Coordination / Sequential Policy Game

• Content map: SMU H3 Game Theory Map

Setup

Definition:

Coordination / Sequential Policy Game

• Players: Two players, Congress and Federal Reserve.
• Strategies: Congress: Budget Balance / Deficit; Fed: Low / High Interest Rates.

Rules

• Start with Congress and the Federal Reserve choosing fiscal and monetary policy.
• Players choose Budget Balance or Deficit and Low or High Interest Rates, either simultaneously or sequentially.
• The player who best responds to the policy environment maximises payoff.
• Either simultaneous or sequential depending on version
• In the sequential tree below, $P1=$ Congress and $P2=$ Federal Reserve

Game Tree

Payoff Matrix

Derivation (Best Response Analysis)

• Congress:
  • If LIR: prefers Deficit $(4 > 3)$
  • If HIR: prefers Deficit $(2 > 1)$
• Fed:
  • If BB: prefers LIR $(4 > 3)$
  • If BD: prefers HIR $(2 > 1)$

Derivation (Nash Equilibrium)

• Mutual best responses occur at:
  • (Deficit, High Interest Rate)

Nash Equilibrium

Result:

The unique equilibrium in the simultaneous version is

with payoff $(2,2)$.

Social Optimum

Result:

The social optimum is

with payoff $(3,4)$, since the sum of payoffs is maximised at $7$.

Insights

Insight:

• Strategic interaction creates inefficiency
• Sequential play can improve outcomes because backward induction selects $BB$ if Congress moves first