Figure 1

The Coordination Game. On each turn in the coordination game, the First Player is given a probability p (unknown to the second player) and asked to encode it as a probabilistic phrase. Table 1 lists the probabilistic phrases that the First Player could use to encode the probability. The Second Player (either a human participant or GPT) is then given only the selected phrase and asked to estimate the original probability. The game is a model of transmission through a communication channel, We focused on only the Decoding phase of the game (enclosed by a dashed red contour). Either GPT-4 or a human participant played the role of Player 2 while the experimenter played the role of Player 1. In a variant of the game we asked GPT-4 or the human participant to estimate not the probability but instead the ambiguity of the probability phrase.