Experimental Design
Experiment 1.
There are two possible states of the world: Blue or Red, each occurring with a known probability. Participants receive imperfect exogenous signals about the true state. In Treatment Explicit, signals are shown as either blue or red; and each signal is more likely to occur under the corresponding true state (i.e., a blue signal is more likely to be drawn if the state is Blue). In treatment Silent, the blue signal is replaced with the absence of a signal, meaning it is not displayed to participants, while the red signal remains explicit. In Treatment Implicit, the signal structure mirrors that of Silent, but participants are given explicit information about the probability of receiving no signal and are informed whenever the signal is absent. In our experimental design, we use a between-subject design for these three treatments.
Experiment 2.
We consider a “colored hats” problem with two players, each wearing a colored hat: either Red or Blue. Both players are informed that at least one of the two hats is Red (or Blue, depending on the realized state of hat colors), and each player observes the color of the other player’s hat. The game is played for multiple periods (open-ended), with the following rules: in each period, players first observe the other player’s action (if any) from the previous period, and then simultaneously decide whether to guess the color of their own hat. Once a player makes a guess, it becomes final and cannot be changed in later periods. The game ends when both players have made a guess, or when both choose to proceed to the next round. Correct guesses made in later periods receive a discounted payoff, ensuring that players with sufficient information have no incentive to delay their guess.
We employ a 2x2 design that varies along two dimensions: game type and action space.
The game type is determined by the true state and consists of two possibilities:
A. The two players wear different hat colors.
B. The two players wear the same hat color.
The action space also has two versions:
a. (“Red”, “Blue”, no action). No action means not making a choice between “Red” and “Blue”.
b. (“Red”, “Blue”, “Not Sure”).
We consider a two-game-type by two-action-space design. The two game types (different hat colors or same hat color) are implemented within participants, while the two action spaces (whether “Not Sure” is a displayed action) are assigned between participants.
Experiment 3.
We adopt a matching with incomplete information environment here (see pre-registration at https://www.socialscienceregistry.org/trials/16825/edit for background information).
We employ a 2x2 design that varies along two dimensions: game type and information structure.
Game types:
A. At the start of the market, all participants are unmatched. Participants can update their beliefs of the state by observing others either form a match or dissolve existing matches.
B. At the start of the markets, all participants are unmatched. Participants can update their beliefs of the state by observing others maintain the unmatched status quo.
Information structures:
a. Only dynamic matching outcomes are observable to everyone in the market.
b. Both dynamic matching outcomes and additional detailed activities, including individual proposals, acceptances, and rejections, are observable to everyone in the market.
We consider a two-game-type by two-market-information-structure design. The two game types (active matching behavior or maintaining the status quo) are implemented within participants, while the two market information structures (whether the proposing and responding activities are publicly displayed) are assigned between participants.