Multi-Criteria Decisions and Competitive Strategy

Introduction and Context

Managers rarely choose on the basis of one objective. A supply-chain design may need to minimise cost while improving resilience, service quality, carbon performance and regulatory compliance. A technology investment may involve financial return, implementation risk, cybersecurity, strategic fit and employee acceptance. These objectives often conflict, and some are measured in money, some in time, some in scores and some through expert judgement.

Multi-criteria decision-making (MCDM) provides a disciplined way to structure such problems. It does not eliminate managerial judgement; rather, it makes assumptions, preferences and trade-offs visible. This chapter develops weighted scoring models, the Analytic Hierarchy Process (AHP), and related methods. It then introduces game theory, strategic interaction, equilibrium and negotiation, showing how decisions change when outcomes depend on competitors, suppliers, regulators or partners.

A central distinction is important. In a decision problem under certainty, an alternative has a known consequence for each criterion. Under risk, probabilities may be assigned to uncertain states. Under strategic interaction, the outcome also depends on choices made by other decision-makers. MCDM primarily structures preferences across criteria; game theory analyses interdependence among decision-makers. In practice, the two perspectives are often combined.

Learning Objectives

By the end of the chapter, readers should be able to:

1. Formulate managerial problems as multi-criteria decision problems.
2. Construct and critically evaluate weighted scoring models.
3. Apply AHP, including pairwise comparisons, priorities and consistency checking.
4. Explain outranking, TOPSIS and sensitivity analysis as complementary approaches.
5. Distinguish dominant strategies, Nash equilibrium, Pareto efficiency and mixed strategies.
6. Apply payoff matrices and backward induction to managerial situations.
7. Analyse negotiation, cooperation, commitment and credible threats.
8. Recognise ethical, behavioural and governance risks in quantitative decision support.

1. The Architecture of a Multi-Criteria Decision

A well-formed MCDM problem contains five elements:

• a decision-maker or group;
• a set of feasible alternatives A = {A₁, A₂, …, Aₘ};
• criteria C = {C₁, C₂, …, Cₙ};
• performance information for each alternative;
• preferences describing the relative importance of criteria and, where necessary, the value of different performance levels.

Criteria may be quantitative, such as annual cost, delivery time or defect rate, or qualitative, such as brand fit and implementation capability. They should be operationally defined and, where possible, measured consistently.

A criterion is a benefit criterion when higher values are preferred, for example reliability or revenue. It is a cost criterion when lower values are preferred, for example cost, emissions or lead time. Confusing these directions can reverse the decision.

1.1 Screening and choice

MCDM usually involves two stages. Screening removes alternatives that fail mandatory requirements, such as legal compliance, minimum capacity or budget. Choice then ranks or selects the remaining feasible alternatives. A high score should never compensate for failure on a non-negotiable constraint unless the decision-maker has explicitly allowed such compensation.

1.2 Measurement scales

Ordinal scales rank alternatives but do not establish equal distances between ranks. Interval scales support meaningful differences but not necessarily meaningful ratios. Ratio scales possess a meaningful zero, such as kilograms or monetary cost. Weighted addition is most defensible when criterion scores have been transformed to comparable value scales, not when arbitrary raw numbers are simply added.

2. Weighted Scoring Models

The simplest compensatory model is the weighted sum. Let sᵢⱼ be the normalised score of alternative i on criterion j, and let wⱼ be the weight of criterion j. The weights are non-negative and sum to one:

The overall value of alternative i is:

Here, Vᵢ is dimensionless, sᵢⱼ is normally on a common scale such as 0–100 or 0–1, and wⱼ represents the decision-maker’s relative importance. The model assumes preferential independence sufficiently strong to justify additive aggregation and allows compensation: poor performance on one criterion can be offset by strong performance on another.

2.1 Normalisation

If raw performance xᵢⱼ is measured on different scales, it must be converted. A common min–max transformation is:

For a benefit criterion:

For a cost criterion:

These formulas assume that the observed minimum and maximum define an appropriate reference range and that the denominator is non-zero. If all alternatives have the same value on a criterion, the criterion does not discriminate and should normally receive zero weight or be handled through a separate rule.

