Game Theory · GT-30
Who moves first — and who can see it — changes the entire strategic logic, even with identical payoffs.
In a simultaneous game, players choose actions without observing each other's choice (represented as a payoff matrix). In a sequential game, one player moves first and the other observes that move before responding (represented as a game tree). The same underlying payoffs can produce completely different equilibrium outcomes depending purely on this timing structure.
The distinction is foundational to extensive-form vs. normal-form game representations, both formalized in von Neumann and Morgenstern's 1944 text, with sequential analysis significantly extended by Selten's subgame-perfection work in the 1960s-70s.
The Mechanism
Same payoffs, different move order — different outcome
As a simultaneous game, this has two pure Nash equilibria and genuine ambiguity about which firm ends up entering. But if Firm A can credibly commit to entering FIRST, and Firm B observes that before deciding — the sequential version resolves cleanly: B's best response to A's committed entry is to stay out, and A captures the (5,0) outcome deterministically.
01 · MOVING FIRST CAN BE A GENUINE ADVANTAGE — BUT ONLY IF OBSERVABLE
The 'first-mover advantage' has a precise mechanical basis
In game theory, moving first only helps if the move is credibly observed by the other player before they act — an unobserved 'first move' provides no strategic advantage at all, since it's functionally identical to a simultaneous game from the second player's perspective. This is why publicly announcing an irreversible commitment (see Commitment Devices) is what actually converts a simultaneous-feeling situation into a genuinely sequential, first-mover-advantaged one.
02 · SEQUENTIAL GAMES ARE SOLVED BY BACKWARD INDUCTION, SIMULTANEOUS ONES BY NASH EQUILIBRIUM
Different structures require different solution tools
Because sequential games unfold over observable stages, backward induction (solving from the final move backward) is the natural technique. Simultaneous games, lacking any such stage structure, require finding Nash equilibria (or mixed-strategy equilibria) directly across the full matrix of possible action combinations.
03 · MANY REAL SITUATIONS ARE AMBIGUOUSLY BOTH
Correctly diagnosing the structure is itself a strategic skill
Many real competitive situations (product launches, pricing decisions, political announcements) have elements of both — competitors don't perfectly observe each other's moves in real time, but decisions also aren't perfectly simultaneous either. Correctly assessing how much of a first-mover advantage genuinely exists (versus being assumed) is often the actual strategic question, more than solving either pure-form game.
Where It Fails / Inversion
Where it fails / inversion
First-mover advantage isn't universal — in many settings (uncertain product-market fit, unproven technology, ambiguous consumer preferences), being the SECOND mover who can observe and learn from the first mover's mistakes is the actual advantaged position (sometimes called 'second-mover advantage' or 'fast-follower' strategy). Assuming moving first is always better ignores that observability, in a sequential game, cuts both ways — the follower gets to see something too.
How To Use It
Worked example · retail store location decisions
Two competing retailers deciding whether to open a location in an underserved market face a genuinely sequential structure if location commitments become public knowledge before the rival must decide (a signed lease, a public announcement, a permit filing). Whichever firm commits first and makes that commitment visible effectively removes the coordination ambiguity of the simultaneous version — the second firm, observing the first has already committed, rationally chooses not to enter the same location, avoiding a costly head-to-head price war neither wants.
How to use it
Before assuming a competitive situation is simultaneous (and therefore ambiguous or requiring a mixed strategy), check whether either side can credibly move first in an observable way. If so, converting your own move into a visible, irreversible commitment can resolve the game in your favor — this is precisely why so much competitive strategy revolves around making moves public and hard to reverse.
See Also