Skip to content

Management Accounting · Decision Theory

Utility Theory and Other Decision Approaches

Updated 10 October 2026 · Fact-checked

Utility theory says a decision maker ranks outcomes by the satisfaction (utility) they give, not by money alone. The shape of the utility curve shows the risk attitude. To solve a question, convert payoffs to utilities, compute expected utility for each option, and pick the highest.

Understand Utility Theory and Other Decision Approaches

Expected monetary value (EMV) treats every rupee as equal. In real life it is not. Losing ₹10,00,000 hurts a small firm far more than it hurts a large group. Utility is the measure of satisfaction or value a decision maker gets from an outcome. It captures personal attitude to money and risk.

Plot money on the horizontal axis and utility on the vertical axis. The shape of the curve shows the risk attitude:

  • Risk averse: the curve rises at a falling rate (concave). Each extra rupee adds less utility. The person prefers a sure amount to a gamble with the same EMV.
  • Risk neutral: the curve is a straight line. Utility rises equally with money. The person simply follows EMV.
  • Risk seeking: the curve rises at an increasing rate (convex). The person likes gambles and may prefer a gamble to a sure amount equal to its EMV.

To build a utility scale, you usually assign utility 0 to the worst outcome and 1 (or 100) to the best outcome. Other outcomes get a utility from the point of indifference. If a manager is indifferent between a sure ₹40,000 and a gamble giving the best outcome with probability 0.7 and the worst otherwise, the utility of ₹40,000 is 0.7. Then you calculate expected utility and choose the highest.

Marginal (incremental) analysis compares the extra revenue and extra cost of a decision. You do an action as long as the extra benefit is at least the extra cost. It ignores sunk and common costs. It is the logic behind special orders, make or buy and further processing decisions.

Game theory deals with decisions where a rival's reaction affects your result. Each player has strategies and a payoff matrix shows results. In a two-person zero-sum game, one player's gain is the other's loss. Each player uses a cautious rule: the row player picks the strategy with the best of the row minimums (maximin), the column player picks the best of the column maximums (minimax). If both are equal, there is a saddle point and the game has a stable value.

Key rules to remember

Expected utility
EU = Σ (probability × utility of outcome)
Use utilities, not money. Choose the action with the highest EU.
Utility of an intermediate outcome
U(x) = p × U(best) + (1 − p) × U(worst)
p is the probability at which the decision maker is indifferent between sure x and the gamble.
Certainty equivalent and risk attitude
Certainty equivalent < EMV: risk averse; = EMV: risk neutral; > EMV: risk seeking
Certainty equivalent is the sure amount the person accepts in place of the gamble.
Marginal analysis rule
Accept if incremental revenue ≥ incremental cost
Use only relevant (future, differing) costs and revenues.
Maximin and minimax (zero-sum game)
Saddle point exists if maximin = minimax
Row player: maximum of row minimums. Column player: minimum of column maximums.

How to solve Utility Theory and Other Decision Approaches questions

Use this order for any question on utility, marginal analysis or game theory.

  1. 1Identify the type: utility based choice, incremental decision, or two-player game.
  2. 2For utility questions, list the outcomes and fix utility 0 for the worst and 1 for the best if not given.
  3. 3Find missing utilities using U(x) = p × U(best) + (1 − p) × U(worst).
  4. 4Calculate expected utility for each action using probabilities; also EMV if asked to compare.
  5. 5Choose the highest expected utility and state the risk attitude from the curve shape or from certainty equivalent versus EMV.
  6. 6For marginal analysis, list only incremental revenue and cost, then compare.
  7. 7For games, mark row minimums and column maximums, check for a saddle point, and state the value of the game.
  8. 8Write a one-line conclusion with the recommendation.

Quickest way: Table-first shortcut

When to use it: Use when the question gives a payoff table with utilities or a small game matrix and time is short.

