The Problem of Multiple Nash Equilibria and Suboptimal Outcomes
When a strategic interaction has more than one Nash equilibrium, it creates a problem of unpredictability. More importantly, it introduces the risk that players, acting independently, can get 'stuck' in a Pareto-inferior equilibrium—an outcome where all players are worse off than they could have been in an alternative, also stable, equilibrium.
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CORE Econ
Ch.4 Strategic interactions and social dilemmas - The Economy 2.0 Microeconomics @ CORE Econ
The Economy 2.0 Microeconomics @ CORE Econ
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Consider a scenario where two farmers, Farmer A and Farmer B, must independently decide whether to grow Crop X or Crop Y. The table below shows the payoffs (e.g., in tons of harvest) for each farmer based on their combined choices. The first number in each cell is Farmer A's payoff, and the second is Farmer B's.
Farmer B: Crop X Farmer B: Crop Y Farmer A: Crop X (3, 2) (6, 6) Farmer A: Crop Y (4, 4) (2, 3) Analyze the outcome where both farmers choose to grow Crop X, resulting in payoffs of (3, 2). Why is this specific outcome not a stable equilibrium?
Justifying a Stable Outcome in a Specialization Game
Two companies, InnovateCorp and TechGiant, are deciding whether to launch a new product in the 'Consumer' market or the 'Enterprise' market. Their potential profits (in millions) are shown in the payoff matrix below. The first number in each pair is InnovateCorp's profit, and the second is TechGiant's.
TechGiant: Consumer TechGiant: Enterprise InnovateCorp: Consumer (10, 10) (30, 50) InnovateCorp: Enterprise (50, 30) (5, 5) A stable outcome, or equilibrium, occurs when neither company can increase its profit by changing its decision alone, assuming the other company's decision remains the same. Based on this principle, which of the following represents the complete set of stable outcomes in this scenario?
Evaluating a Strategic Decision in a Specialization Game
Two farmers, Farmer 1 and Farmer 2, must independently decide whether to grow Crop X or Crop Y. The table below shows the payoffs for each farmer based on their combined choices. The first number in each cell is Farmer 1's payoff, and the second is Farmer 2's.
Farmer 2: Crop X Farmer 2: Crop Y Farmer 1: Crop X (1, 5) (4, 4) Farmer 1: Crop Y (3, 2) (2, 1) A stable outcome occurs when, given the other farmer's choice, neither farmer can improve their own payoff by unilaterally changing their crop.
Match each possible outcome with the description that correctly analyzes its stability.
Consider a game where two farmers, Anil and Bala, each choose to grow either Rice or Cassava. The outcome where Anil grows Rice and Bala grows Cassava is a stable equilibrium. This means that if Anil were to switch to growing Cassava (while Bala continues to grow Cassava), Anil's payoff would necessarily decrease.
Creating a Stable Specialization Outcome
Evaluating Stable Outcomes in a Specialization Game
Two software companies, CodeStream and DevFlow, are deciding whether to develop a new app for the 'Mobile' or 'Desktop' platform. Their potential profits (in millions) are shown in the payoff matrix below. The first number in each pair is CodeStream's profit, and the second is DevFlow's.
DevFlow: Mobile DevFlow: Desktop CodeStream: Mobile (15, 15) (40, 60) CodeStream: Desktop (60, 40) (10, 10) The outcome where CodeStream chooses 'Desktop' and DevFlow chooses 'Mobile' is a stable equilibrium. Which statement below correctly explains why this outcome is stable?
Analyzing a Path to Equilibrium
The Problem of Predicting Outcomes with Multiple Nash Equilibria
Pareto Superiority of the Specialization Equilibrium in the Anil and Bala Game
Getting Stuck in a Pareto-Inferior Equilibrium
The Problem of Multiple Nash Equilibria and Suboptimal Outcomes