Sequential Game
What is Sequential Game?
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.
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.
Sequential Game: a worked example
In the ultimatum game, Ana proposes how to split $100 with Ben, and Ben then accepts or rejects; a rejection leaves both with nothing. Solve the last decision first. Facing an offer of $1, Ben compares $1 from accepting against $0 from rejecting, so he accepts, and the same holds for any positive offer. Ana works that out in advance and offers the smallest amount she can, $1, keeping $99 for herself. The theory therefore predicts a split of $99 and $1, though people in real experiments often reject small offers, which is one reason the game is studied so heavily.
The mistake students make with sequential game
Students try to solve a sequential game from the top down, asking what the first player should do before working out how the second player will react. That gets the logic backwards, because the first player's best move depends on the response it will trigger. Always start at the final decision node and work up. The related error is converting the tree into a payoff matrix, which erases the turn order and can hand you an equilibrium that rests on a threat the second player would never carry out.
Sequential Game questions
How do you solve a sequential game?
You solve a sequential game by backward induction, starting at the last decision and working toward the first. At each final node, choose the move that pays that player most and delete the branches they would reject. Earlier players then choose knowing exactly which branch each later choice leads to.
What is the difference between a sequential and a simultaneous game?
In a sequential game the later player sees the earlier player's move before choosing, and in a simultaneous game nobody sees anything before committing. That difference changes the tool: sequential games use a game tree, simultaneous games use a payoff matrix. It also changes the answer, since a commitment only has bite if the rival can observe it.
Does the player who moves first always win?
No, moving first only helps when the commitment is visible and hard to undo. In games where the rival can simply tailor a response, such as undercutting an announced price, moving first hands the rival useful information. Whether the first or second mover gains depends on the payoffs, so work through the tree instead of assuming.
Related terms
Common comparisons
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