Decision-making process, attitude to risk and competition: formula sheet

Key formulas

Rational decision-making sequence

Define problem → Set objectives and criteria → Gather information → Generate options → Evaluate options → Choose → Implement → Monitor and review

Learn it as a sequence. Exact step names vary between sources, so use the logic, not fixed labels.

Satisficing

Choose the first option that meets the minimum acceptable criteria

Contrast with optimising, where you seek the best option. Satisficing reflects bounded rationality.

Expected value criterion (if options are quantified)

EV = Σ (probability × outcome)

One way to evaluate options under uncertainty. It ignores attitude to risk, so mention that limit.

Expected value of an option

EV = Σ pᵢ × xᵢ

pᵢ is the probability of state i and xᵢ the payoff in that state. The probabilities must sum to 1.

Maximin rule

Choose the option with the largest value of (minimum payoff)

Use payoffs where higher is better. If the table shows costs, the equivalent rule is minimax cost.

Maximax rule

Choose the option with the largest value of (maximum payoff)

Optimistic rule. Ignores downside completely.

Regret

Regret(option, state) = best payoff in that state − payoff of the option in that state

Calculate down each column. Regret is never negative.

Minimax regret rule

Choose the option with the smallest value of (maximum regret)

Take the maximum regret along each row, then pick the smallest.

Folding back a tree

Chance node value = Σ p × value of branch; decision node value = best branch value

Subtract costs on the branches taken. Work right to left.

Expected value of perfect information

EVPI = EV with perfect information − best EV without information

EV with perfect information = Σ p × best payoff in each state. It is the most you should pay for information.

Expected value

E[X] = Σ pᵢ xᵢ

Probability-weighted average of the money outcomes. Risk neutral decisions use this.

Expected utility

E[U(X)] = Σ pᵢ U(xᵢ)

Apply U to each outcome first, then weight by probability. Choose the option with the highest value.

Certainty equivalent

U(CE) = E[U(X)], so CE = U⁻¹(E[U(X)])

The sure amount equal in utility to the gamble.

Risk premium

Risk premium = E[X] − CE

Positive for risk averse, zero for risk neutral, negative for risk seeking.

Risk averse

U′(x) > 0 and U″(x) < 0 (concave)

Then E[U(X)] < U(E[X]) for a non-degenerate gamble (Jensen's inequality).

Risk seeking

U′(x) > 0 and U″(x) > 0 (convex)

Then E[U(X)] > U(E[X]).

Risk neutral

U(x) = a + bx with b > 0

Then E[U(X)] = U(E[X]).

Porter's five forces

Industry profit potential = f(entrants, substitutes, buyers, suppliers, rivalry)

This is a framework, not a numerical formula. Name all five forces and judge each as high, medium or low.

Perfect competition conditions

Many sellers + identical product + free entry/exit + price takers

All conditions must hold. Firms earn only normal profit in the long run.

Profit-maximising output rule

MR = MC

Applies to firms in any market structure. In perfect competition, price = MR, so P = MC.

Monopoly pricing position

P > MR = MC at the profit-maximising output

Price is read from the demand curve at that output. Applies to a firm facing a downward-sloping demand curve.

Oligopoly feature

Interdependence: my best action depends on rivals' actions

Use game theory ideas such as price wars or collusion when answering.

Dominant strategy test

Strategy A is dominant for a player if payoff(A) ≥ payoff(any other) against every rival choice, and > in at least one case

A strictly dominant strategy is better against every rival choice. Compare payoffs column by column (or row by row), using only your own payoffs.

Nash equilibrium test

For each player: payoff at the cell ≥ payoff from switching, with the rival's choice fixed

Check every cell. A cell can be an equilibrium even if neither player has a dominant strategy. There can be more than one, or none in pure strategies.

Best response method

Mark each player's best payoff against each rival choice; a cell with both marks is a Nash equilibrium

This is the safest routine for any matrix size.

Prisoner's dilemma pattern

Temptation > Reward (both cooperate) > Punishment (both defect) > Sucker's payoff

Ranking of one player's payoffs. Defecting dominates, but both defecting is worse than both cooperating.

Quick revision

• Decision process: define objective, generate options, gather information, evaluate, choose, implement, review.
• Expected value = Σ (probability × outcome); it suits a risk-neutral decision-maker making repeated decisions.
• Maximin picks the option with the best worst outcome; it is a cautious criterion.
• Maximax picks the option with the best best outcome; it is an optimistic criterion.
• Minimax regret picks the option with the smallest largest regret, where regret = best outcome in that state − your outcome.
• Decision trees: squares are decisions, circles are chance events; roll back from right to left.
• A risk-averse person has a concave utility function; a risk-seeking person has a convex one.
• Expected utility compares options by Σ (probability × utility), not by money value.
• Porter's five forces: rivalry, threat of new entrants, threat of substitutes, buyer power, supplier power.
• A dominant strategy is best whatever the rival does; a Nash equilibrium is where neither player gains by changing alone.
• In the prisoner's dilemma, each side's rational choice can leave both worse off than cooperating.
• Always state assumptions and name the criterion you used when you recommend an option.

Common mistakes

• Listing the steps without applying them to the case. Fix: Attach a fact from the scenario to every step. Marks go to application.
• Skipping the setting of objectives and criteria. Fix: Always state objectives and criteria first. You cannot evaluate options without them.
• Taking the minimum regret instead of the maximum regret in each row. Fix: First take the maximum regret of each option. Then choose the option with the smallest of those maxima.
• Calculating regret across rows instead of down columns. Fix: Fix a state (column). Find the best payoff in it. Subtract each option's payoff from that best.
• Comparing expected monetary values when a utility function is given. Fix: Apply U to each outcome first. Compare E[U(X)], not U(E[X]).
• Calculating U(E[X]) instead of E[U(X)]. Fix: Write out each outcome's utility in a column, multiply by its probability, then add.
• Listing the five forces without applying them to the case. Fix: Attach a fact from the question to every force and say what it means for profit.
• Confusing the threat of substitutes with rivalry among existing firms. Fix: Rivals sell the same type of product. Substitutes meet the same need in a different way, such as a savings scheme replacing a life policy.
• Comparing a player's payoffs across the wrong direction, for example the row player comparing numbers along a row. Fix: The row player compares only their own payoffs within the same column. The column player compares their own payoffs within the same row.
• Saying Nash equilibrium and dominant strategy are the same thing. Fix: Dominant means best against every rival choice. Nash means best against the rival's actual choice at that cell. A game can have a Nash equilibrium with no dominant strategy.

Exam tips

• Always apply the steps to the case. A bare list of steps earns few marks.
• Show the review and feedback step. Examiners link it to the control cycle idea.
• Use the exact terms bounded rationality and satisficing when discussing limits.
• In MCQs, watch for options that reverse the order of steps or drop objectives. The objectives come before evaluating options.
• For discussion questions, balance the answer: benefits of the model, then limits, then a practical conclusion.
• Read whether the table shows profits or costs before you apply any rule. Say which you assume if the question is unclear.
• Show the regret table in full. Even if you slip on the final step, method marks are available for correct regret values.
• In written questions, always add a short comment on what each criterion assumes. Expected value suits risk-neutral, repeated decisions. Maximin suits cautious decision makers.