arXiv subjects

Julian Gutierrez

Publications and source records attributed to Julian Gutierrez.

At least 19 recordsLinked to original sources

arXiv2026

Parametric and Generative Forecasts of EPEX Day-Ahead Energy Market Curves

We propose two methodologies for modelling aggregated supply and demand curves in the EPEX SPOT Day-Ahead market, emphasizing generative models as a way to recover distributional variability. The first is a low-dimensional parametric representation that yields deterministic point forecasts; the second is a high-dimensional order-level representation that samples from a conditional distribution of plausible curves. Both model the full curve structure, enabling the analysis of price sensitivity, volume sensitivity, and price impact. The parametric representation uses plateau levels, elastic-region boundaries, and polynomial coefficients, forecast with eXtreme Gradient Boosting. The main contribution is the generative representation, which uses price arrivals and volume-increment marks and is implemented with conditional Denoising Diffusion Probabilistic Models. Using French EPEX data from 2021 to 2024, we evaluate both approaches through curve reconstruction and a price-maker storage optimization problem. The parametric implementation provides a deterministic reference, while the diffusion-based implementation produces distributions of plausible curves and achieves higher realized profits and smaller gaps to an oracle benchmark in the storage application.

cs.LG↗

arXiv2025

A Co-evolutionary Approach for Heston Calibration

We evaluate a co-evolutionary calibration framework for the Heston model in which a genetic algorithm (GA) over parameters is coupled to an evolving neural inverse map from option surfaces to parameters. While GA-history sampling can reduce training loss quickly and yields strong in-sample fits to the target surface, learning-curve diagnostics show a widening train--validation gap across generations, indicating substantial overfitting induced by the concentrated and less diverse dataset. In contrast, a broad, space-filling dataset generated via Latin hypercube sampling (LHS) achieves nearly comparable calibration accuracy while delivering markedly better out-of-sample stability across held-out surfaces. These results suggest that apparent improvements from co-evolutionary data generation largely reflect target-specific specialization rather than a more reliable global inverse mapping, and that maintaining dataset diversity is critical for robust amortized calibration.

q-fin.PR↗

arXiv2023

Characterising and Verifying the Core in Concurrent Multi-Player Mean-Payoff Games (Full Version)

Concurrent multi-player mean-payoff games are important models for systems of agents with individual, non-dichotomous preferences. Whilst these games have been extensively studied in terms of their equilibria in non-cooperative settings, this paper explores an alternative solution concept: the core from cooperative game theory. This concept is particularly relevant for cooperative AI systems, as it enables the modelling of cooperation among agents, even when their goals are not fully aligned. Our contribution is twofold. First, we provide a characterisation of the core using discrete geometry techniques and establish a necessary and sufficient condition for its non-emptiness. We then use the characterisation to prove the existence of polynomial witnesses in the core. Second, we use the existence of such witnesses to solve key decision problems in rational verification and provide tight complexity bounds for the problem of checking whether some/every equilibrium in a game satisfies a given LTL or GR(1) specification. Our approach is general and can be adapted to handle other specifications expressed in various fragments of LTL without incurring additional computational costs.

cs.GT↗

arXiv2023

Incentive Engineering for Concurrent Games

We consider the problem of incentivising desirable behaviours in multi-agent systems by way of taxation schemes. Our study employs the concurrent games model: in this model, each agent is primarily motivated to seek the satisfaction of a goal, expressed as a Linear Temporal Logic (LTL) formula; secondarily, agents seek to minimise costs, where costs are imposed based on the actions taken by agents in different states of the game. In this setting, we consider an external principal who can influence agents' preferences by imposing taxes (additional costs) on the actions chosen by agents in different states. The principal imposes taxation schemes to motivate agents to choose a course of action that will lead to the satisfaction of their goal, also expressed as an LTL formula. However, taxation schemes are limited in their ability to influence agents' preferences: an agent will always prefer to satisfy its goal rather than otherwise, no matter what the costs. The fundamental question that we study is whether the principal can impose a taxation scheme such that, in the resulting game, the principal's goal is satisfied in at least one or all runs of the game that could arise by agents choosing to follow game-theoretic equilibrium strategies. We consider two different types of taxation schemes: in a static scheme, the same tax is imposed on a state-action profile pair in all circumstances, while in a dynamic scheme, the principal can choose to vary taxes depending on the circumstances. We investigate the main game-theoretic properties of this model as well as the computational complexity of the relevant decision problems.

cs.GT↗

arXiv2023

Designing Equilibria in Concurrent Games with Social Welfare and Temporal Logic Constraints

In game theory, mechanism design is concerned with the design of incentives so that a desired outcome of the game can be achieved. In this paper, we explore the concept of equilibrium design, where incentives are designed to obtain a desirable equilibrium that satisfies a specific temporal logic property. Our study is based on a framework where system specifications are represented as temporal logic formulae, games as quantitative concurrent game structures, and players' goals as mean-payoff objectives. We consider system specifications given by LTL and GR(1) formulae, and show that designing incentives to ensure that a given temporal logic property is satisfied on some/every Nash equilibrium of the game can be achieved in PSPACE for LTL properties and in NP/{\Sigma}P 2 for GR(1) specifications. We also examine the complexity of related decision and optimisation problems, such as optimality and uniqueness of solutions, as well as considering social welfare, and show that the complexities of these problems lie within the polynomial hierarchy. Equilibrium design can be used as an alternative solution to rational synthesis and verification problems for concurrent games with mean-payoff objectives when no solution exists or as a technique to repair concurrent games with undesirable Nash equilibria in an optimal way.

