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
- Microeconomics: Definition, Meaning and Scope
- Methods of Analysis in Economics
- Problem of Choice & Production Possibility Curve
- Concept of Market & Market Mechanism in Economics
- Concept of Demand and Supply in Economics
- Concept of Equilibrium & Dis-equilibrium in Economics
- Cardinal Utility Theory: Concept, Assumptions, Equilibrium & Drawbacks
- Ordinal Utility Theory: Meaning & Assumptions
- Indifference Curve: Concept, Properties & Shapes
- Budget Line: Concept & Explanation
- Consumer Equilibrium: Ordinal Approach, Income & Price Consumption Curve
- Applications of Indifference Curve
- Measuring Effects of Income & Excise Taxes and Income & Excise Subsidies
- Normal Goods: Income & Substitution Effects
- Inferior Goods: Income & Substitution Effects
- Giffen Paradox or Giffen Goods: Income & Substitution Effects
- Concept of Elasticity: Demand & Supply
- Demand Elasticity: Price Elasticity, Income Elasticity & Cross Elasticity
- Determinants of Price Elasticity of Demand
- Measuring Price Elasticity of Demand
- Price Elasticity of Supply and Its Determinants
- Revealed Preference Theory of Samuelson: Concept, Assumptions & Explanation
- Hicks’s Revision of Demand Theory
- Choice Involving Risk and Uncertainty
- Inter Temporal Choice: Budget Constraint & Consumer Preferences
- Theories in Demand Analysis
- Elementary Theory of Price Determination: Demand, Supply & Equilibrium Price
- Cobweb Model: Concept, Theorem and Lagged Adjustments in Interrelated Markets
- Production Function: Concept, Assumptions & Law of Diminishing Return
- Isoquant: Assumptions and Properties
- Isoquant Map and Economic Region of Production
- Elasticity of Technical Substitution
- Law of Returns to Scale
- Production Function and Returns to Scale
- Euler’s Theorem and Product Exhaustion Theorem
- Technical Progress (Production Function)
- Multi-Product Firm and Production Possibility Curve
- Concept of Production Function
- Cobb Douglas Production Function
- CES Production Function
- VES Production Function
- Translog Production Function
- Concepts of Costs: Private, Social, Explicit, Implicit and Opportunity
- Traditional Theory of Costs: Short Run
- Traditional Theory of Costs: Long Run
- Modern Theory Of Cost: Short-run and Long-run
- Modern Theory Of Cost: Short Run
- Modern Theory Of Cost: Long Run
- Empirical Evidences on the Shape of Cost Curves
- Derivation of Short-Run Average and Marginal Cost Curves From Total Cost Curves
- Cost Curves In The Long-Run: LRAC and LRMC
- Economies of Scope
- The Learning Curve
- Perfect Competition: Meaning and Assumptions
- Perfect Competition: Pricing and Output Decisions
- Perfect Competition: Demand Curve
- Perfect Competition Equilibrium: Short Run and Long Run
- Monopoly: Meaning, Characteristics and Equilibrium (Short-run & Long-run)
- Multi-Plant Monopoly
- Deadweight Loss in Monopoly
- Welfare Aspects of Monopoly
- Price Discrimination under Monopoly: Types, Degree and Equilibrium
- Monopolistic Competition: Concept, Characteristics and Criticism
- Excess Capacity: Concept and Explanation
- Difference Between Perfect Competition and Monopolistic Competition
- Oligopoly Market: Concept, Types and Characteristics
- Difference Between Oligopoly Market and Monopolistic Market
- Oligopoly: Collusive Models- Cartel & Price Leadership
- Oligopoly: Non-Collusive Models- Cournot, Stackelberg, Bertrand, Sweezy or Kinked Demand Curve
- Monopsony Market Structure
- Bilateral Monopoly Market Structure
- Workable Competition in Market: Meaning and Explanation
- Baumol’s Sales Revenue Maximization Model
- Williamson’s Model of Managerial Discretion
- Robin Marris Model of Managerial Enterprise
- Hall and Hitch Full Cost Pricing Theory
- Andrew’s Full Cost Pricing Theory
- Bain’s Model of Limit Pricing
- Sylos Labini’s Model of Limit Pricing
- Behavioural Theory of Cyert and March
- Game Theory: Concept, Application, and Example
- Prisoner’s Dilemma: Concept and Example