Solving the two envelopes problem with the Intermediate Amount Strategy

TL;DR

This paper proposes an Intermediate Amount Strategy for the two envelopes problem, leveraging prior beliefs to improve decision-making and increase expected returns when choosing whether to switch envelopes.

Contribution

It introduces a novel strategy based on prior beliefs that enhances decision-making in the two envelopes problem, surpassing traditional approaches.

Findings

The strategy increases the probability of correctly identifying the larger amount.

Players using the strategy achieve higher expected returns.

The symmetrical case where both players use the strategy is also analyzed.

Abstract

This paper introduces a strategy in the two envelopes problem that utilizes the prior beliefs of two players about the amount of money that their envelopes can contain. This strategy gives them more information about the decision of switching they have to make when one of the envelopes is opened and the amount it contains is revealed. The player who implements this strategy can predict which amount is larger with a probability greater than 1/2 so that he will have a greater expected return from the game than that of the other player who will not use the same strategy. The symmetrical case in which both players implement the same strategy is also analyzed.