  1. Replace money by utility values in the table at once.
  2. Multiply each row by the probabilities and add across.
  3. Circle the highest expected utility.
  4. For a game, write row minimums on the right and column maximums at the bottom, then compare the best of each.
  5. Tick an MCQ by checking the curve: bending down is risk averse, straight is neutral, bending up is risk seeking.

Common mistakes in Utility Theory and Other Decision Approaches

  • Using EMV instead of expected utility when utilities are given

    EMV is the habit from earlier decision problems.

    Fix: Once utilities are supplied, multiply probabilities by utilities only.

  • Mixing up the shapes of the curves for risk averse and risk seeking

    Students memorise labels without the logic of diminishing or increasing extra utility.

    Fix: Risk averse means diminishing gain per rupee, so concave. Risk seeking means increasing gain, so convex.

  • Including sunk or common costs in marginal analysis

    All costs in the question look relevant.

    Fix: Include only costs that change with the decision.

  • Applying maximin to the wrong player in a game

    Row and column roles get confused.

    Fix: Row player (maximiser) takes the maximum of row minimums. Column player takes the minimum of column maximums.

  • Declaring a saddle point when the two values differ

    Students stop after finding one value.

    Fix: Compare maximin with minimax. A saddle point exists only if they are equal.

Worked examples

Example 1

A manager can choose Project X or Project Y. Outcomes are ₹0 (utility 0), ₹50,000 (utility 0.6) and ₹1,00,000 (utility 1). Project X gives ₹50,000 for sure. Project Y gives ₹1,00,000 with probability 0.5 and ₹0 with probability 0.5. Which project should be chosen, and what is the manager's risk attitude?

Show the solution
  1. Project X: expected utility = 1.0 × 0.6 = 0.6.
  2. Project Y: expected utility = 0.5 × 1 + 0.5 × 0 = 0.5.
  3. EMV of Y = 0.5 × 1,00,000 + 0.5 × 0 = ₹50,000, which equals the sure amount in X.
  4. Same EMV, but the manager prefers the sure amount (0.6 > 0.5).

Answer: Choose Project X (expected utility 0.6 against 0.5). The manager prefers certainty at equal EMV, so is risk averse.

Example 2

Two firms choose strategies. Firm A (rows) has A1 and A2. Firm B (columns) has B1 and B2. Payoffs to A (in ₹ lakh) are: A1: B1 = 4, B2 = 2; A2: B1 = 3, B2 = 1. Find the best strategies and the value of the game.

Show the solution
  1. Row minimums: A1 = 2, A2 = 1. Maximin = 2 (A1).
  2. Column maximums: B1 = 4, B2 = 2. Minimax = 2 (B2).
  3. Maximin = minimax = 2, so a saddle point exists at A1, B2.

Answer: Firm A plays A1 and Firm B plays B2. The value of the game is ₹2 lakh in favour of A.

Exam tips

  • Read whether the question gives utilities or only money. Only utilities need expected utility.
  • In theory answers, draw the three utility curves in a quick sketch and label the axes.
  • For marginal analysis, show a short incremental statement and then a one-line decision.
  • In game questions, show row minimums and column maximums clearly to earn step marks.
  • Keep definitions short: one line each for utility, saddle point and incremental cost.

Practice questions from Decision Theory

Utility Theory and Other Decision Approaches in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Utility Theory and Other Decision Approaches: frequently asked questions

What is the difference between EMV and expected utility?

EMV weighs money outcomes by probability and treats each rupee equally. Expected utility weighs the utility of outcomes, so it reflects the decision maker's attitude to risk. The two can recommend different actions.

How do I identify risk averse, neutral and seeking from a curve?

A concave curve (rising at a falling rate) is risk averse. A straight line is risk neutral. A convex curve (rising at an increasing rate) is risk seeking.

What is a saddle point in game theory?

It is the cell where the maximin of the row player equals the minimax of the column player. It gives the stable value of the game, and neither player gains by changing strategy.

Is marginal analysis the same as marginal costing?

They are related but not the same. Marginal analysis compares incremental revenue and incremental cost of a choice. Marginal costing is a costing system that treats only variable costs as product costs.