Difficulty: Intermediate to Advanced | Prerequisites: Demand and Elasticity notes, Market Structures notes
Most business decisions are made without full information, and many involve rivals whose actions affect your outcomes. Game theory provides a structured way to think about strategic interactions (pricing wars, market entry, R&D races), while decision-making under uncertainty equips managers with tools (expected value, decision trees, real options) for situations where outcomes depend on events they cannot control. These two topics round out the managerial economics toolkit.
Game theory models strategic situations where your best move depends on what the other player does. Nash equilibrium is the central concept: a set of strategies where no one gains from changing theirs alone. Decision-making under uncertainty uses probability-weighted analysis and scenario tools to choose the best course of action when outcomes are not known in advance.
Game theory
The study of strategic decision-making where the outcome for each participant depends on the actions of all participants. Think of it as the formal framework for "if I do X, they will do Y, so I should do Z."
Nash equilibrium
A combination of strategies (one per player) where no player can improve their payoff by unilaterally changing their own strategy, given what the others are doing. In simple terms, everyone is doing the best they can given everyone else's choices, so nobody has a reason to deviate.
Dominant strategy
A strategy that yields a higher payoff for a player regardless of what the other players do. If you have a dominant strategy, you play it no matter what.
Prisoner's dilemma
A classic game where two players each have an incentive to defect (cheat), even though mutual cooperation would leave both better off. It illustrates why rational self-interest can lead to collectively worse outcomes.
Payoff matrix
A table showing the payoffs to each player for every possible combination of strategies. It is the standard way to represent a simultaneous-move game.
Expected value (EV)
The probability-weighted average of all possible outcomes of a decision. In simple terms, it is what you would earn on average if you repeated the decision many times.
Decision tree
A diagram that maps out the sequence of decisions and chance events, branching at each node. Each branch shows the probability of that event and the resulting payoff, allowing the manager to "fold back" the tree and choose the path with the highest expected value.
Sensitivity analysis
A technique that tests how the optimal decision changes when key assumptions (costs, probabilities, demand estimates) are varied. It tells you how robust your decision is.
Monte Carlo simulation
A method that runs thousands of random trials using probability distributions for uncertain variables to produce a distribution of possible outcomes. Think of it as stress-testing your plan against a wide range of scenarios.
Real options approach
The application of financial options thinking to real (non-financial) investments. It recognises that managers can expand, delay or abandon projects as new information arrives, and that this flexibility has value.
Players choose their strategies at the same time (or without knowing what the other has chosen).
The payoff matrix lays out every combination of strategies and the resulting payoff for each player.
To find Nash equilibrium: for each player, identify their best response to every possible strategy of the other player. Where best responses coincide, you have a Nash equilibrium.
A dominant strategy is optimal regardless of the rival's choice. If one exists, play it.
A dominated strategy is one that always yields a worse payoff than some alternative. Rational players eliminate dominated strategies.
Iterative elimination: remove each player's dominated strategies, then re-examine the reduced game. Continue until no more strategies can be eliminated.
Both players have a dominant strategy to defect, even though mutual cooperation would produce a better joint outcome.
Managerial relevance: price wars in oligopolies often have this structure. Both firms would benefit from keeping prices high, but each has an incentive to undercut.
Repeated games change the dynamic: if firms interact repeatedly, cooperation can be sustained through strategies like tit-for-tat (cooperate first, then mirror the rival's previous move).
Oligopoly pricing: game theory helps predict whether firms will compete on price or tacitly collude.
Market entry: an incumbent may threaten a price war to deter entry, but the threat is credible only if following through is rational (the concept of credible commitment).
R&D and innovation races: first-mover advantages create winner-take-all dynamics that game theory can model.
Negotiation: understanding the other party's payoffs and outside options (BATNA) improves bargaining outcomes.
EV = Σ (probability of outcome × value of outcome)
A risk-neutral decision-maker chooses the option with the highest expected value.
Limitation: EV ignores risk preferences. A risk-averse manager may reject a high-EV project if the downside is catastrophic.
Structure: square nodes represent decisions (the manager chooses), circle nodes represent chance events (nature decides).
Solving a decision tree:
Map out all decision points, chance events, probabilities and payoffs.
Work backwards from the end ("fold back"): at each chance node, compute the expected value; at each decision node, choose the branch with the highest value.
The result tells you the optimal strategy at each decision point.
Decision trees are particularly useful when decisions are sequential (the outcome of an earlier decision affects later choices).
Vary one assumption at a time (e.g. demand, cost, probability of success) and observe how the optimal decision changes.
Identifies which variables the decision is most sensitive to, telling the manager where to invest in better information.
Often presented as a tornado diagram (horizontal bar chart showing the range of outcomes for each variable).
Assigns probability distributions (not single point estimates) to uncertain variables.
Runs thousands of iterations, each drawing random values from those distributions.
Produces a distribution of possible outcomes, giving the manager not just an average but a sense of the range and the likelihood of extreme results.
Traditional NPV analysis assumes a now-or-never decision. Real options recognise that managers can:
Delay: wait for more information before committing.
Expand: scale up if early results are promising.
Abandon: cut losses if a project underperforms.
The option to delay, expand or abandon has value, just as a financial option does.
This is especially relevant for large, irreversible investments (building a factory, entering a new market) where uncertainty is high.
