Artificial intelligence methods in the CO 2 permission market simulation Jarosław Stańczak *, Piotr Pałka **, Zbigniew Nahorski * * Systems Research Institute, Polish Academy of Sciences ** Institute of Control and Computation Engineering, Warsaw University of Technology

Introduction Observations of climate change indicate that global climate warming is becoming a real threat for human civilization. Many researchers claim that emission of CO 2 and other greenhouse gases is responsible for this. Thus, great efforts are being made to reduce these emissions. An accepted method to make this burden lighter is to implement a system of emission limits and tradable emission permits.

The Kyoto Protocol and the market of CO 2 emission permits This approach to emission reduction has been accepted by many countries of the world under the Kyoto Protocol. Countries participating in an emission permits system have limitations imposed on their emissions. If the limitations are too low for some countries, they can buy permits from other countries, or reduce their emissions by applying new technologies to produce „clean” energy. An accepted solution should depend on their decisions, based on thorough economic optimization. This economic optimization is in general quite difficult problem, thus artificial intelligence methods like evolutionary algorithms or multi-agent systems are applied to solve it. To make an efficient optimization it is necessary to build a proper model of the emission permits market.

A standard static model of the permission trade - central planner C i (x i ) – the costs of decreasing emission from an initial value x 0i down to x i ; y i – the number of acquired permits; K i – Kyoto target for participant i; x i – emission of participant i ; n – the number of participants.

Limitations of the central planner model Standard model does not allow free transactions between participants; Calculated quantities of permits and money should be compulsory trade Standard model does not calculate prices and quantities of conducted transactions; Price negotiations are not considered in standard model; Preferences of participants are not considered in standard model. The central planner may not know all parameters of cost functions with high accuracy.

New dynamic model Introduces transactions between participants; Introduces negotiations of transaction prices and amounts of traded permits; Participants independently make decisions to make contracts on the basis of negotiated prices; Participants do not know their optimal price level, but probably better know their cost functions than a central planner; The number of transactions is not known in advance; Profitable transactions move market toward equilibrium; It is possible to apply agent-based methods to simulate such a market model.

Dynamic model for multi-agent system G i – maximum reduction in the total costs of decreasing emissions resulting from trading; T – number of transactions conducted; C ji (x ji ) – the costs of decreasing emissions in region i from initial value x 0i to value x ji after j transactions; K i – Kyoto target for country i; n – number of participants; x ji – emissions of participant i after j transactions; s ji – the number of units of emissions acquired by participant i in transaction j; s max – the maximum number of units allowed to be traded in one transaction; p ji – price of permits bought/sold by participant i in transaction j.

Applied AI methods of permission market analysis and simulation - specialized evolutionary algorithm - multi-agent system

AI methods of permission market simulation - specialized evolutionary algorithm 1. Random initialization of the population of solutions. 2. Reproduction and modification of solutions using genetic operators. 3. Evaluation of the solutions obtained. 4. Selection of individuals for the next generation. 5. If a stop condition is not satisfied, go to 2. Algorithm 1. Standard evolutionary algorithm. 1. Initialization of individuals (agents). 2. Modification of individuals’ states using specialized operators. 3. Evaluation of new individuals’ states. 4. If a stop condition is not satisfied, go to 2. Algorithm 2. Specialized evolutionary method for market simulation.

AI methods of permission market simulation - multi-agent system System composed of two or more autonomous software agents; Agents communicate with each other and striving for their own purposes; Multi-agent system should achieve some overarching objectives; The multi-agent system does not implement these objectives directly, but through individual objectives of each of the agents and their interactions; Each agent represents single party, guided by its own interests; Agent comes to interact with others; Agent’s motivation is the desire to achieve certain gains from the exchange of permits;

Problem encoding – information required by agents/individuals The marginal cost associated with a given number of permits possessed by the country (shadow price); The real current price of a permit for sale/purchase; The real current value of a permit for sale/purchase; Current number of units for sale/purchase; The net number of units sold/purchased; Current emissions level; Previous emissions level (before the present transaction); Present and previous value of the objective function.

Genetic operators – models of trade methods Bilateral trade - two randomly chosen countries conduct negotiations and if they agree, the tran s action is done ; Tender - the country considered offers a number of permits for sale, other countries offer to buy, the best option is chosen and the contract is d one.

Multi-agent platform – roles and behaviors of agents applied Roles of negotiating agent and the Morris Column agent ; Bilateral trades and t ender behaviors implemented; The bilateral trade and tender were performed using specialized roles and behaviors.

The data applied in computer simulations Cost functions CANZ – Canada, Australia, New Zealand; EEFSU – East Europe and Former Soviet Union. Shadow price functions

The central planner results

Bilateral trade results Results of simulation using multi-agent system. Results of simulation using evolutionary method.

Tender trade results Results of simulation using multi-agent system. Results of simulation using evolutionary method.

Transaction prices in bilateral contracts Results of simulation using multi-agent system. Results of simulation using evolutionary method.

Conclusions Results of emission market simulation obtained using considered AI methods are very similar; AI methods are able to deal with complicated economic systems with many interactions between their elements and participants; Economic systems can be quite easily modeled, simulated and controlled using AI systems; Future work will concentrate on introducing different kinds of transactions between participants and uncertainty of reported emissions.