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Game Theory is a long standing method of analysing the way in which participants interact within a market space, recently agent based approaches have been utilised to understand even more about these interactions. This agent based approach can be utilised to understand very complex market designs, such as those for an electricity market, with there being potential room for identifying potential problems with market power. By looking at the way in which a set of intelligent agents form optimal bids in a constrained electricity market, it is possible to identify where potential weaknesses are in the market design. Agents simulate the market repeatedly, aiming to find the Nash-Equilibrium point for the the market at the given time step. By predicting other agents reactionary moves, they can identify the best course of action, with this information it is possible to identify the contributing factors that have caused the agent's choice of action. As such, this work sets out to identify where and when an electricity market can be forced into undesirable situations, only as a result of optimised bidding and existing market constraints.