BUSS1040 · Economics For Business Decision Making
Strategic Interaction II: Sequential Games & Oligopoly
Topic 8 moves to sequential games, where players move in turn and you read the situation off a game tree. The solution method is backward induction — solve the last decision first and work back — which delivers the subgame-perfect equilibrium (SPE) and rules out incredible threats. The chapter then applies strategy to oligopoly: Cournot firms choosing quantities via reaction functions, and repeated games where cooperation can be sustained by trigger strategies. It is examined as short-answer (solve a tree by backward induction; state the SPE) plus oligopoly reasoning.
What this chapter covers
- 011. Sequential games and the game tree (decision nodes and ordered moves)
- 022. Backward induction: solve the last mover's decision first, then work back
- 033. Subgame-perfect equilibrium (SPE): the outcome backward induction selects
- 044. Credible vs incredible threats (SPE eliminates threats a rational player would not carry out)
- 055. First-mover vs second-mover advantage and commitment / entry deterrence
- 066. Cournot oligopoly: firms choose quantities; each best-responds via a reaction function
- 077. Cournot output lies between monopoly (lowest) and perfect competition (highest)
- 088. Repeated games: trigger strategies (grim trigger, tit-for-tat) can sustain cooperation
Sequential game: backward induction and the subgame-perfect equilibrium
- 2 marksBackward induction: solve the incumbent's node first. If the entrant has entered, the incumbent compares Fight (payoff 1) with Accommodate (payoff 2) ⇒ Accommodate (2 > 1).
- 2 marksFold that back to the entrant's decision: anticipating Accommodate, entering gives the entrant 2, while staying out gives 1 ⇒ the entrant chooses Enter (2 > 1).
- 1 markThe threat to Fight is an incredible threat — once entry has happened, fighting is worse for the incumbent, so a rational incumbent would not carry it out.
- 1 markState the SPE: (Enter; Accommodate) with payoffs (2, 2). Subgame-perfection rules out the non-credible 'Fight' threat.
Key terms
- Game tree
- A diagram of a sequential game showing decision nodes in the order players move, the branches (strategies) at each node, and the payoffs at the end of each path. It replaces the payoff matrix when timing matters.
- Backward induction
- The method for solving a sequential game: start at the final decision and choose the best action there, then work backward, each earlier player anticipating the optimal later play. It yields the subgame-perfect equilibrium.
- Subgame-perfect equilibrium (SPE)
- A Nash equilibrium that is also optimal in every subgame — i.e. it prescribes rational play at every node, not just along the equilibrium path. Backward induction always produces an SPE.
- Incredible threat
- A threatened action that a rational player would not actually carry out because it is worse for them when the moment comes. SPE eliminates such threats, so they cannot influence earlier decisions.
- Cournot oligopoly
- A model where a few firms simultaneously choose quantities, each best-responding to the others' output via a reaction function. The Cournot equilibrium output lies between the monopoly quantity and the perfectly competitive quantity.
- Repeated game & trigger strategy
- A game played many times, allowing reputation and retaliation. A trigger strategy (e.g. grim trigger or tit-for-tat) cooperates until a defection, then punishes — which can sustain cooperation that is impossible in a one-shot game, provided players are patient enough.
Strategic Interaction II: Sequential Games & Oligopoly FAQ
Why do I solve a game tree backward instead of forward?
Because each player decides knowing what rational players will do AFTER them. The only way to predict the future moves is to solve the last decision first — the final mover simply picks their best payoff — then fold that result back so the second-to-last mover can anticipate it, and so on to the first move. Solving forward would have you guessing later behaviour; backward induction nails it down. This is exactly how the subgame-perfect equilibrium is found.
What makes a threat 'incredible', and why does it matter?
A threat is incredible if carrying it out would hurt the threatener once the relevant node is reached — so a rational opponent knows it is a bluff. In the entry game, the incumbent threatens to 'fight' a new entrant, but fighting (payoff 1) is worse than accommodating (payoff 2) once entry has happened, so the threat will not be executed. Subgame-perfection ignores incredible threats, which is why the entrant enters anyway. Credible commitment (e.g. building capacity in advance that makes fighting genuinely optimal) is how a firm can make a deterrent threat believable.
Where does the Cournot outcome sit relative to monopoly and perfect competition?
In between. A monopoly restricts output the most (highest price, lowest Q). Perfect competition produces the most (lowest price, P = MC). Cournot oligopolists, each choosing quantity while best-responding to rivals, collectively produce MORE than a monopoly but LESS than perfect competition — so price and total output land between the two extremes. As the number of Cournot firms rises, the outcome approaches the competitive one.
How can repeated play sustain cooperation that a one-shot game cannot?
In a one-shot prisoner's dilemma, defection is dominant, so cooperation collapses. But if the game is repeated (especially indefinitely) and players are patient, a trigger strategy — cooperate until the other defects, then punish forever (grim trigger) or match the last move (tit-for-tat) — makes defecting costly: the short-run gain is outweighed by lost future cooperation. So cooperation can be a sustainable equilibrium of the repeated game, which is the theory behind why some cartels hold together (and why they break when the end is in sight).
How is Topic 8 examined?
As short-answer: draw or read a game tree, solve it by backward induction, state the subgame-perfect equilibrium and identify any incredible threat. Oligopoly questions ask you to find or interpret Cournot reaction functions and to explain where Cournot output sits versus monopoly and perfect competition, or to argue when repeated play can sustain collusion. Together with Topic 7, game theory is a regular multi-part block in the high-weighted Topics 6–12 half of the final.
Exam move
Drill backward induction until it is automatic: label the final decision nodes, pick the best payoff there, prune the other branches, then move one step up and repeat to the root — the surviving path is the SPE. Train yourself to spot incredible threats, because that is where the marks and the intuition live: a 'punish' or 'fight' branch that is sub-optimal once you reach it gets eliminated. For oligopoly, be able to state and use a Cournot reaction function and to rank Cournot output between monopoly (least) and perfect competition (most). Finally, rehearse the repeated-game argument — patient players plus a trigger strategy can sustain cooperation a one-shot game cannot — since it ties Topics 7 and 8 together and is a favourite explanation question.