A target-based score may be preferable when performance has a desirable target rather than a simple monotonic direction. For example, a delivery time that is too short may be as problematic as one that is too long. Such value functions should be specified with stakeholders rather than assumed.

2.2 Worked example: supplier selection

A firm evaluates three suppliers. Weights are cost 0.35, quality 0.30, delivery reliability 0.20 and sustainability 0.15. Scores are already converted to a 0–100 value scale.

The weighted scores are:

Gamma ranks first, narrowly ahead of Beta. The result does not mean Gamma is objectively best. It means Gamma has the highest value under the stated criteria, scores and weights.

2.3 Sensitivity analysis

A decision should not be reported without testing whether plausible changes alter the ranking. One-way sensitivity varies one weight while maintaining the total weight constraint, or varies a score within a credible interval. If small changes reverse the ranking, the decision is fragile and management may need more information or a staged commitment.

For two alternatives A and B, the weight on criterion k at which they tie can be found by solving:

The result is meaningful only if the other weights and scores remain fixed and the resulting weight lies within [0, 1]. Scenario analysis is often more realistic than changing one parameter in isolation.

3. The Analytic Hierarchy Process

AHP, developed by Thomas Saaty, decomposes a decision into a hierarchy: goal, criteria, subcriteria and alternatives. It uses pairwise comparisons to elicit relative importance. The method is useful when direct weighting is difficult, when qualitative judgements matter, or when several stakeholders must discuss preferences.

For two elements, a decision-maker states how strongly one is preferred over the other using a reciprocal scale commonly ranging from 1 to 9. Aᵢⱼ expresses the importance of element i relative to j; therefore Aⱼᵢ = 1 ÷ Aᵢⱼ and Aᵢᵢ = 1.

A pairwise comparison matrix is:

The priority vector w is commonly estimated by the principal eigenvector:

where λₘₐₓ is the largest eigenvalue. A practical approximation is to normalise each column and average across rows. This approximation is especially convenient for teaching and small applications.

3.1 Consistency

Human judgements may be inconsistent. If criterion A is judged three times as important as B and B twice as important as C, perfect consistency would imply A six times as important as C. AHP measures departure from such consistency using:

and:

Here n is the matrix order, CI is the consistency index and RI is the average random index for matrices of order n. A CR below approximately 0.10 is often treated as acceptable, although the threshold is a diagnostic convention rather than a universal law. High inconsistency should prompt discussion, not automatic rejection.

3.2 Illustrative AHP comparison

Suppose three criteria—cost, quality and resilience—are compared. The matrix is:

Column sums are 1.75, 3.333 and 8. Normalising each column and averaging rows gives approximate priorities:

• Cost: 0.558
• Quality: 0.320
• Resilience: 0.122

The weights sum to 1. These priorities indicate that cost is judged most important, but they do not establish the performance of alternatives. A second set of pairwise comparisons is required for alternatives under each criterion. The global priority of an alternative is obtained by multiplying its local priority under each criterion by the criterion priority and summing across criteria.

3.3 Strengths and limitations of AHP

AHP makes tacit judgements explicit, supports hierarchical decomposition and offers a consistency diagnostic. It is accessible in workshops and can combine quantitative and qualitative evidence. However, the 1–9 scale can create artificial precision; rankings may be sensitive to hierarchy design; and rank reversal can occur under some forms of comparison and normalisation. Pairwise comparisons also become burdensome: n elements require n(n − 1) ÷ 2 comparisons. AHP should therefore be used as a structured conversation and audit trail, not as a machine that discovers an objective answer.

4. Related Multi-Criteria Methods

4.1 Outranking methods

ELECTRE and PROMETHEE compare alternatives by asking whether one sufficiently outranks another, while allowing veto thresholds. They are appropriate when poor performance on a critical criterion should not be fully compensated by other strengths. Their outputs may be partial rankings rather than one complete order. Thresholds, concordance and discordance parameters require careful stakeholder interpretation.

