UOE

Sequential Games & Backward Induction

Understanding Our Economy — Interactive Game Trees · CTREE 2026

Equilibrium: Bunker sets high emissions → Worker stays · Payoff (Bunker 169, Worker 51) Set high emissions Set very high emissions Stay Leave Stay Leave ( 169 , 51 ) ( 60 , 50 ) ( 210 , 10 ) ( 60 , 50 ) Crossed out: not the Worker's best response at this node Worker (left node) Worker (right node) Bunker first mover

Legend

Bunker (Blue)

The polluting firm. Blue branches show Bunker's choices.

Payoff listed first:
(Bunker, Worker)
Worker (Red)

Community member affected by pollution. Red branches show Worker's choices.

Payoff listed second:
(Bunker, Worker)
Equilibrium

The backward induction equilibrium path — what rational players will actually do.

Pruned branch

A dominated action — the player has a strictly better option, so rational players won't choose this.

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What's happening

This is a sequential game from Chapter 1. Bunker moves first, then the Worker responds. Press Next step → to build up the game tree one element at a time.

Equilibrium: Worker sets low emissions → Bunker stays · Payoff (Worker 159, Bunker 61) Worker earns 159 here vs. only 51 in Ch.1 — first-mover advantage! Set low emissions Set very low emissions Stay Leave Stay Leave ( 159 , 61 ) ( 50 , 60 ) ( 210 , 10 ) ( 50 , 60 ) Crossed out: not Bunker's best response at this node Bunker (left node) Bunker (right node) Worker as Mayor

Legend

Worker-Mayor (Red)

The Worker is now Mayor — and moves first. Red branches show the Mayor's policy choices.

Payoff listed first:
(Worker, Bunker)
Bunker (Blue)

The firm now responds to the Mayor's decision. Blue branches show Bunker's choices.

Payoff listed second:
(Worker, Bunker)
Equilibrium

Compare the Worker's payoff here (159) to Ch.1 (51) — same game, order of play reversed.

Pruned branch

Bunker's dominated action — choosing the opposite gives a strictly higher payoff.

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What's happening

In Chapter 2 the Worker becomes Mayor and moves first. Same players, same payoffs — but the order of play changes everything. Press Next step → to build the tree.

Keyboard: next  ·  back  ·  r restart  ·  1/2 switch chapter