We have several emission trading schemes at work currently and one eminent market among them is the one for GHG emissions under Kyoto Protocol starting 2009. For emissions to be tradable, property right must be securely set. Especially monitoring has to be reliable and timely, and leakage must be taken care of adequately. But this in turn implies that there is a discrepancy between the period where the amount of emission is ascertained and the period during which trading is supposedly bringing efficiency to the emission reduction. For instance, EU-ETS ended its first trading period at the end of 2007, but the emission level becomes available only after several months passed. Therefore, the so-called trueup period is necessary so that trading has to go on until the emission data are finalized. In the case of EU-ETS, the emission until 2007 can be traded till April 2008, and similar trueup period is set aside for the first commitment period of Kyoto Protocol. One of the concern arising from the earlier period over the discussion of the details of Kyoto Protocol was the possible frenziness of the market in this trueup period. Because some surprise is possible as to the extent of emission, one of the Annex B (ratifying Kyoto Protocol) may find it in a severe shortage of the emission amount in the registry and has no possibility left to reduce actual emission but to purchase emission amount from the market. Upon foreseeing such a possibility, some seller nation or private brokers may find a profit taking opportunity.

There could be a multitude of issues concerning trueup period. And it fits to the game theoretical modeling of financial markets. However, the basic tool for such analysis has not been fully developed yet. There is a literature in finance known as the execution problem. There is the optimal strategy for one agent holding financial securities who has to sell off given amount of securities until a certain date in the market. For example, see Bertsimas and Lo (1998), Almgren and Chriss (2000), Huberman and Stanzl (2000), Almgren

I. Dincer et al. (eds.), Global Warming, Green Energy and Technology,

DOI 10.1007/978-1-4419-1017-2_25, © Springer Science+Business Media, LLC 2010

(2003), and Obizhaeva and Wang (2005). All who behave strategically is the very agent in their models, which are partial equilibrium analyses. Ishii (2008) introduces small traders similar to market makers in Kyle (1985), and extends the model to a general equilibrium model. In many aspects, trueup period problem fits to this problem. A further extension of the execution problem to multiagents with visible and invisible but many rational agents together with noise traders were made possible in Ishii (2008). Below, we show one attempt of such adaptation.

Let us suppose there are n Annex B nations falling short of the assigned amount. Other Annex B nations are already safe in the sense that they are sure to achieve the assigned amount and leftover emissions can be carried to become emissions for the next commitment period (provided that such period exists), called banking. Still there are many other market participants. If an Annex B party's holding of emissions falls short of the assigned amount, then the penalty is of 30% more of the shortage being subtracted from the assigned amount of the next commitment period. If the other party holds the emission at the end period, we assume that it is treated as if it is a part of emission belonging to the nation to which they belong to.

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