4.2 TOPSIS

TOPSIS selects the alternative closest to an ideal solution and farthest from a negative-ideal solution. After normalisation and weighting, let vᵢⱼ be the weighted score. The Euclidean distance from the positive ideal is:

The distance from the negative ideal is:

The relative closeness is:

where vⱼ⁺ and vⱼ⁻ are the best and worst criterion values after direction has been standardised. A larger Cᵢ is preferred. TOPSIS is intuitive but can be affected by the normalisation method and assumes that distance in the transformed space represents preference.

4.3 Choosing a method

Weighted sums are transparent and efficient when compensation is acceptable. AHP is useful for hierarchical judgement and consistency discussion. Outranking is preferable where vetoes, thresholds or non-compensation matter. TOPSIS is useful when closeness to an ideal profile is meaningful. Method selection should follow the decision structure, not software availability.

5. Group Decisions, Bias and Governance

Group MCDM can combine individual weights by discussion, voting, geometric means or formal aggregation. Aggregation should be documented: a board’s average preference is not necessarily the preference of any particular stakeholder. Dominant personalities, anchoring, availability bias and strategic misrepresentation can distort judgements.

Good governance includes a written problem statement, definitions of criteria, data provenance, rationale for weights, conflict-of-interest declarations, version control and an independent challenge. Separate factual scores from value judgements. Perform sensitivity analysis and preserve minority views when uncertainty is material. A model should support accountability, not conceal responsibility behind a numerical ranking.

AI-assisted scoring can accelerate data collection and scenario analysis, but it may reproduce historical discrimination, use proxies for protected characteristics or generate unsupported confidence. Human review, explainability, access controls, bias testing and a right to challenge are essential in consequential decisions. Automated recommendations should not be treated as neutral simply because they are computational.

6. Strategic Interaction and Game Theory

A game is a formal representation of strategic interaction. It specifies players, available strategies, information, timing and payoffs. A payoff may represent profit, utility, market share, risk-adjusted value or a multi-criteria utility score. A player chooses strategically when the best action depends on what another player does.

A normal-form game lists players’ strategies and payoffs for every combination. In a two-player game, the payoff in each cell is written (u₁, u₂), where u₁ belongs to Player 1 and u₂ to Player 2.

6.1 Dominance and best response

A strategy strictly dominates another if it gives a higher payoff for every possible action of the opponent. A rational player does not use a strictly dominated strategy. A best response is the strategy that maximises a player’s payoff given the opponent’s strategy.

A Nash equilibrium is a strategy profile in which no player can improve their payoff by changing strategy unilaterally. Nash equilibrium is a stability concept, not necessarily a socially desirable outcome.

6.2 Illustrative pricing game

Two competing firms choose High price or Low price. Payoffs are:

For Firm A, Low yields 10 rather than 8 when B chooses High, and 5 rather than 3 when B chooses Low. Low strictly dominates High. The same is true for Firm B. Therefore (Low, Low) is the Nash equilibrium, with payoffs (5, 5), even though (High, High) gives both firms 8. This is a coordination and incentive problem: unilateral deviation from High is attractive, so the higher joint outcome is not stable without credible commitments or enforcement.

6.3 Pareto efficiency and social welfare

An outcome is Pareto efficient if no player can be made better off without making another worse off. A Nash equilibrium may be Pareto inefficient, as the pricing example demonstrates. A social planner may maximise total payoff:

but managerial decisions may require weights for distributional fairness, consumer welfare, employment or environmental effects. Maximising W is not automatically ethically sufficient.

6.4 Mixed strategies

Some games have no equilibrium in pure strategies. A mixed strategy assigns probabilities to pure strategies. If Player 1 chooses action A with probability p, the opponent may be indifferent between actions when their expected payoffs are equal. For actions X and Y:

A player randomises only when the probabilities make the opponent indifferent among the opponent’s relevant choices. Mixed strategies are useful in competitive bidding, product launches, inspection and cybersecurity, where predictability can be exploited.

