Understanding Bidding Behavior in Multi-unit Experimental Auctions with Latent Class Models

  • October 20, 2023
  • 0

Tanga Mohr and John Whitehead [1]
Department of Economics 
Appalachian State University


The Regional Greenhouse Gas Initiative (RGGI) is a cap-and-trade program that covers the electric power sector in more than 10 northeastern states. The cap-and-trade program creates markets for a limited number CO2 allowances, reducing greenhouse gases. Laboratory experiments were used to inform RGGI about the most efficient design for the primary auction and the secondary markets (e.g., Shobe et al. 2010). These experiments were single unit auctions but RGGI conducts multi-unit auctions. The purpose of this research is to explore the efficiency of multi-unit auction designs in the RGGI context.


In first price auctions, bidders pay their bid. Theory predicts that bidders in first price auctions of a single unit will shade their bids. In second price auctions, all winning bidders pay the same market clearing bid. Theory predicts that bids will be equal to value in second price auctions of a single unit. Theory is not so clear in first and second price multi-unit auctions (Khezr and Cumpston 2022).

Real auctions are incentivized; i.e., subject earnings are real and depend on bidding behavior. Hypothetical auctions are not incentivized; i.e., subject earnings are fixed and do not depend on bidding behavior. We expect incentivized subjects to make bids closer to theoretical predictions (noting that theoretical predictions are not sharp in multi-unit auctions) (see Mohr and Whitehead 2023).


We conducted multi-unit induced value auctions using the VECONLAB platform. In induced value auctions, subjects are told how much an item is worth and then make a bid for that item. Each subject has demand for three units and the induced value for each unit differs in each round and over 6 rounds of bidding. We have 74 subjects in four treatments:

Real, 1st price auction (n=25)
Hypothetical, 1st price auction (n=14)
Real, 2nd price auction (n=17)
Hypothetical, 2nd price auction (n=18)

The randomly assigned induced values from from $51 to $150. The means of the bids and induced values suggest that experimental subjects shade their bids in each treatment. 

Table 2. Variable means

1st price, real
1st price, hypo
2nd price, real
2nd price, hypo


Induced Value

Sample size


We use latent class regression models to explore various bidding strategies that were used by subjects. The model is:

Bid = a + b*Value + c*Hypointr

where Bid is the Bid, Value is the induced value and Hypointr is the interaction between the hypothetical treatment and the induced value.

Using naive OLS models with clustered standard errors (assuming that all subjects behave in the same way), we find no differences in bidding behavior in the first price auctions between real and hypothetical treatments (see Table 2). In the second price auction, hypothetical bids are 16% below real bids. 

Table 2. Ordinary least squares regression with clustered standard errors
(Dependent variable = Bid)

Using latent class models we identify two different types of bidding behavior for both auctions. In the first price auctions one class suggests that subjects in the hypothetical session bid their value and shade their bids by 75% in the real sessions. In the other class, all subjects shade their bids by 65%.

In the second price auctions one class suggests that real and hypothetical subjects shade their bids by 84% and 88%, respectively. In the other class, real and hypothetical subjects shade their bids by 72% and 53%, respectively.

Table 2. Latent class ordinary least squares regression with clustered standard errors
(Dependent variable = Bid)


We find some evidence that real and hypothetical bidding behavior is different in first and second price auctions. Hypotheical bids are greater than real bids in one class in the first price auction. Hypothetical bidders tend to bid their value which would lead to zero profits. In the 2nd price auctions where we might expect bidders to bid their value, subjects in both real and hypothetical auctions shade their bids. In one class of behavior, subjects in the hypothetical treatments shade their bids by significantly more than subjects in the real treatment. Latent class models can lend additional insights to experimental auction behavior. We plan to conduct more real (i.e., incentivized) first and second price auctions in the future. [2] 


Khezr, Peyman, and Anne Cumpston. “A review of multiunit auctions with homogeneous goods.” Journal of Economic Surveys 36, no. 4 (2022): 1225-1247.

Mohr, Tanga, and John C. Whitehead. “External validity of inferred attribute non-attendance: Evidence from a laboratory experiment with real and hypothetical payoffs.” Department of Economics Working Paper No. 23-05. 2023.

Shobe, William, Karen Palmer, Erica Myers, Charles Holt, Jacob Goeree, and Dallas Burtraw. “An experimental analysis of auctioning emission allowances under a loose cap.” Agricultural and Resource Economics Review 39, no. 2 (2010): 162-175.


[1] This study was funded by the Walker College of Business Dean’s Club. It was conducted with a student at Appalachian State University who was going to use it for an Honors Thesis. The student ghosted on us and we’re left with the responsibility of producing a poster for the Dean’s Club poster session (a requirement for securing Dean’s Club funding). 

[2] Updated October 21