Bayesian Nash equilibria and monetary policy
with freedom, while the cooperator faces a severe penalty (10 years). Conversely, if both prisoners choose to defect, they each receive a moderate penalty (5 years). Although co-operation seems logical, by both being self-interested at the chance of being free, they defect on each other. This results in a sentence of 5 years each. This outcome is the Nash equilibrium, the outcome where no player has an incentive to deviate from their choice unilaterally.
Bayesian game theory
Consider an alternative scenario to the prisoner's dilemma, where two firms in a market compete on pricing but lack complete information about each other's cost structures and pricing strategies. Each firm must make decisions based on their beliefs about the competitor's type (low-cost or high-cost producer) and adjust these beliefs as more information becomes available. Some might say this is more realistic than regular game theory as truly perfect information is uncommon (Jones, D., 2024). Bayesian game theory, an extension of classical game theory, is particularly apt for situations where players have incomplete information about each other – a common scenario in real economic interactions. It evolved to address scenarios where not all players are fully informed about the characteristics or types of other players, introducing a probabilistic approach to their strategies and outcomes (they learn as the game progresses). In the context of central banking, Bayesian game theory is fitting due to the inherent asymmetry of information between central banks and market participants. This asymmetry, determined by transparency, necessitates a framework where market participants continuously update their inflation expectations and economic decisions based on unfolding information from the central bank. I will use this framework to determine the optimal transparency for a central bank to minimize inflation expectations traps. This lies at the Bayesian Nash equilibrium, the point at which neither player has an incentive to deviate as the mutual payoff is at its highest.
The Expectations Trap Hypothesis
In the 1970s, high inflation hit the United States. Most attribute this to continuous quantitative easing implemented by the Federal Reserve. The Expectations Trap Hypothesis was a concept developed by Chari, Christiano and Eichenbaum in 1998, theorizing that the Fed was pushed into producing the high inflation by a rise in the public’s inflation expectations. In their words: ‘ When a central bank is pressured to produce inflation because of a rise in inflation expectations, the economy has fallen into an expectations trap . We call this hypothesis about inflation the expectations trap hypothesis. ’ An expectations trap is a situation where private agents’ expectations of inflation pressure the central bank into altering inflation. Once the expectations rise, private agents make economic decisions (based on their expectations) which forces the central bank into a dilemma, they can either accommodate the expectations with monetary policy, or ignore them and risk recession. If they choose to accommodate, the safest option, inflation will rise, and they have therefore fallen into the expectations trap. Two mechanisms of this trap have been proposed: a cost-push trap, presented by Chari et al. (1998) or a working-capital trap, presented by Christiano and Gust (2000). The cost-push trap goes as follows: higher inflation expectations lead workers to demand higher wages. Firms, holding similar expectations, will accommodate these demands as they believe they can pass the cost into their prices amid the incoming inflation. The central bank can either produce the inflation which the market
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