7. Sequential Games and Strategic Commitment

In a sequential game, players move at different times and later players observe some or all earlier actions. Backward induction solves a finite perfect-information game by first identifying the final player’s best response and then considering the earlier player’s choice. A threat is credible only if it is optimal to carry out when the relevant decision point arrives.

For example, an incumbent may announce that it will start a price war if a new firm enters. If fighting would be costly and accommodating entry would be better once entry occurs, the threat is not credible. Investment in excess capacity, contractual commitments or reputation may alter payoffs and make deterrence credible, but such actions can raise regulatory and ethical concerns.

Information also matters. In signalling games, an informed party takes an action intended to reveal or manipulate information. In screening, the less-informed party designs choices to induce different types to separate. Managers should distinguish genuine signals—such as verifiable investment—from cheap talk that has no cost or consequence.

8. Cooperation, Coalitions and Repeated Interaction

One-shot competition may produce inefficient outcomes, while repeated interaction can support cooperation. A firm may sustain a cooperative price or service standard if the present value of continued gains exceeds the short-term benefit from defection. Cooperation is more plausible when actions are observable, future interaction is likely, retaliation is proportionate and legal constraints permit coordination.

Repeated-game reasoning must not be used to justify price fixing, market allocation or other prohibited collusion. Competition law in many jurisdictions treats explicit or tacit coordination with particular concern. Strategic analysis should therefore include legal review, not merely payoff improvement.

Coalitions arise when players coordinate resources or negotiate joint action. Their stability depends on how benefits and costs are allocated. A coalition that creates value but distributes it unfairly may dissolve even when cooperation is collectively efficient.

9. Negotiation as a Strategic Decision Problem

Negotiation involves at least two parties with partly conflicting interests and potential gains from agreement. A useful framework distinguishes:

• reservation value: the least acceptable outcome for a party;
• BATNA: best alternative to a negotiated agreement;
• aspiration level: a desired outcome;
• bargaining zone: the set of agreements acceptable to all parties;
• distributive issues: allocation of a fixed or partly fixed value;
• integrative issues: opportunities to create value through different priorities.

If Party 1’s reservation value is R₁ and Party 2’s reservation value is R₂, a feasible bargaining zone exists only when the proposed agreement satisfies both reservation constraints. Reservation values are not the same as opening offers. A strong BATNA improves bargaining power because it reduces dependence on agreement.

Negotiators should exchange information selectively, use objective standards, package issues rather than concede item by item, and record contingent agreements where uncertainty is important. Fairness perceptions influence implementation and future relationships. A mathematically favourable agreement can fail if it is viewed as illegitimate or if its commitments cannot be monitored.

10. Integrated Applied Case: Choosing a Logistics Partnership

Background

The fictional Meridian Foods Group must select a regional logistics partner for a three-year contract. Management has shortlisted Northstar, RouteOne and GreenLink. The decision involves cost, service reliability, resilience and emissions. A major retailer requires documented emissions reporting, while stockouts would damage customer relationships.

Problem

The procurement team initially recommends Northstar because it has the lowest quoted cost. Operations favours GreenLink because of its reliable service and alternative depots. Finance asks for a transparent, auditable model, and the legal team warns that the selected provider must meet data and safety requirements.

Analysis

The team first screens out any provider failing mandatory safety certification. All three pass. It then establishes weights through an AHP workshop: cost 0.30, reliability 0.30, resilience 0.20 and emissions 0.20. The team documents the pairwise comparisons and checks consistency. Performance is converted to a 0–100 scale.

Weighted values are:

GreenLink ranks first. However, procurement performs sensitivity analysis. If cost weight rises substantially and sustainability is treated as less important, RouteOne may become competitive. The team therefore does not treat the ranking as automatic. It negotiates a pilot contract with GreenLink, including service-level penalties, emissions data verification, contingency capacity and a review after six months.

Strategic interaction

GreenLink knows that Meridian has alternatives, while Meridian knows that switching after implementation would be costly. The contract creates credible commitments: performance thresholds, audit rights and termination provisions. GreenLink may invest in resilience if the contract rewards verified capacity rather than merely promising it. Meridian avoids revealing its maximum willingness to pay and uses RouteOne’s credible offer as a BATNA.

