Monetary EconomicsGame and Monetary Policymaking

Content

• Basic Element of Game Theory• Prisoners’ Dilemma and Solution• Game: Central Bank versus Public• Inflation cost minimization and optimal

level of inflation• Commitment, Credibility and Institutions

Game Theory: Basic Elements• Players: those who play the game (normally two).• Actions: a list of action that can be taken by the players.• Strategy: What is the course of actions to be taken? Dominant Strategy: A strategy that a player would want to follow regardless of other player’s behavior.• Payoff: the benefits (or losses) accrued to each player at the

end of the game.• Solution: the final outcome of the games – i.e. action taken by

each player and its corresponding benefits. Nash Equilibrium: Neither player want to deviate taking the other player’s behavior as given.• These are normally presented in Game Matrix or Game Tree.

Game Theory: Basic Elements• How many times the game is played? One-shot game vs. Repeated game• Are the players’ moves simultaneous? Simultaneous vs. Sequential• Non-cooperative vs. cooperative game.• Some Basic Games - Prisoners’ Dilemma - Pigs in a Box - Battle of the Sexes - Copycat Game - Game of the Chicken

Prisoners’ Dilemma• There are two prisoners whose aim is to minimize the years of

imprisonment. • They have committed a crime jointly. Each prisoner is

interviewed separately and there are no contacts whatsoever between them.

• They decide individually to confess or deny the crime taking into account possible decisions of the other prisoner (strategic game).

• Each prisoner chooses his dominant strategy, that is the behavior giving the best result regardless of the decision of the other prisoner.

Prisoners’ Dilemma

Game: Central Bank vs. Public• Public: setting the a nominal wage in the supply of labor

services and the real price level is unknown.• The public, however, has a target real wage. Accordingly, the

public will form expectations about what inflation would be.• Given expected real wage, public (workers) decide on their

optimal level supply and dislike supplying too high or too low employment services.

• Central bank wants to have higher employment. However, this can be done only by inflating (inflation-employment tradeoff).

• Also, if possible, the Central wishes to achieve low inflation.• Conditional on workers’ expectation, Central Bank set the

actual inflation rate.

PAYOFF      

Central Bank sets Inflation Rate

                                Public Expectation of Inflation LOW HIGH

LOW

0, 0

-1, -2

HIGH

-1, 1

0, -1

Game Outcome

Prediction:Economy ends up at higher level of inflation with no output benefit forthcoming.

ISSUE: CAN THE ECONOMY ACHIEVE LOW INFLATION LEVEL?

Another Look(Barro and Gordon, 1983)

• The first term: Cost of inflation• The second term: gains from inflating or operating above the

natural rate of output.• Policy maker mimimizes the above cost of inflation, treating

the expected inflation fixed.

𝑍=𝐶𝑜𝑠𝑡𝑠=𝑎2

(𝜋 )2−𝑏(𝜋−𝜋𝑒)

Inflation Cost Minimization• Solution

• Again, the inflation is too high since both workers and policymakers would prefer lower inflation and to remain at full employment. But, is lower inflation feasible?

• The parameter (b) is policymakers’ gain from output and (a) is the policymakers’ costs of inflation.

• Prediction: b tends to be high : - natural rate of unemployment is high - during a recession - during times when government spending increases sharply

𝜋=𝑏𝑎

Repeated Game• Can lower inflation achievable in repeated game?• Suppose that the game is played repeatedly and workers will

punish policymakers once if policymakers deviate from their announced plan.

• Policymakers – announced the targeted inflation for next year, which is lower than b/a, denoted as INFT

• The workers will set expectation at INFT• If policymakers stick to the announced target, the subsequent

period of expected inflation would be INFT• However, if policymakers cheat, then workers will set

expectation at b/a as a form of punishment.• QUESTION: what level of INFT is sustainable? That is,

policymakers have no temptation to cheat.

OUTCOME• Barro and Gordon (1983) show that the range of sustainable

level of inflation would be:

• DISCUSSION: Can we achieve a lower inflation in the current setting? Is inflation solely the results of fiat system or is it due to policymakers’ behavior (TIME INCONCISTENCY).

𝑏𝑎≥ 𝜋∗≥

𝑏𝑎 ( 𝑟2+𝑟 )