ECO316H1 Lecture Notes - Lecture 9: Subgame Perfect Equilibrium, Subgame, Nash Equilibrium
Document Summary
Variant of cournot duopoly where firms act sequentially. Firm 2 chooses output after observing output of firm 1. Terminal histories: set of all sequences (q1, q2) of outputs for the firms. Player function: p(o)=1 and p(q1)=2 for all q1. Payoffs: payoff of each firm to terminal history (q1, q2) is its profit. Firms have infinite output choices within range of feasible outputs. Firm 2: a function where is firm 2"s output if firm 1"s output is q1. Call optimal value where is firm 2"s best response function in cournot"s model. Subgame perfect equilibrium is where is a function. First mover"s profit twice as much as second mover. Find firm 1 iso-profit curve that is tangent to firm 2 best response function. Given firm 2"s best response function, can find firm 1"s optimal output. Moving first is better than moving simultaneously or moving second.
