Game Theory

Game theory analyzes strategic situations: decisions where your best move depends on what others do, and theirs on what you do. Pricing against a competitor, negotiating a contract, deciding whether to cooperate with a partner, designing an auction, or setting incentives for a team are all games. The method is to describe the game precisely, predict stable outcomes, and then look for moves that change the game itself, which is often worth more than playing it better.

Input required

• The players — who makes decisions, and what each wants.
• The options each player has, and the order of moves.
• The payoffs — what each outcome is worth to each player, even roughly (ranks are enough).
• Information — what each player knows about the others' options, payoffs, and past moves.
• Repetition — whether this is one-off or an ongoing relationship.

If details are missing, state assumptions or ask the questions below once, then proceed.

Questions to ask first

Ask in one batch of at most five questions, skipping any already answered, then proceed:

1. Who are the other decision-makers, and what do they want?
2. What can each side do, and who moves first?
3. How does each outcome rank for you and for them?
4. Will you deal with these parties again, and can reputations carry over?
5. Can anything be committed to, communicated, or changed (contracts, deadlines, side deals) before the choice is made?

Method

1. Define the game. List players, actions, timing (simultaneous or sequential), information, and payoffs.
2. Build the payoff table (normal form) for simultaneous moves, or a game tree (extensive form) for sequential ones.
3. Eliminate dominated strategies. If an option is worse than another whatever the opponent does, drop it. Repeat.
4. Find equilibria. A Nash equilibrium is a set of choices where no player gains by changing alone. Check whether it is unique, and whether it is good for everyone (a Prisoner's Dilemma equilibrium is stable but collectively bad).
5. For sequential games, solve backward. Start from the last move, assume the player picks their best, and work back to the first decision. Discard threats that would not be rational to carry out.
6. Account for repetition. Repeated games can sustain cooperation through reciprocity (tit-for-tat), reputation, and the "shadow of the future". A known final round unravels it.
7. Account for information. With hidden information, consider signaling (costly actions that credibly reveal type), screening (offers that sort types), and bluffing (mixed strategies).
8. Look for ways to change the game. Add or remove players, commitments, binding agreements, side payments, linked issues, changed payoffs, more transparency, or different timing.
9. Test robustness. Rerun with different payoff assumptions for the other side; if the answer flips, note which assumption is critical.

Output format

• The game — players, moves, information, in a few lines.
• Payoff table or tree (yours first in each cell):

| You \ Them | Cooperate | Defect | |---|---|---| | Cooperate | 3, 3 | 0, 5 | | Defect | 5, 0 | 1, 1 |

• Analysis — dominant strategies, equilibrium, and whether it is efficient.
• Recommendation — your move, with the reasoning.
• Ways to change the game — two or three options.
• Key assumptions about the other side's payoffs and rationality.

Ground rules

• Model their incentives, not your hopes. Use the other side's interests as they see them.
• Payoffs include more than money — reputation, relationships, fairness, and risk attitude.
• People are not perfectly rational. Use equilibrium as a baseline, then adjust for known behavior (fairness norms, errors).
• Keep it ethical. Analysis is for better decisions and fairer deals, not for deceiving or exploiting people.
• Simplify first. A small game that is understood beats a large one that is not.

Self-check before answering

• Are all players, moves, order, and information stated?
• Are payoffs written from each player's point of view?
• Was the equilibrium checked for efficiency, and were ways to improve it considered?
• Are the assumptions about the other side explicit?

Common pitfalls

• Ignoring the other side's incentives — treating them as a fixed environment.
• Assuming one-shot when it is repeated (or the reverse).
• Believing empty threats — a threat you would not carry out is not credible.
• Over-modeling — a payoff table with invented precision.
• Missing the larger game — winning one round while losing the relationship.
• Assuming zero-sum — many situations have gains from cooperation.

Example prompt

Two competitors and I are deciding whether to cut prices this quarter. Set this up as a game, find the likely equilibrium, and tell me whether there's a way to avoid a price war.

Learn more

• Decision Analysis for a single decision-maker facing uncertainty.
• Expected Value Analysis for payoffs under probabilities.
• Second Order Thinking for tracing others' reactions informally.
• Adversary for reasoning from an opponent's point of view.
• Prospect Theory for how real people weigh gains and losses.