Outcome

The pilot is awarded to GreenLink subject to measurable service and reporting obligations. The decision is not simply the highest numerical score; it combines MCDM, contract design, negotiation and strategic analysis. The model also identifies what must be monitored after selection.

Learning points

1. Screening constraints should precede compensatory scoring.
2. Weights represent preferences, not facts.
3. Sensitivity analysis identifies fragile recommendations.
4. Contracts can change the payoffs and credibility of strategic actions.
5. A decision model should continue into implementation and review.

11. Best Practices and Limitations

Best practice begins with a decision question that is specific, feasible and linked to a decision right. Criteria should be non-duplicative where possible; otherwise one concern may be counted twice. Measures should reflect outcomes rather than easily manipulated proxies. Stakeholders should distinguish uncertainty about facts from disagreement about values.

Important limitations include preference instability, poor data, correlated criteria, strategic manipulation, omitted alternatives and false precision. A model can be internally consistent yet externally irrelevant. Normalisation may change results; weights may hide political choices; equilibrium predictions may fail when players are boundedly rational, emotional or poorly informed.

Use ranges rather than single estimates when uncertainty is substantial. Conduct scenario, threshold and robustness analysis. Document assumptions and revisit them when market conditions, regulation or organisational priorities change. Where consequences are irreversible, use staged decisions, real options or pilot programmes rather than committing solely because one alternative ranks first.

Chapter Summary

Multi-criteria decision-making structures choices involving several objectives. Weighted scoring is transparent but relies on comparable value scales, appropriate weights and an additive, compensatory logic. AHP uses hierarchical decomposition and pairwise comparisons, with consistency diagnostics, but its judgements and scale should not be mistaken for objective measurement. Outranking methods accommodate vetoes and non-compensation, while TOPSIS evaluates distance from ideal and negative-ideal solutions.

Sensitivity analysis, governance and stakeholder scrutiny are essential because rankings depend on assumptions. Game theory complements MCDM by analysing situations in which outcomes depend on others’ actions. Dominance, best responses, Nash equilibrium, Pareto efficiency, mixed strategies, backward induction and credible commitment explain competitive and cooperative behaviour. Negotiation analysis adds BATNA, reservation values, bargaining zones and value creation. Effective managerial decisions integrate quantitative models with ethics, law, implementation capability and ongoing review.

Key Terms

Multi-criteria decision-making: A structured approach to choosing among alternatives evaluated on multiple criteria.

Alternative: A feasible option available to the decision-maker.

Criterion: A dimension used to evaluate alternatives.

Benefit criterion: A criterion for which higher performance is preferred.

Cost criterion: A criterion for which lower performance is preferred.

Normalisation: Transformation of measurements to a common scale.

Weighted sum: Aggregation of criterion scores using importance weights.

Compensation: Allowing strong performance on one criterion to offset weak performance on another.

AHP: A hierarchical method using pairwise comparisons to derive priorities.

Pairwise comparison: Judgement of the relative importance of two elements.

Consistency ratio: A diagnostic of inconsistency in AHP comparisons.

Outranking: A relation indicating that one alternative is sufficiently preferred to another under specified rules.

TOPSIS: A method selecting alternatives close to an ideal and distant from a negative ideal.

Game theory: Analysis of decisions in which outcomes depend on multiple strategic actors.

Dominant strategy: A strategy producing a better payoff regardless of the opponent’s action.

Best response: The payoff-maximising action given another player’s action.

Nash equilibrium: A strategy profile from which no player benefits by unilateral deviation.

Pareto efficiency: A state in which improving one party requires worsening another.

BATNA: The best alternative to a negotiated agreement.

Credible commitment: An action or promise that remains optimal or enforceable when tested.

