Sequential Game: Backward Induction

Backward induction can be used to solve sequential games and find the perfect Nash equilibrium. It works by reasoning backward from the end of the game to determine optimal actions.

Consider two pharma companies, Nova and Erks, competing with two options: collude or engage in a price war.

Nova, a market leader with more control, decides first whether to start a price war or collude. If Nova chooses to collude, Erks gets a turn to decide.

Applying backward induction, the analysis begins at node B, where Erks must choose between colluding, which results in a payoff of 500 dollars, or opting for a price war, which offers a higher payoff of 600 dollars.

Since the price war yields more, Erks will choose it. Knowing this, Nova Pharma will also choose a price war at node A, resulting in a 100-dollar payoff.

If, for some reason, Nova decides to collude, the payoff will be zero, as Erks will choose a price war due to the high payoff.

Given the available choices, Nova will choose a price war, leading to payoffs of 100 dollars for Nova and 300 dollars for Erks and achieving equilibrium at Node A.