Sequential Moves in Applications 🎯

students, in many real situations, decisions happen one after another instead of all at once. A firm may enter a market first, then a rival decides whether to compete. A seller may post a price, then a buyer responds. Two companies may negotiate, with one side making the first offer and the other side reacting. These situations are studied in extensive-form games, where a game tree shows who moves, when they move, and what choices they have.

In this lesson, you will learn how sequential moves change strategy and outcomes. By the end, you should be able to:

Analyze a sequential-move application using a game tree.
Explain when the first mover or second mover has an advantage.
Connect tree analysis to real-world strategy in business and negotiation.

The key idea is simple but powerful 💡: when players move in sequence, the later player can react to the earlier player’s action. That reaction changes what the first player should do. The best plan depends on anticipating the future.

1. Why sequence matters in strategic thinking

In simultaneous games, players choose without knowing the other’s move. In sequential games, the order of play matters because later choices can depend on earlier ones. This creates contingent plans, meaning a player’s strategy says what to do under every possible earlier outcome.

For example, suppose a new coffee shop considers opening near a college campus. If it enters, an existing shop might lower prices or improve service. If the new shop expects a fierce response, it may stay out. The important point is not just what happens today, but what each player believes will happen next.

A game tree helps organize this thinking. Each branch represents a possible choice, and each end point represents an outcome. When solving these games, we usually work backward from the end of the tree to the beginning. This is called backward induction. It means asking, “If the game reaches this point, what will the next player do?” Then use that answer to decide the earlier move.

This method is especially useful in business entry, pricing, and negotiation because managers must think ahead. A current decision can shape a future response, and that future response can shape profit, market share, or bargaining power 📈.

2. Analyzing entry and pricing decisions

A classic application is market entry. Imagine students as the manager of a small company deciding whether to enter a market dominated by a large firm. The small firm moves first by choosing Enter or Stay Out. If it enters, the large firm responds with either Fight or Accommodate.

The game tree might look like this in words:

First move: small firm chooses Enter or Stay Out.
If Stay Out, payoffs are stable and nothing else happens.
If Enter, the large firm chooses Fight or Accommodate.

Now think dynamically. The large firm compares its own payoff from fighting versus accommodating. If fighting is costly and hurts profits, it may choose to accommodate. If so, the small firm may be willing to enter because it expects a decent payoff. But if the large firm can punish entry in a way that is actually profitable for it, the small firm may stay out.

This shows why sequential reasoning matters. The first mover is not choosing in a vacuum. It is choosing while anticipating a response. A weak-looking first move may still be wise if it leads to a good reaction. A strong-looking move may fail if the follower can undo its benefits.

Example: entry deterrence

Suppose the small firm gets payoff $2$ from entering if the large firm accommodates, but only $-1$ if the large firm fights. If staying out gives the small firm $0$, then the small firm compares $2$, $-1$, and $0$.

If the large firm knows that fighting is costly and will choose accommodate, then the small firm enters. But if the large firm can commit to a tough response, the threat may keep the small firm out. This is why commitment can be powerful in sequential games.

A key lesson is that threats must be credible. A credible threat is one that a player would really carry out when the time comes. If the large firm says it will fight but would actually prefer accommodating once entry occurs, then the threat is not credible. Backward induction reveals this by checking the best choice at each later stage.

3. Pricing and Stackelberg-style competition

Sequential moves also appear in pricing. In many markets, one firm sets a price first and another firm reacts. This is similar to a Stackelberg setting, where a leader moves first and a follower moves second.

A simple example is two competing airlines on the same route. If one airline announces its fare first, the other airline may set a slightly lower or higher fare depending on demand. The first airline is not just picking a number; it is choosing a price while predicting how the follower will answer.

Why can the first mover sometimes gain an advantage? Because moving first may allow it to shape the follower’s best response. If the leader chooses a quantity or price that leaves the follower with fewer profitable options, the leader may capture a larger share of the market.