Review Questions

Short Answer Questions

1. Why must benefit and cost criteria be treated differently during normalisation?
2. What assumptions underlie a weighted-sum model?
3. What does a high AHP consistency ratio indicate?
4. Distinguish a Nash equilibrium from a Pareto-efficient outcome.
5. What is the role of a BATNA in negotiation?

Long Answer Questions

1. Explain the stages of constructing a robust MCDM model, from problem definition to sensitivity analysis.
2. Compare weighted scoring, AHP, outranking and TOPSIS in terms of assumptions and managerial usefulness.
3. Explain how dominance, best responses and Nash equilibrium can be used to analyse competitive pricing.
4. Discuss the strengths and limitations of using expert judgement in AHP.
5. Explain how contracts and commitment devices can alter a sequential game.

Analytical / Application Questions

1. Construct a weighted scoring model for selecting a business-school learning platform. Define four criteria, assign defensible weights, score three alternatives and test whether the ranking is robust.
2. Two firms can either share a distribution centre or operate separately. Develop a payoff matrix, identify possible equilibria and discuss whether a contract could support cooperation.
3. A procurement team’s recommendation changes whenever the cost weight moves by five percentage points. Diagnose the causes of this instability and propose an improved decision process.

Multiple Choice Questions with Answers

Question 1

In a weighted-sum model, what must the criterion weights normally satisfy?

A. They must all be greater than 1.

B. They must be non-negative and sum to 1.

C. They must be measured in monetary units.

D. They must be identical for every decision.

Correct Answer: B. They must be non-negative and sum to 1.

Question 2

Which transformation is appropriate for a cost criterion in min–max normalisation?

A. (xᵢⱼ − minimum) ÷ (maximum − minimum)

B. (maximum − xᵢⱼ) ÷ (maximum − minimum)

C. xᵢⱼ ÷ maximum

D. maximum ÷ xᵢⱼ

Correct Answer: B. (maximum − xᵢⱼ) ÷ (maximum − minimum)

Question 3

What is the main purpose of the AHP consistency ratio?

A. To measure the monetary cost of an alternative

B. To determine whether all criteria have equal weights

C. To diagnose inconsistency in pairwise judgements

D. To calculate a competitor’s market share

Correct Answer: C. To diagnose inconsistency in pairwise judgements

Question 4

If an alternative has weighted scores 80 and 90 on two criteria with weights 0.4 and 0.6, its weighted value is:

A. 82

B. 84

C. 86

D. 88

Correct Answer: C. 86

Question 5

A strategy is strictly dominant when it:

A. produces the highest total industry profit

B. gives a higher payoff for every opponent strategy

C. is selected by every player

D. is always socially efficient

Correct Answer: B. gives a higher payoff for every opponent strategy

Question 6

A Nash equilibrium is a situation in which:

A. all players receive identical payoffs

B. total welfare is maximised

C. no player can improve by changing strategy unilaterally

D. each player uses a mixed strategy

Correct Answer: C. no player can improve by changing strategy unilaterally

Question 7

In TOPSIS, the preferred alternative generally has:

A. the greatest distance from the ideal solution

B. the smallest distance from the negative ideal

C. the greatest relative closeness to the ideal solution

D. the lowest score on every criterion

Correct Answer: C. the greatest relative closeness to the ideal solution

Question 8

What does backward induction analyse in a finite sequential game?

A. The final player’s best response before earlier choices are evaluated

B. Only simultaneous choices

C. The average of all possible payoffs

D. Whether all strategies are dominant

Correct Answer: A. The final player’s best response before earlier choices are evaluated

Question 9

Which statement about Pareto efficiency is correct?

A. Every Nash equilibrium is Pareto efficient.

B. A Pareto-efficient outcome maximises each player’s payoff individually.

C. No player can be made better off without making another worse off.

D. It requires equal payoffs among players.

Correct Answer: C. No player can be made better off without making another worse off.

Question 10

A BATNA is best described as:

A. The first offer made in a negotiation

B. The best alternative if no negotiated agreement is reached

C. The maximum amount a negotiator can spend

D. A guaranteed agreement between competitors

Correct Answer: B. The best alternative if no negotiated agreement is reached