FORMAS DE ABORDAR LA DISCRIMINACIÓN ARBITRARIA EN LA ESCUELA

For future research we propose various directions.

• Extensions of the model: The model defined in this thesis is a starting point for research on this topic. The model incorporates the standard, most important, features of the transmission cost allocation in the electricity grid and allows for applying appropriate cost allocation rules. By means of our model we are able to analyse the currently used cascade rule, but we are not yet able to analyse new rules that incorporate the bilateral flow between voltage levels. Due to the changes on the production side of electricity, it would be interesting to have a more inclusive model, that can also be used in view of the changes in the future. In Chapter 6 we already provided some possible extensions of the model, there are however many

more extensions possible. We could for example add producers as agents. We can also endow the agents with more information, besides the demand and the voltage level, such as the peak and low demand, the demand curve, the location and so on. This extra information can provide more individual-oriented solution concepts.

• Cost allocation at the level of individual agents: In our model we consider solution concepts that allocate cost shares to unions of agents. The reason for this is that we focussed solely on one step in the currently employed cost allocation method (see Chapter 1). For future research it would be very interesting to consider solution concepts that allocate cost shares to individual agents. In this direction two approaches can be considered. First, a game or problem can be defined for each voltage level, such that the cost shares that are allocated to these levels can be allocated amongst the agents attached to a voltage level by means of other solution concepts. A second approach would be to redefine the entire model and analyse solution concepts for individual agents directly on the problem or game, without first allocating costs to unions of agents, e.g. Ramsey pricing. As there has to be a distinction between agents based on some features, these solution concepts could become quite complex as it would be desirable that this single rule satisfies many different properties. In the first approach (the currently employed approach) there is already a distinction between agents, namely the voltage level they are attached to, such that the next step would be to determine what properties solution concepts for each voltage level should obey. These solution concepts can differ per level and be based on the main cost drivers of that voltage level. Another possibility is to use the first approach, but redefine the partition of the agents, for example based on location instead of voltage level. Now the total grid costs can first be allocated to these new unions and thereafter be allocated amongst the agents within the unions.

• Cooperation between producers and consumer: In Chapter 4 and 5 we defined the problem and the cooperative game on the set of agents, representing the consumers. In the future also a problem and especially a game could be defined on the set of electricity producers, or on both. As an increasing number of consumers also become producers, referred to as prosumers, more electricity flow on a local scale occurs. In view of this it would be interesting to incorporate producers and consumers to see if a more efficient cooperation can evolve, where consumers and producers on a more local scale work together. When only considering producers, it can be analysed how to obtain an efficient collaboration between producers, that minimizes the costs.

• Introduction of producers tariff: By means of an extension of this model we could analyse the introduction of a producers tariff. Currently the producers tariff is set to zero and hence producers do not pay for the grid costs (Autoriteit Consument en Markt, 2013). We could analyse the effect on the costs for the unions and if we would use the model proposed in the previous item, including producers

and consumers, we could also consider the effect on the cooperation between these two groups.

• Ordered union values: In Chapter 5 we considered union values for the electric- ity demand game. These union values however do not incorporate the order of the partition. The ordering of the partition is implicitly modelled in the game, but not in the unions value structure or corresponding properties. For future research it would be interesting to elaborate on this chapter and define ordered union values.

• Other characteristic functions: Linking up to the above mentioned item, in Chapter 5 the game could be defined differently. A characteristic function is not uniquely defined for a problem and is dependent on the interpretation of the costs for coalitions. In our game we assumed that the electricity grid is there and each agent or union is charged for all the upstream levels it uses, even if it is the only agent or union using the grid (stand-alone costs). Most likely however, the stand- alone costs for unions or agents are in real-life lower than defined by our game. For example in the situation where the electricity does not have to come from the most upstream level, but is produced by production facilities on the same level. Hence, one possibility is to redefine the game such that for example the stand-alone costs for a union are the cost of its own level plus some extra amount to foresee in the demand of that level, but without making use of other levels. An example of a simplified version of the game is presented in Chapter 5, for which the problem as well as the game were redefined.

• Cascade rule applications: A final suggestion for future work is to consider other applications of the cascade rule. The rule has potential to be adapted for and applied to other problems. It could for example be used in the polluted river game of Ni and Wang (2007), when the demands are replaced by volumes of pollution.