If you’re preparing for a midterm, final, or qualifying-style exam in a graduate course, small misunderstandings can cascade into big errors. Online tutoring can help you identify exactly where the logic breaks and fix it quickly.
This post explains the topic as it is typically taught in graduate programs, emphasizing careful definitions, assumptions, and methodical steps. The goal is not just to state formulas, but to show how and when they apply. The discussion is designed to be accurate, self-contained, and appropriate for graduate-level work.
For guided help, see Game Theory Tutoring or the parent page Economics Tutoring. More worked examples are collected in the Economics Post Hub. If you’re stuck on backward induction or subgames, visit Troubleshooting: Theory.
Setup
Two players split a pie of size $10$: Player 1 proposes, Player 2 accepts or rejects.
- Offer $x\in\{0,1,\dots,10\}$ to Player 2.
- If Accept: payoffs $(10-x,\;x)$.
- If Reject: payoffs $(0,0)$.
Worked Example
Compare two candidate offers, $x=1$ and $x=4$.
$$ \text{Accept payoff}=x \qquad\text{vs.}\qquad \text{Reject payoff}=0. $$
So Player 2 accepts any $x\ge 1$ (and is indifferent at $x=0$).
$$ \pi_1(1)=10-1=9, \qquad \pi_1(4)=10-4=6. $$
Player 1 offers $x^*=1$, yielding payoffs $(9,1)$.
$$ (x^*,\text{Accept})=(1,\text{Accept}), \qquad (\pi_1,\pi_2)=(9,1). $$
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