Gra sekwencyjna: indukcja wsteczna

Backward induction solves sequential games by analyzing the game starting from the end and working backward to the beginning. Players anticipate how competitors will react at each stage, then use that information to determine their own optimal actions. This method reveals the perfect Nash equilibrium by ensuring each player's decision accounts for rational responses from others.

FreshFizz stays out because backward induction reveals that if it enters, CoolBrew will also enter, earning $900 while FreshFizz gets only $100. By staying out, FreshFizz maintains a stable $300 profit from current operations. Entering leads to much lower payoff, so staying out maximizes FreshFizz's profit given CoolBrew's rational response.

At each decision node, a player chooses the action that maximizes their payoff, knowing what the other player will rationally do afterward. For example, Erks chooses a price war over collusion because it yields $600 instead of $500. Players work backward from final outcomes, selecting moves that deliver the highest personal payoff given anticipated competitor responses.

Nova Pharma knows that if it chooses to collude, Erks will select a price war for a $600 payoff, leaving Nova with zero. If Nova chooses a price war first, it earns $100 while Erks gets $300. Anticipating Erks' rational choice, Nova selects the price war to secure $100 rather than zero, achieving equilibrium at Node A.

The equilibrium outcome reflects each player's best response to the other's anticipated action. In the pharma example, Nova chooses a price war earning $100, and Erks chooses a price war earning $300. This equilibrium emerges because both companies use backward induction to anticipate rational responses, resulting in predictable, stable outcomes neither player wants to change.

Backward induction is valuable because it reveals what rational competitors will actually do, allowing firms to make informed strategic decisions. By working backward from final payoffs, companies can anticipate competitor moves and choose strategies that maximize their own profit. This predictability helps firms avoid costly mistakes and achieve equilibrium outcomes based on rational choice.

The order of moves determines who has the advantage of moving first and anticipating responses. In the beverage example, FreshFizz moves first but discovers that entering triggers CoolBrew's entry, reducing FreshFizz's payoff. The first mover must account for the second mover's rational response, which often disadvantages the first mover if the second mover benefits from entry deterrence credibility applied strategically.