Cost signals and collusion

This is an experimental economics study. We analyze a market with two sellers and one buyer in the PC laboratory. The game we examine has the following stages:
1.With probability s the sellers establish a cartel.
2.Each seller draw independently their type, H or L, where q is the probability of high type. A high type has production cost c_{H}, the low type has production cost c_{L}. Type is private information.
3.Sellers simultaneously and independently make announcements, h or l. A cartel always announces h,h
4.The buyer observes announcements, chooses a seller, and offers either p_{H} or p_{L} for one unit
5.The transaction goes through if accepted by the seller.

We focus on parameter combinations supporting an equilibrium with the following characteristics:
1.Without any information (empty signals), the buyer offers price p_{L}
2.With s=0 (no collusion) the unique equilibrium is separating
3.With s=1, point 1 implies that the buyer offers p_{L}
4.There exists positive values of s, at which the buyer offers p_{H}, conditional on signals h,h.

The experiment is designed to test the main predictions of our model. To do so we have four treatments that vary with respect to the probability the sellers establish a cartel s. Based on model prediction 1, we predict that sellers signal their true type when allowed to choose signal, and that this behavior is invariant to s. Further, based model prediction 2, we predict that buyers' offer conditional on observing two high signals depends on whether s is above or below the separation cut-off ((1-Δ)/Δ).

2022-08-21

2022-10-01

Our main treatment measures are the signals chosen by sellers (conditional on types) and the price offers from the buyers (conditional on signals).

Design

The experiment is designed to test the main predictions of the model. To do so we have four treatments that vary with respect to the probability the sellers establish a cartel s. Based on model prediction 1, we predict that sellers signal their true type when allowed to choose signal, and that this behavior is invariant to s. Further, based model prediction 2, we predict that buyers' offer conditional on observing two high signals depends on whether s is above or below the separation cut-off ((1-Δ)/Δ).

Implementation

It is straight forward to implement a parameterized version of the market game (as given by the five stages above) in the lab. Our treatment variable is s, and we use the following parameters: q=0.5 ; p_{H}=80 ; p_{L}=50 ; c_{H}=55 ; c_{L}=10 ; v=100. With these parameters we have p_{L}-c_{L}>(1/2)(p_{H}-c_{L}), and the pooling equilibrium does not exits. Further, the cut-off ((1-Δ)/Δ)=0.667, and, hence, collusion is effective when s<0.667.
Our main treatment measures are the signals chosen by sellers (conditional on types) and the price offers from the buyers (conditional on signals). In particular, let θ∈{0,1} denote the true signal of a seller, taking value 0 if the signal is not true and 1 if the signal is true. Further, let p|_{h,h} denote the price offer from a buyer receiving two high signals. We also measure sellers' profits, and whether buyers makes an offer to the seller with the lowest signal. The following table gives an overview of the four treatments and equilibrium predictions:

T₁(s=0) T₂(s=0.25) T₃(s=0.5) T₄(s=0.75)
θ = 1 1 1 1
p|_{h,h}= p_{H} p_{H} p_{H} p_{L}

We use blocks of 9 subjects. Subjects stay within blocks, and unique subjects are used in all treatments. In our analysis we regard average behavior within blocks as independent observations. A session may include several blocks. Subjects play 30 games. Prior to the first game subjects randomly draw roles so that there are 3 buyers and 6 sellers in each block. These roles are fixed for all games. Before each game, subjects in a block are randomly matched into markets consisting of 1 buyer and 2 sellers.
In the experiment, price offers and payoffs are denominated in experimental currency units (ECU). The exchange rate is set to equalize expected payoffs between treatments. At the conclusion of the session subjects are paid privately based on accumulated payoffs in ECU from all games played.
A high cost seller that accepts to sell when offered the low price incurs a loss of 5 ECU. As an insurance against negative payoffs, all subjects are allocated 150 ECU before play starts.
The experiment is implemented by zTree (Fischbacher, 2007) and subject management is handled through ORSEE (Greiner 2015).

Random assignment of subjects into treatments. Subjects are drawn from the population of students that have signed up for lab-experiments at the BI Norwegian Business School.

Subjects are randomized into treatments, and into blocks within each treatment. We use blocks of subjects within treatments as our unit of observation.

No

No clusters.

We plan to have 9 subjects in each block and 5 blocks per treatment. That is, we plan to include 9x5x4=180 subjects.

We use blocks of subjects within treatments as our unit of observation. That gives us 5 independent observations per treatment.