Sequential Games

Sequential games involve players making decisions one after another, with each player observing prior decisions before choosing their own strategy. The order of decisions is crucial, as each choice influences subsequent ones and the overall outcome. This contrasts with simultaneous games where players act without knowing others' choices.

Decision trees visually map each possible decision and its consequences, allowing players to anticipate responses and plan strategies effectively. By illustrating decision nodes and payoffs at each stage, trees help companies identify optimal moves and understand how their choices affect competitors' subsequent decisions and final outcomes.

Nash equilibrium is a stable state where neither player has an incentive to change their strategy given the other player's choice. In sequential games, players use decision trees to identify this equilibrium by working backward through decision nodes, finding strategies that maximize profits while accounting for competitors' rational responses.

The first mover shapes the game's outcome by choosing a strategy that influences the second player's available options and payoffs. For example, if a company chooses aggressive pricing, competitors must respond to that market condition. This initial move advantage allows the first player to steer the game toward favorable outcomes.

Yes, sequential games can result in mutual benefit when both players choose cooperative strategies. For instance, if both companies maintain prices and invest in quality, they each earn higher profits than through price wars. Decision trees reveal these cooperative outcomes, helping players recognize when collaboration maximizes joint payoffs.

Move order determines which player controls the game's direction and which player must react. The first mover can commit to a strategy that forces the second player into less favorable positions. Understanding this sequence through decision trees helps companies anticipate competitor responses and choose strategies that maximize their payoffs at each decision point.

Companies map pricing strategies using decision trees to evaluate payoffs for each choice. By analyzing how competitors respond to price wars versus quality investments, firms identify which initial move yields the highest profit. This analysis reveals whether aggressive pricing or quality focus better positions them given anticipated competitor reactions.