Simulation Results
SIMULATIONS OF THE PRIMARY MARKET
Uniform Auction Price vs Second Price Auction:
We observe in the output plots that the number of allowances unsold from auction to auction is roughly the same for both auction price mechanisms - this makes sense, as allowance requirements do not vary with the price. The price distribution is more interesting - as one might expect, we see a much more diverse set of prices with the second price auction mechanism, with a much higher ceiling and mean. The prices may not be realistic, but the effect is - given that agents bid at most their true value with the assurance that they are likely to pay a significantly lower price than their bid, bidding prices would be higher and more diverse.
Results of Testing Different Variations:
As shown in the table above, tweaking each variable slightly while holding the rest constant mostly produces results that are intuitive. A higher allowance count translates to lower per-allowance prices and an increase in the rate of allowance reduction per annum leads to higher overall prices.
Mechanism II (Second Price Auction), as expected, creates an environment where prices are driven higher, with a larger standard deviation - this is especially significant in an environment such as the one we created in our model, where we intentionally allow for a large band of value profiles to be generated among the agents.
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The results of raising the reserve prices are slightly less intuitive, however, and might be an emergent property of the way our simulation model was designed, as opposed to the behavior you might expect to find in an actual market. We could not find a feasible way to implement the models to test limiting behavior, so it may well be a result of the distributions used to generate some initial parameters. Since agent strategies are held constant, however, with some caution, we might be able to make several interesting propositions.
For example, a higher price floor may encourage more agents to vote closer to the floor in some situations, as the mean prices appear to be either close or lower with a lower reserve price. Standard deviation is also much smaller. In real life, this could be an interesting area of psychology or strategy to follow up on, but we refrain from claiming that this is anything concrete.
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SIMULATIONS OF THE SECONDARY MARKET
Followed by a primary market cleared under Mechanism I (uniform clearing price), we implement a secondary market that allows companies who do not manage to buy all allowances they need in the primary market to trade with traders, who bid to trade in the secondary market in order to make a profit. The above two graphs show the clearing prices distribution (left) and trading volumes (right) in the secondary market.
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In comparison with the metrics observed in the primary market, the secondary trading prices are relatively higher. We expect it to be the outcome because the incentive for traders to participate in the cap and trade is to make a profit by reselling allowances in the secondary market, thus driving up the secondary price, compared to the primary counterpart.
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The trading volume in the secondary market is much smaller than that in the primary market. The rationale is that there are much more companies than traders in the allowances trading. Given all agents' wealth follow the same distribution regardless of the agent type, there are more allowances in the hand of companies than allowances in the hand of traders.
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We also keep track of the number of companies who manage to buy all of their required allowances before and after the secondary market and observe a non-trivial change. (The example simulation posted on the Github shows the number going from 0 to 8.) Going forward, we can improve the efficiency of the secondary market by either refining our clearing mechanism for the secondary market or repeating the clearing process multiple times until all the allowances in the hand of the traders are sold out.