Chapter 5 Game Theory Analysis of the Effect of Consignment Auctions
C. Imperfect information situation with proportional consignment auctions
Earlier, this study discussed the result of analyzing proportional consignment auctions as presented in Khezr and Mac Kenzie (2016). Now, the aforesaid assumptions will be partially adjusted to analyze equilibrium price in proportional consignment auctions.
Let’s assume that the allowances allocated to companies have become fewer than those previously allocated ( , ) and that allowances obtained from consignment auctions remain unchanged from previous consignment auctions ( ). Under these assumptions, the cost function of all companies and the allowances demand function for phase 2 are the same as formulas (6) and (7), respectively, but is replaced with
.
, (16)
→ . (17)
The following conditions apply to market clearing:
. (18)
The formula is the same as in consignment auctions.
Consequently, in proportional consignment auctions, the equilibrium price for phase 2 is determined as below, which is the same as formula (8).
,
> ,
< . (19)
Accordingly, there is also efficient distribution of allowances during proportional consignment auctions.
As is the case in consignment auctions, the most logical behavior for companies in proportional consignment auctions (phase I) is to buy more allowances than allocated when for phase I is lower than the expected equilibrium price for phase II , and buy fewer allowances when for phase I is higher than . Thus, under equilibrium of proportional consignment auctions (phase I), each company’s strategy (submitted demand function) can be similar to formula (13), as below.
. (20)
Then, is indicated as similar to formula (15) as below.
(21)
If is derived from , total demand in the market is calculated as , which leads to oversupply. Thus, if all companies submit the demand function in formula (20), the market clearing price will be lower than , and companies may bring down total cost by increasing demand.
Consequently, the demand function defined by formula (20) cannot meet equilibrium conditions.
Accordingly, let’s adjust company strategy or demand function as below, which is the same as formula (13) for consignment auctions in an uncertain situation:
. (22)
Taking into account that if all companies submit demand function as in formula (19), the market clearing price for phase I will be below , this demand function reflects upwardly adjusted demand. In this case,
is indicated as being the same as formula (15),
, (23)
and as a result market clearing conditions for phase I are indicated as . It is assumed that the market is competitive enough to make it impossible for individual companies to be able to influence the market clearing price, and under such equilibrium, companies have no incentive to engage in arbitrage trading by
changing demand volume. As a result, the phase I equilibrium price equals . Consequently, the equilibrium price for phase I in proportional consignment auctions is determined in the same way as for consignment auctions.
Point 4. In an imperfect information situation, the equilibrium price of proportional consignment auctions (phase I) becomes the expected equilibrium price for phase II. Under equilibrium, the average allowances companies win in proportional consignment auctions increase ( ) over allocated allowances ( ), with allowances won during proportional consignment auctions varying by risk-seeking propensity and the price forecast for phase II equilibrium.
In a nutshell, in proportional consignment auctions, as they are initially allocated fewer allowances than their total allowances, companies have to spend more to purchase allowances equivalent to than in consignment auctions. However, there is no difference in the basic attributes of equilibrium.
5. Sub-conclusion
According to the above analysis, if companies seek to engage in arbitrage trading in consignment auctions, this serves as price discovery. This price discovery also occurs in proportional consignment auctions, which means that the equilibrium price of (proportional) consignment auctions is the same as the price forecast for equilibrium in phase II.
However, it should be noted that if companies are unable to predict the equilibrium price for phase II, that price in consignment auctions will eventually differ from the equilibrium price for phase II. Earlier, it was mentioned that interpretation of the results of analyzing consignment auctions in an imperfect information situation, individual companies’ unsystematic forecasting errors are offset in the process of collecting demand functions, but if certain variables affecting all economic players - such as macroeconomic variables - change after phase I, this will cause a gap between equilibrium prices in phase I and phase II. Accordingly, the price discovery function demonstrated in this study’s analysis does not mean a perfect forecast on the phase II equilibrium price, but should be interpreted as the result of collected equilibrium price forecasts for phase II by participants in consignment auctions.
Thus, it can be said that as more companies join in on consignment auctions, the price discovery function of those auctions will be more meaningful. In effect, transactions are constantly in the secondary market of carbon emissions allowances in Korea. Prices occurring as a result can also be seen as reflecting the average market value of allowances estimated by companies buying and selling or their price forecasts. Thus, unless price forecasts from a majority of companies are reflected, consignment auctions will not feature meaningful price discovery.
The price discovery function of consignment auctions has a differential meaning in that consignment auctions reflect price forecasts of all companies participating in allowances trading when they are allocated allowances, or before the secondary market functions.
It was earlier discussed that the price forecasts of companies with low risk-seeking propensity had little influence on the equilibrium price for phase I. Accordingly, if risk-seeking propensity is very low, this will substantially reduce the number of companies whose price forecasts are reflected in consignment auctions. In these circumstances, the price discovery function of consignment auctions will have little meaning. According to this study’s analysis, it seems that the substantial meaning of consignment auctions hinges on companies’ risk-seeking propensity.
Key implications of the analysis were mentioned earlier, but it is also necessary to address its limitations. The analysis assumes that companies participate in consignment auctions with a speculative incentive to engage in arbitrage trading. This assumption seems to be valid as it matches the outcome of consignment auction analysis in a perfect information situation. Another strategy that companies can opt for in an imperfect information situation is to submit demand function based on their marginal abatement cost - similar to what they do in phase II. If all companies follow this strategy, the result of consignment auctions (phase I) will still reflect equilibrium for phase II.
Amid uncertainty in the market, company strategies seem largely classified into three types: 1) a speculative strategy pursuing arbitrage trading, 2) maintaining allocated allowances in an attempt to reduce cost or uncertainty, and 3) submitting demand function through estimation of marginal abatement cost. This study’s model reflected
risk-seeking propensity for the first type as and for the second type as . The third type was not reflected. A more realistic model would include all three types for analysis, but the third type was not taken into consideration, in the interest of simplifying the model. However, as equilibrium for the third type also reflects the equilibrium price for phase II, as that triggered by the pursuit of arbitrage trading, it is estimated to exert a neutral effect on equilibrium price forecasts. Consequently, the outcome of this study’s analysis would not significantly differ from the outcome of using a model that reflects all three types. The fact that the impact of arbitrage trading on consignment auctions has not been covered by previous studies makes this study particularly meaningful.
Chapter 6 Grand Summary and Conclusion