Optimal cheating in monetary policy with individual evolutionary learning

We study individual evolutionary learning in the setup developed by Deissenberg and Gonzalez (2002). They study a version of the Kydland-Prescott model in which in each time period monetary authority optimizes weighted payoff function (with selfishness parameter as a weight on its own and agent's payoffs) with respect to inflation announcement, actual inflation and the selfishness parameter. And also each period agent makes probabilistic decision on whether to believe in monetary authority's announcement. The probability of how trustful the agent should be is updated using reinforcement learning. The inflation announcement is always different from the actual inflation, and the private agent chooses to believe in the announcement if the monetary authority is selfish at levels tolerable to the agent. As a result, both the agent and the monetary authority are better off in this model of optimal cheating. In our simulations, both the agent and the monetary authority adapt using a model of individual evolutionary learning (Arifovic and Ledyard, 2003): the agent learns about her probabilistic decision, and the monetary authority learns about what level of announcement to use and how selfish to be. We performed simulations with two different ways of payoffs computation - simple (selfishness weighted payoff from Deissenberg/Gonzales model) and "expected" (selfishness weighted payoffs in believe and not believe outcomes weighted by the probability of agent to believe). The results for the first type of simulations include those with very altruistic monetary authority and the agent that believes the monetary authority when it sets announcement of inflation at low levels (lower than critical value). In the simulations with "expected" payoffs, monetary authority learned to set announcement at zero that brought zero actual inflation. This Ramsey outcome gives the highest possible payoff to both the agent and the monetary authority. Both types of simulations can also explain changes in average inflation over longer time horizons. When monetary authority starts experimenting with its announcement or selfishness, it can happen that agent is better off by changing her believe (not believe) action into the opposite one that entails changes in actual inflation