Mathematical Economics · Game Theory
What is Game Theory?
A complete guide to strategic decision-making — how economists model the choices of rational players when outcomes depend on what everyone else does.
Think about the last time you negotiated a price, chose a lane on the motorway, or decided whether to study harder than your classmates. In each situation, the best choice for you depended not just on your own preferences — it depended on what everyone else was doing. That interdependence is exactly what game theory studies.
📘 Key Term
Game Theory is the mathematical study of strategic interactions among rational decision-makers (called players), where each player’s outcome depends on the choices made by all participants. It was formalised by John von Neumann and Oskar Morgenstern in Theory of Games and Economic Behavior (1944) and later extended by John Nash.
The Core Elements of Any Game
Every game theory model contains four essential building blocks:
1. Players
The decision-makers in the game. Could be firms, governments, individuals, or even countries.
2. Strategies
The complete set of actions available to each player — their entire plan of action.
3. Payoffs
The reward (or penalty) each player receives depending on the combination of strategies chosen.
4. Information
What each player knows — about the game structure, other players’ strategies, and payoffs.
Types of Games
Not all strategic situations are the same. Game theory classifies games along several dimensions:
Cooperative vs Non-Cooperative: In cooperative games, players can form binding agreements. In non-cooperative games — the more common focus in economics — each player acts independently.
Simultaneous vs Sequential: In simultaneous games, all players choose at the same time (modelled using a payoff matrix). In sequential games, players take turns and can observe prior moves (modelled using a game tree).
Zero-Sum vs Non-Zero-Sum: In zero-sum games, one player’s gain is exactly another’s loss (e.g. poker). In non-zero-sum games, total payoffs can increase or decrease — which opens space for mutually beneficial cooperation.
💡 Key Insight
Most real-world economic situations — oligopoly pricing, trade negotiations, auction bidding — are non-zero-sum, sequential games with imperfect information. Game theory provides the tools to analyse all of them rigorously.
Real-World Applications
Game theory is not abstract — it is embedded in everyday economic life:
🏭 Oligopoly Markets: When Amazon lowers prices, should Walmart follow? The strategic interaction between a small number of firms is classic game theory.
🌍 International Trade: Should the US impose tariffs if China does? Both countries face a payoff matrix where retaliation strategies determine mutual welfare.
📡 Spectrum Auctions: Governments use game-theoretic auction designs to allocate radio spectrum to telecoms companies efficiently.
💊 Pharmaceutical R&D: Whether to invest in a cure depends partly on whether rivals are investing too — a strategic decision modelled using game theory.
⚠️ Common Error
Students often confuse a player’s strategy with a player’s action. A strategy is a complete contingency plan — it specifies what a player will do in every possible situation, including situations that may never arise. An action is a single choice made at one point in the game. This distinction matters enormously in sequential games.
Case Study: Game Theory in OPEC
OPEC Oil Production Decisions
OPEC member countries collectively benefit from restricting oil supply to keep prices high. But each individual country has an incentive to cheat — producing more than its quota to earn extra revenue while others keep production low.
This is a classic game theory problem. If all members cheat, prices collapse and everyone is worse off. If all comply, prices are high but the temptation to defect is strong. The repeated nature of OPEC meetings (a repeated game) partially sustains cooperation through the threat of future punishment.
📊 Outcome: Compliance rates in OPEC fluctuate precisely because the payoff structure makes cheating individually rational but collectively destructive — exactly as game theory predicts.
Practice Questions
Q1. Define a ‘game’ in the context of game theory and identify its four core elements. [4 marks]
Answer: A game is a formal model of strategic interaction in which rational players make decisions whose outcomes depend on the choices of all participants. The four elements are: (1) Players — the decision-makers; (2) Strategies — the complete action plans available to each player; (3) Payoffs — the outcomes received given the combination of strategies chosen; and (4) Information — what each player knows about the game, other players, and payoffs.
Q2. Explain why the OPEC oil cartel is an example of a non-zero-sum game. [4 marks]
Answer: OPEC is non-zero-sum because the total payoffs across all members are not fixed. If all members cooperate and restrict supply, total industry profits rise — both parties can gain. If all defect and overproduce, prices fall and total profits decline — all parties lose. Since collective outcomes vary depending on cooperation, total payoffs change, making it non-zero-sum. This contrasts with zero-sum games like poker where one player’s gain is always another’s loss.
References
1. Von Neumann, J. and Morgenstern, O. (1944) Theory of Games and Economic Behavior. Princeton University Press.
2. Nash, J.F. (1950) ‘Equilibrium Points in N-Person Games’, Proceedings of the National Academy of Sciences, 36(1), pp. 48–49.
3. Osborne, M.J. and Rubinstein, A. (1994) A Course in Game Theory. MIT Press.
4. Dixit, A. and Nalebuff, B. (1991) Thinking Strategically. W.W. Norton.
5. Myerson, R.B. (1991) Game Theory: Analysis of Conflict. Harvard University Press.