PhD Vacancy: Game Theory Optimisation modelling applied to climate change questions

To answer research questions surrounding climate change, effective modelling of future energy markets is required. Such models provide insights from planning, operations and regulatory perspectives. Profit-maximising generators use them to gain insights on possible trading strategies while policy-makers use them to analyse consumer costs and carbon emissions for different proposed policy mechanisms.

Game Theory Optimisation (GTO) is a developing methodology that can be used to model energy markets. GTO involves solving multiple constrained optimisation problems in equilibrium. Each optimisation problem represents a market participant optimising their individual decisions whilst accounting for the decisions of all other market participants. GTO models can take many forms including: linear, non-linear, stochastic and integer programming, in addition to equilibrium modelling.

Potential Project #1

When modelling electricity markets, GTO models typically assume that decisions are made in a risk-neutral framework [1]. A notable exception can be found in [2].  However, risk-neutral decision making does not match with the reality of modern electricity markets. When making decisions, electricity market participants are greatly influenced by market uncertainties, for instance, prices, demand and the availability of renewables. Such uncertainties mean an uncertainty in profit outcomes including, potentially, outcomes that lead to substantial losses. Seeking to avoiding such losses leads to risk averse decision making.

For instance, in the new Irish electricity market, energy generators submit bids on the amount of electricity they plan to generate, one day in advance. If they overestimate their generation, they face financial penalties. For generators who produce electricity from wind, this is particularly risky as wind levels are difficult to forecast. Consequently, such generators are more likely to make risk-averse decisions. In addition, electricity generators also make long-term decisions, for instance, whether to invest in a generating unit or not. Similarly, generators may also wish to consider investing a power-to-gas facility. A power-to-gas unit enables generators to use electricity to produce natural gas (via electrolysis) when electricity prices are cheap. This gas could be stored and then used to produce electricity when electricity prices are higher, thus making a profit for the generators.


Long-term investment decisions require significant capital with revenues from the investments not coming until after the facilities are build. With revenues deepening on uncertain market parameters, these decisions are inherently risky for (potential) electricity market participants.


This PhD project will study how to model risk-averse decisions making (both short and long-term decisions) in an electricity market where market power is present. GTO models, such as stochastic MCPs [1], will be considered in combination with risk measures such as Conditional Value at Risk (CVaR) [2].

Potential Project #2

Sellers in a market have market power when they can strategically maximise their profits by influencing the level of demand through the selling price they set. Such behaviour often occurs in modern wholesale electricity markets. Game Theory Optimisation (GTO) can model market power in electricity markets.   Such models in the literature typically assume that either all electricity generators have market power [3] or else none do [4]. However, in reality, it is more likely that some larger electricity generators have market power while smaller generators do not [1]. Such a market structure is challenging to model mathematically, particularly when both long-term (e.g., investment into generation) and short-term (e.g., operation of generation) decisions need to be considered. Furthermore, when these decisions are made using uncertain information about the future, e.g., weather patterns, stochasticity needs to be incorporated.

This PhD project will address the challenge of modelling modern electricity markets that exhibit market power behaviour with the aim of answering several climate action research questions. For instance, what are the optimal future strategies for energy firms and do these align with nations’ climate reduction targets? What effect does will a power-to-gas facility have on consumer costs and carbon emissions? Can micro- and self-generation help countries meet carbon reduction targets?


Game Theory Optimisation techniques such as stochastic Equilibrium Problems with Equilibrium Constraints (s-EPECs), stochastic Mathematical Programs with Equilibrium Constraints (s-MPECs) and Mixed Integer Programming (MIP) will be considered [5].


Stipend: €18,000 per annum in addition to research costs


For further details please contact: Dr. Mel Devine (


Mel Devine, PhD,
Ad Astra Fellow and Assistant Professor,
College of Business,
Energy Institute,
University College Dublin,
Belfield, Dublin 4,



[1] Devine, M.T., Bertsch, V., (2018), Examining the benefits of load shedding strategies using a stochastic mixed complementarity equilibrium model. European Journal of Operational Research, 267, 643 – 658.

[2] Egging, R., Pichler, A., Kalvø, Ø. I., & Walle–Hansen, T. M. (2017). Risk aversion in imperfect natural gas markets. European Journal of Operational Research259(1), 367-383.

[3] Ye, Y., Papadaskalopoulos, D., & Strbac, G. (2017). Investigating the ability of demand shifting to mitigate electricity producers’ market power. IEEE Transactions on Power Systems33(4), 3800-3811.

[4] Tuohy, A., Meibom, P., Denny, E., & O’Malley, M. (2009). Unit commitment for systems with significant wind penetration. IEEE Transactions on power systems24(2), 592-601.

[5] Gabriel, S. A., Conejo, A. J., Fuller, J. D., Hobbs, B. F., & Ruiz, C. (2012). Complementarity modeling in energy markets (Vol. 180). Springer Science & Business Media.

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