Module 12.4 Sequential Games Lecture

Sequential Move Games

• Definition: Games where players make decisions one after another instead of simultaneously. This structure is often represented using a game tree.

Game Tree Example: Brianna and Carlos

• Scenario: Brianna chooses to study or slack off first.

• Carlos’s Decision: He makes his choice after observing Brianna's action.

  • Possible choices for Brianna:

  • Study

  • Slack Off

  • Possible choices for Carlos (after observing Brianna):

  • If Brianna studies:

    • Carlos can choose to:

    • Study: Payoff (4, 4) for both

    • Slack Off: Payoff (3, 5)

  • If Brianna slacks:

    • Carlos can choose to:

    • Study: Payoff (5, 3)

    • Slack Off: Payoff (-2, -2)

Payoff Matrix

Problem Solving Strategy: Backward Induction

• Process: Start from the last mover's decision and move backward.

• Carlos’s Best Responses:

  • If Brianna studies: Carlos should slack off (higher payoff).

  • If Brianna slacks: Carlos should study (higher payoff).

Brianna's Optimal Decision

• With knowledge of Carlos's responses:

  • If she studies, she gets 3 (because Carlos slacks off).

  • If she slacks off, she gets 5 (because Carlos studies).

• Decision: Brianna chooses slack off for a payoff of 5.

Nash Equilibrium

• Outcome: Brianna gets 5 and Carlos gets 3.

• Both have no incentive to deviate from this decision; thus it represents the Nash equilibrium.

Advantages of Backward Induction

• Clarity in Decisions: Allows players to anticipate the other's moves.

• Single Nash Equilibrium: Unlike simultaneous games which can have multiple equilibria, sequential games driven by backward induction typically have a single equilibrium due to the first mover's strategic advantage.

Real-World Applications

• Business Decisions: Determining entries into markets based on competitors' actions.

• Social Dynamics: Loaning money, where individuals consider reputations.

• Historical Example: A cowboy's reputation in the Old West influenced behavior without direct confrontation.

Game Theory Across Disciplines

• Game theory is broadly applicable beyond economics, influencing areas like:

  • Psychology

  • Political Science

  • Legal Studies

  • Evolutionary Biology

• Educational Opportunities: Institutions like Texas A&M offer specialized courses in game theory and experimental economics.