Principles_ProblemSet4 with solutions

Page 1: Pest Control Game and Altruism

• Principles of Economics Overview

  • Recap of the Pest control game regarding Anil's preferences.

Statements Analysis regarding Dominant Strategy Equilibrium (DSE)

• a. The outcome (I, T) is attained as a DSE if Anil is completely selfish and Bala is somewhat altruistic.

  • Conclusion: Needs analysis based on the argument of selfishness and altruism.

• b. The outcome (I, T) is attained as a DSE if Anil is somewhat altruistic and Bala is very altruistic.

  • Conclusion: Analysis of indifference curves necessary to determine outcomes.

• c. The outcome (I, T) cannot be attained as a DSE.

• d. The outcome (I, I) is attained as a DSE only if both Anil and Bala are somewhat altruistic.

  • Explanation: Anil’s dominant strategy = T; Bala’s dominant strategy = I.

Indifference Curves and Payoffs

• -Indifference Curve Analysis:

  • Different scenarios based on altruism and selfishness affecting choices in the game.

  • Reference to payoffs based on cooperation or betrayal strategies (I, I) vs (T, T).

Page 2: Bruce's Cooperative Project

• Question 2: Bruce's Cooperative Project Analysis

  • Members contribute to a project with a cost and income distribution framework.

• Statement Evaluations:

  • a. The socially optimal outcome when no one works.

  • b. The DSE is when everyone works.

  • c. Bruce is better off not working irrespective of others.

  • d. Bruce’s net income when all work together.

Dominant Strategy Analysis for Bruce's Scenario

• Net Income Calculations:

  • Total incomes calculated based on participation levels.

• Dominant Strategy:

  • Analysis reveals the dominant strategy not to work leads to equitably lower costs.

Page 3: Sequential Game Dynamics

• Question 3: Sequential Players in the Pest Control Game

• a. First mover with knowledge of a reciprocal second mover.

  • Strategy consideration leading to a norm-respecting choice.

• b. Reciprocal first mover against a self-interested second mover.

  • Dominant strategy implications lead back to terminator choice for payoff maximization.

Page 4: Joint Project Effort Analysis

• Question 4: Effort Contribution in Group Work

• a. Analysis of strategies leading to dominated strategies and Nash equilibria:

  • Working hours analyzed leading to strategic choices among 0 hours being non-dominated.

  • DSE noted as all members contributing 0 hours; not Pareto efficient.

• b. Sequential decision-making dynamics.

  • Impact on contributions restarts assessment but reveals unchanged dominant strategies.

Page 5: Changes in Group Dynamics Affecting Payoff Structures

• Question 5: Adjusting Efforts with Group Preferences

• c. New payoff structure and its inverse relation leads to a distinct revert to effort maximization.

  • Dominant strategy is now to contribute maximum efforts for Pareto efficiency.

• d. Integrating time preferences into the utility function.

  • New strategies emerge based on how time expenses interplay with group interaction, changing previous equilibria.

• Conclusion: Strap to various outcomes based on group interactivity leading to diverse payoff structures that require comprehensive evaluation for Nash equilibria.