Monetary Economics Game 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 LOWHIGH 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.

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

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).