard example | An entrant moves, then the incumbent decides whether to fight | Two firms choosing between rival technical standards |
Different axes: one is about order, the other about aligned interests
These labels are not alternatives, because they sort a game on different axes. Sequential describes timing: players move in turns and whoever moves later sees what already happened. Coordination describes payoffs: both players do better when their choices match, whichever choice that is. A game can be sequential without rewarding matching at all, and a coordination game is usually written as a simultaneous move. Take two firms picking between technical standard A and standard B. If both choose A each earns 3, if both choose B each earns 2, and if they split neither earns anything. That is a coordination game, since matching beats mismatching for both. Played simultaneously it has two equilibria in pure strategies, A with A and B with B, and no player can do better by deviating alone from either. There is also a mixed equilibrium in which each firm picks A with probability 0.4, and it is the worst of the three: expected payoff comes out at 1.2 apiece, under the 2 they would collect by both settling on the weaker standard. Nothing in the payoff table says which of these happens. That silence, not the timing, is the problem a coordination game sets.
Add an order of moves and the ambiguity often disappears
Give those same payoffs a sequence and the prediction sharpens. Let one firm announce its standard first, with the other choosing after it has seen the announcement. Solve backward from the end: whatever the leader picked, the follower's best reply is to match, since matching pays 3 or 2 while differing pays nothing. Knowing that, the leader announces A and collects 3 rather than 2. One path survives, and the selection problem that left the simultaneous version undetermined is gone. This is why firms rush to publish specifications, why a platform signs one large partner early, and why announcing a launch date can be worth more than the launch. Timing does not always settle matters so cleanly. Change the payoffs so the leader prefers standard A while the follower prefers standard B, with matching still better than splitting, and the first move becomes an advantage worth fighting over rather than a favor to everybody. The follower still matches, but it matches on the leader's preferred standard and ends up with less than the alternative would have paid. The point to carry into any /glossary/sequential-game question is that backward induction hands you the outcome, while the payoff structure tells you who profits from holding the first move.
Frequently asked questions
Can a game be sequential and a coordination game at the same time?
Yes. Sequential refers to the order of moves while coordination refers to payoffs that reward matching, so both labels can apply to one game. A coordination game played in turns is common, and it usually has a single predicted outcome because the second player simply copies the first.
How do you pick between two Nash equilibria in a coordination game?
Comparing payoffs does not settle it, since both are stable. Economists appeal to payoff dominance when one equilibrium is better for everybody, to risk dominance when one is safer against a mistake by the other side, or to outside information such as convention, a public announcement, or which option arrived first.
Why is backward induction used for sequential games?
Because the last player's choice depends on nothing except the payoffs in front of it, so that decision can be settled first. Working back up the tree, each earlier player chooses knowing exactly how everyone after will respond. The method also rules out threats the threatener would not actually want to carry out.
Related comparisons
Get AP Econ exam tips in your inbox
Occasional emails with study tips, new interactive graphs, and exam-season reminders. Free, no spam.
No spam. Unsubscribe anytime. Read our privacy policy.
Keep track of what you have studied
A free EconLearn account adds progress tracking, your quiz history, and achievements. Studying here is free either way, and there is nothing to pay for as a student.
Create a free accountAlready have one? Sign in
Last updated