Sequential games involve players making decisions one after another, with each player considering the prior decisions of other players before deciding their own strategy. The order of these decisions is crucial, as each decision influences subsequent ones, affecting the overall outcome. Decision trees are valuable tools in illustrating these games, helping visualize each possible decision and its consequences, allowing players to anticipate and plan strategies effectively.

Consider two coffee shop chains, BrewCo and BeanHouse, competing in the same city. Each chain has two options: lower prices or maintain pricing while investing in quality improvements. A random draw decides who moves first, and BrewCo makes the initial move. This initial move is significant, as it influences BeanHouse's subsequent choices.

If BrewCo lowers prices, it increases sales volume, gaining $150, while BeanHouse maintains its pricing and earns $350 from its loyal customers. The game ends here, as BrewCo's aggressive pricing strategy shapes the outcome. However, if BrewCo maintains its prices and invests in quality, BeanHouse decides what move to make next. If BeanHouse lowers prices, it captures market share and earns $500, while BrewCo's profit drops to zero due to its higher costs. Conversely, if BeanHouse maintains its prices, both benefit from improved brand loyalty, each earning $400.

The decision tree for this game maps out these options, illustrating how different choices impact profits. This analysis helps both companies identify the Nash equilibrium, a stable state where neither has an incentive to change their strategy. By reaching this equilibrium, both chains align their strategies to maximize profits and maintain market stability.