Collective Experimentation: An Experiment

Summary:

Model Outline

We adapt Strulovici (2010) model of collective experimentation for the context of lab experiments. We consider a simple three period game voting game with three players in which players choose between a safe and a risky alternative. Players can be of two types: high or low, depending on whether the player receives a high or a low payoff if the risky alternative is implemented.  At the first stage, players vote on whether to start experimenting or not.  If they start experimenting, they receive a set of public signals. The signal can be “High” or “Uncertain.” If the signal is “High,” the player would receive high payoff from risky alternative for sure if the risky alternative where to be implemented. If the signal is “Uncertain,” the player does not know which payoff would receive in case of implementing risky alternative. Signals are not precise; if the player is of high type (i.e. would receive high payoff) there is a probability q with which his type would be disclosed with the signal. In the second stage players decide whether to continue experimenting, and if they continue they proceed to the next set of signals. And finally in the third stage they decide whether to implement the risky alternative or not. If the risky alternative is implemented in the third stage, the payoffs are disclosed with certainty.  In this setting, we show that no news are better than partial news, i.e. a player is more willing to continue experimenting if no one else received a high signal before the second stage than if there is one good signal received by another player. We also show that for some sequences of signals majority voting at every stage would cause deviating from the socially optimal sequence of decisions, and propose optimal mechanism that implements the social optimum as the equilibrium in the voting game.

Experimental Design

We conduct a three-stage collective experimentation game with three voters under two voting rules: Simple majority rule and a Time-varying quorum rule, which implements the social optimal sequence of decisions in equilibrium. At each stage, simple majority rule selects one of the two actions that have majority votes. The first action S is “safe” yields constant payoff s to all individuals. The second action R is “risky” and can be, for each individual, either “good” or “bad.” The types (good and bad) are independently distributed across the group. If R is bad for some individual i, it pays him l; while if R is good for i, it pays him h. The risky action payoff for good type h is higher than safe action payoff s, and s is higher than risky action payoff for bad type l. Each individual starts with half chance that R is good for him. This probability is same for all and is common knowledge. Thereafter, if the safe action is chosen at any stage, collective experimentation ends and each individual receives s. If the risky action is chosen at a stage, individuals will receive a new set of signals regarding their type as public information. An individual with “good” type receives two possible signals: “good type for sure” or “uncertain”, each with half chance. An individual with “bad” type always receives “uncertain” signal. Under Time-varying quorum rule, the game progresses similarly to Simple majority rule, except alternatives which have a majority votes are selected at 1st and 3rd stage, and risky action is always selected regardless of the votes at 2rd stage.

 

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