Prisoner’s Dilemma: Concept and Example

Here in this section, we study the prisoner’s dilemma game where the non-cooperative equilibrium makes both players worse off than if they were able to cooperate. The problem with the Nash equilibrium is that it does not necessarily lead to Pareto-efficient outcomes.

Suppose there are two persons, prisoner A and prisoner B and both have been caught for committing a bank robbery. In order to procure a confession from them, they are interrogated separately so that they cannot communicate with each other. The payoff matrix for this game is given in Table.

The Strategic form of the game can be written as:

Players: Two players-Prisoner A and Prisoner B.

Strategy: Each player can either confess or not confess his crime.

Payoff Matrix: The payoffs show the years of imprisonment.

• The upper left-hand corner of the payoff matrix tells us that if both prisoners confess the crime, both would get imprisonment of 5 years each.
• The upper right-hand corner tells us that if prisoner A confesses and prisoner B does not confess, then prisoner A would get 10 years of imprisonment, and prisoner B would go free.
• The lower left-hand corner tells us that if prisoner A not confesses and prisoner B confesses, then prisoner A would get no imprisonment, and prisoner B would get 10 years of imprisonment.
• The lower right-hand corner tells us that if prisoner A does not confess a crime and prisoner B also not confesses, then both get 8 years of imprisonment each.

Here each prisoner faces uncertainty regarding how the other person will behave, i.e. whether he will confess or not confess. So each person has to make an independent choice whether to confess or not confess a crime.

Prisoner A reasons as follows:

First: If prisoner B confesses a crime, and prisoner A also chooses the same, then prisoner A will get 5 years of imprisonment. But if prisoner A chooses not to confess, then prisoner A will get no imprisonment. Thus, the best strategy of Player A is not to confess a crime. So, person A claimed my best strategy is not to confess.

Secondly: If prisoner B does not confess a crime and prisoner A also chooses the same, then prisoner A will get 8 years of imprisonment. But if prisoner A chooses to confess, then prisoner A will get 10 years of imprisonment. Thus, the best strategy of Player B is not to confess a crime. So, person B claimed my best strategy again is not to confess. Prisoner B will also reason in the same way.

As a result, they both end up not confessing a crime and getting 8 years of imprisonment. This is the Nash Equilibrium. But if they had been able to communicate with each other, they would both have confessed to the crime and gotten 5 years of imprisonment.

Once again, the non-cooperative equilibrium makes both prisoners worse off than if they were able to cooperate, i.e. if both are making decisions, they end up not confessing to a crime.

Read More- Microeconomics

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2. Methods of Analysis in Economics
3. Problem of Choice & Production Possibility Curve
4. Concept of Market & Market Mechanism in Economics
5. Concept of Demand and Supply in Economics
6. Concept of Equilibrium & Dis-equilibrium in Economics
7. Cardinal Utility Theory: Concept, Assumptions, Equilibrium & Drawbacks
8. Ordinal Utility Theory: Meaning & Assumptions
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11. Consumer Equilibrium: Ordinal Approach, Income & Price Consumption Curve
12. Applications of Indifference Curve
13. Measuring Effects of Income & Excise Taxes and Income & Excise Subsidies
14. Normal Goods: Income & Substitution Effects
15. Inferior Goods: Income & Substitution Effects
16. Giffen Paradox or Giffen Goods: Income & Substitution Effects
17. Concept of Elasticity: Demand & Supply
18. Demand Elasticity: Price Elasticity, Income Elasticity & Cross Elasticity
19. Determinants of Price Elasticity of Demand
20. Measuring Price Elasticity of Demand
21. Price Elasticity of Supply and Its Determinants
22. Revealed Preference Theory of Samuelson: Concept, Assumptions & Explanation
23. Hicks’s Revision of Demand Theory
24. Choice Involving Risk and Uncertainty
25. Inter Temporal Choice: Budget Constraint & Consumer Preferences
26. Theories in Demand Analysis
27. Elementary Theory of Price Determination: Demand, Supply & Equilibrium Price
28. Cobweb Model: Concept, Theorem and Lagged Adjustments in Interrelated Markets
29. Production Function: Concept, Assumptions & Law of Diminishing Return
30. Isoquant: Assumptions and Properties
31. Isoquant Map and Economic Region of Production
32. Elasticity of Technical Substitution
33. Law of Returns to Scale
34. Production Function and Returns to Scale
35. Euler’s Theorem and Product Exhaustion Theorem
36. Technical Progress (Production Function)
37. Multi-Product Firm and Production Possibility Curve
38. Concept of Production Function
39. Cobb Douglas Production Function
40. CES Production Function
41. VES Production Function
42. Translog Production Function
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44. Traditional Theory of Costs: Short Run
45. Traditional Theory of Costs: Long Run
46. Modern Theory Of Cost: Short-run and Long-run
47. Modern Theory Of Cost: Short Run
48. Modern Theory Of Cost: Long Run
49. Empirical Evidences on the Shape of Cost Curves
50. Derivation of Short-Run Average and Marginal Cost Curves From Total Cost Curves
51. Cost Curves In The Long-Run: LRAC and LRMC
52. Economies of Scope
53. The Learning Curve
54. Perfect Competition: Meaning and Assumptions
55. Perfect Competition: Pricing and Output Decisions
56. Perfect Competition: Demand Curve
57. Perfect Competition Equilibrium: Short Run and Long Run
58. Monopoly: Meaning, Characteristics and Equilibrium (Short-run & Long-run)
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60. Deadweight Loss in Monopoly
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63. Monopolistic Competition: Concept, Characteristics and Criticism
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65. Difference Between Perfect Competition and Monopolistic Competition
66. Oligopoly Market: Concept, Types and Characteristics
67. Difference Between Oligopoly Market and Monopolistic Market
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69. Oligopoly: Non-Collusive Models- Cournot, Stackelberg, Bertrand, Sweezy or Kinked Demand Curve
70. Monopsony Market Structure
71. Bilateral Monopoly Market Structure
72. Workable Competition in Market: Meaning and Explanation
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75. Robin Marris Model of Managerial Enterprise
76. Hall and Hitch Full Cost Pricing Theory
77. Andrew’s Full Cost Pricing Theory
78. Bain’s Model of Limit Pricing
79. Sylos Labini’s Model of Limit Pricing
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82. Prisoner’s Dilemma: Concept and Example