However, the first mover is not always better off. Sometimes the follower benefits from being able to observe the leader and react efficiently. In other cases, the first mover ends up constrained by its own earlier choice.

Example: quantity leadership

Imagine a firm choosing output first, and a rival choosing output second. The second firm observes the first firm’s output and responds with its own best output. The leader anticipates this and chooses output accordingly.

If the leader chooses a high output, the follower may reduce its own output because prices fall. If the leader chooses a lower output, the follower may produce more. The leader’s choice is therefore strategic and depends on the expected response curve of the follower.

This is a major difference between simultaneous and sequential competition. In sequential play, one firm can move the market outcome by moving first. But the value of being first depends on the shape of the follower’s best response. students, this is why game trees are so useful: they show not just actions, but reactions.

4. Negotiation and bargaining examples

Negotiation is another place where sequential moves matter. Suppose two companies are trying to agree on a contract. One side makes an offer, and the other side can accept or reject. If it rejects, a new offer may be made later, or both sides may walk away.

The first offer can influence the final agreement. For example, if a buyer offers a low price first, the seller may respond with a counteroffer. If the seller has alternatives, it may reject a weak offer. If the buyer knows this, it may choose a more realistic first offer to avoid wasting time.

In bargaining, the order of moves can affect who captures more of the gains from trade. A player who moves first may anchor the discussion and shape expectations. A player who moves second may benefit from more information and can tailor the response.

Still, the second mover does not always have the advantage. If delay is costly, or if the first mover can credibly commit to an offer, the first mover may set terms that others must accept. In real life, deadlines, expiration dates, and limited alternatives can make commitment important.

Real-world interpretation

Think about a house sale. A seller sets an asking price, and buyers respond with bids. The seller’s first move can attract attention or scare buyers away. Buyers then react based on market conditions, other available houses, and how urgently they need a home. Sequential reasoning helps explain why some asking prices lead to quick sales while others do not.

5. First-mover and second-mover advantages

A common question is whether moving first is better than moving second. The correct answer is: it depends.

When the first mover may have an advantage

It can shape the follower’s options.
It may commit to a plan that changes later behavior.
It can claim scarce resources early, such as prime locations or customers.
It may create a reputation that affects future play.

When the second mover may have an advantage

It can observe the first mover’s action before choosing.
It can avoid mistakes by reacting to new information.
It may exploit the first mover’s commitment.
It can choose the best response after seeing the path chosen.

In dynamic games, the advantage goes to the player whose decision is more informative or more influential. A follower who learns from the leader may do better. A leader who forces the follower into a narrow response may do better.

The important part is not to guess. The tree shows the structure. Backward induction shows the likely outcome. Then you compare payoffs to determine who benefits more.

Conclusion

Sequential-move applications help explain many real decisions in business and negotiation. Entry, pricing, and Stackelberg-style competition all involve players who act in order and respond to one another. students, the main lesson is that strategy in these games is dynamic: each move depends on what comes before and what is expected next.

Game trees make the structure visible, and backward induction helps find credible outcomes. First movers can sometimes gain power by committing early, but second movers can sometimes gain by reacting to information. Real-world strategy depends on the exact sequence of play, the credibility of threats and promises, and the payoffs tied to each branch.

Study Notes

Extensive-form games model situations where players move in sequence.
A game tree shows choices, timing, and possible outcomes.
A contingent plan tells a player what to do after every possible earlier move.
Backward induction means solving from the end of the tree back to the beginning.
A credible threat is a threat a player would actually carry out if the moment arrives.
In market entry, the first mover must anticipate how incumbents will respond.
In pricing and Stackelberg competition, the leader moves first and the follower reacts.
In negotiation, the order of offers can affect the final split of gains.
First-mover advantage comes from commitment and shaping responses.
Second-mover advantage comes from observing and reacting to earlier choices.
The best strategy in sequential games depends on the full tree, not just one move.