EV = \sum_{i=1}^{n} p_i \cdot x_iwhere p_i is the probability of outcome i and x_i is the payoff of outcome i.
Decision tree fold-back: at each chance node, compute the EV. At each decision node, select the branch with the highest EV.
Oligopoly pricing in the airline industry is a repeated game. When one carrier drops fares on a route, rivals must decide whether to match (triggering a price war) or hold firm (losing market share). Game theory explains why fare wars tend to be short-lived: the threat of future retaliation (tit-for-tat) disciplines behaviour over time.
Real options thinking is how pharmaceutical companies manage R&D portfolios. A drug candidate moves through Phase I, II and III trials. At each stage, the company can continue (expand), pause (delay) or kill the project (abandon), depending on trial results. The flexibility to stop at any gate is what makes the enormous upfront spending rational.
Students often assume Nash equilibrium is the "best" outcome for both players. It is not necessarily. In the prisoner's dilemma, the Nash equilibrium is mutual defection, which is worse for both players than mutual cooperation.
Students confuse a dominant strategy with a Nash equilibrium. A dominant strategy is one that is best regardless of what the rival does. A Nash equilibrium exists even when neither player has a dominant strategy.
Students sometimes treat expected value as a guaranteed outcome. It is an average over many repetitions; in any single decision, the actual outcome may differ significantly.
Students forget that real options have value. Ignoring the flexibility to delay or abandon a project undervalues it relative to a rigid NPV calculation.
⚠️ Reading and solving a payoff matrix (finding Nash equilibria, identifying dominant strategies) is one of the most common exam exercises in this topic.
⚠️ Decision tree calculations appear regularly. Practise folding back trees with two or three decision points and multiple chance nodes.
⚠️ The prisoner's dilemma is a favourite essay and short-answer topic. Be prepared to explain why rational self-interest leads to a suboptimal joint outcome, and how repeated interaction changes the analysis.
⚠️ Know how to set up and interpret an expected value calculation, including cases where the risk-neutral recommendation differs from what a risk-averse manager would choose.
True or false: In a Nash equilibrium, every player is playing a dominant strategy. (False. Nash equilibrium requires only that each player's strategy is a best response to the others' strategies, not that it dominates all alternatives.)
Fill in the blank: In a decision tree, square nodes represent _______ and circle nodes represent _______. (Decisions; chance events)
True or false: Expected value always gives the safest choice. (False. EV maximises average return, not safety. A risk-averse manager may prefer a lower-EV option with less variance.)
Fill in the blank: The real options approach adds value by recognising the manager's ability to _______, _______, or _______ a project. (Delay, expand, abandon)
Q: How can a firm operating in an oligopoly use game theory to decide whether to match a competitor's price cut?
A: The firm should construct a payoff matrix comparing the outcomes of matching vs. not matching, given the competitor's possible responses. If matching leads to a price war that erodes profits for both firms, the Nash equilibrium may involve both firms cutting prices (prisoner's dilemma structure). However, if the interaction is repeated, the firm might hold its price and signal willingness to retaliate later (tit-for-tat), which can sustain higher prices over time.
Q: A firm considering opening a new factory must invest $2 million. Outline how decision trees or sensitivity analysis could help this firm make a go/no-go decision under uncertainty.
A: Using a decision tree: map the initial invest/don't invest decision. From the invest branch, create chance nodes for demand outcomes (e.g. high demand with probability 0.6, payoff $5 million; low demand with probability 0.4, payoff $1 million). EV of investing = (0.6 x $5m) + (0.4 x $1m) - $2m = $3m + $0.4m - $2m = $1.4m. Since EV > 0, the project is worth pursuing on an expected-value basis. Sensitivity analysis would then test how the decision changes if the probability of high demand drops (say to 0.3) or if construction costs overrun.
Q: Explain the difference between a one-shot prisoner's dilemma and a repeated prisoner's dilemma. Why does repetition matter?
A: In a one-shot game, both players defect because there is no future interaction to reward cooperation. In a repeated game, players can adopt conditional strategies like tit-for-tat: cooperate first, then mirror the rival's last move. The threat of future punishment (retaliation) makes cooperation a sustainable equilibrium. This is why oligopolists in stable industries often maintain tacitly coordinated pricing.
Q: A project has two possible outcomes: a 70% chance of earning $500,000 and a 30% chance of losing $200,000. Calculate the expected value and advise whether a risk-neutral manager should proceed.
A: EV = (0.7 x $500,000) + (0.3 x -$200,000) = $350,000 - $60,000 = $290,000. The expected value is positive, so a risk-neutral manager should proceed. A risk-averse manager might still hesitate given the 30% chance of a $200,000 loss, depending on the firm's financial position and risk tolerance.
This connects to Market Structures and Pricing because game theory is the analytical backbone of oligopoly analysis. It also connects to Demand and Elasticity: the payoffs in a pricing game depend on how elastic demand is, which determines how much volume a firm gains or loses when it changes price.
Game theory, Nash equilibrium, dominant strategy, dominated strategy, prisoner's dilemma, payoff matrix, simultaneous game, sequential game, tit-for-tat, credible commitment, expected value, decision tree, fold-back, sensitivity analysis, tornado diagram, Monte Carlo simulation, real options, option to delay, option to expand, option to abandon, NPV, risk-neutral, risk-averse, oligopoly pricing, managerial economics MGT 301