cs.LO↗

arXiv2023

Machine Learning architectures for price formation models with common noise

We propose a machine learning method to solve a mean-field game price formation model with common noise. This involves determining the price of a commodity traded among rational agents subject to a market clearing condition imposed by random supply, which presents additional challenges compared to the deterministic counterpart. Our approach uses a dual recurrent neural network architecture encoding noise dependence and a particle approximation of the mean-field model with a single loss function optimized by adversarial training. We provide a posteriori estimates for convergence and illustrate our method through numerical experiments.

math.OC↗

arXiv2023

Principal-Agent Boolean Games

We introduce and study a computational version of the principal-agent problem -- a classic problem in Economics that arises when a principal desires to contract an agent to carry out some task, but has incomplete information about the agent or their subsequent actions. The key challenge in this setting is for the principal to design a contract for the agent such that the agent's preferences are then aligned with those of the principal. We study this problem using a variation of Boolean games, where multiple players each choose valuations for Boolean variables under their control, seeking the satisfaction of a personal goal, given as a Boolean logic formula. In our setting, the principal can only observe some subset of these variables, and the principal chooses a contract which rewards players on the basis of the assignments they make for the variables that are observable to the principal. The principal's challenge is to design a contract so that, firstly, the principal's goal is achieved in some or all Nash equilibrium choices, and secondly, that the principal is able to verify that their goal is satisfied. In this paper, we formally define this problem and completely characterise the computational complexity of the most relevant decision problems associated with it.

cs.GT↗

arXiv2023

k-Prize Weighted Voting Games

We introduce a natural variant of weighted voting games, which we refer to as k-Prize Weighted Voting Games. Such games consist of n players with weights, and k prizes, of possibly differing values. The players form coalitions, and the i-th largest coalition (by the sum of weights of its members) wins the i-th largest prize, which is then shared among its members. We present four solution concepts to analyse the games in this class, and characterise the existence of stable outcomes in games with three players and two prizes, and in games with uniform prizes. We then explore the efficiency of stable outcomes in terms of Pareto optimality and utilitarian social welfare. Finally, we study the computational complexity of finding stable outcomes.

cs.GT↗

arXiv2023

Cooperative Concurrent Games

In rational verification, the aim is to verify which temporal logic properties will obtain in a multi-agent system, under the assumption that agents ("players") in the system choose strategies for acting that form a game theoretic equilibrium. Preferences are typically defined by assuming that agents act in pursuit of individual goals, specified as temporal logic formulae. To date, rational verification has been studied using non-cooperative solution concepts - Nash equilibrium and refinements thereof. Such non-cooperative solution concepts assume that there is no possibility of agents forming binding agreements to cooperate, and as such they are restricted in their applicability. In this article, we extend rational verification to cooperative solution concepts, as studied in the field of cooperative game theory. We focus on the core, as this is the most fundamental (and most widely studied) cooperative solution concept. We begin by presenting a variant of the core that seems well-suited to the concurrent game setting, and we show that this version of the core can be characterised using ATL*. We then study the computational complexity of key decision problems associated with the core, which range from problems in PSPACE to problems in 3EXPTIME. We also investigate conditions that are sufficient to ensure that the core is non-empty, and explore when it is invariant under bisimilarity. We then introduce and study a number of variants of the main definition of the core, leading to the issue of credible deviations, and to stronger notions of collective stable behaviour. Finally, we study cooperative rational verification using an alternative model of preferences, in which players seek to maximise the mean-payoff they obtain over an infinite play in games where quantitative information is allowed.

cs.GT↗

arXiv2022

A random-supply Mean Field Game price model

We consider a market where a finite number of players trade an asset whose supply is a stochastic process. The price formation problem consists of finding a price process that ensures that when agents act optimally to minimize their trading costs, the market clears, and supply meets demand. This problem arises in market economies, including electricity generation from renewable sources in smart grids. Our model includes noise on the supply side, which is counterbalanced on the consumption side by storing energy or reducing the demand according to a dynamic price process. By solving a constrained minimization problem, we prove that the Lagrange multiplier corresponding to the market-clearing condition defines the solution of the price formation problem. For the linear-quadratic structure, we characterize the price process of a continuum population using optimal control techniques. We include numerical schemes for the price computation in the finite and infinite games, and we illustrate the model using real data.

math.AP↗

arXiv2022

On the Complexity of Rational Verification

Rational verification refers to the problem of checking which temporal logic properties hold of a concurrent multiagent system, under the assumption that agents in the system choose strategies that form a game-theoretic equilibrium. Rational verification can be understood as a counterpart to model checking for multiagent systems, but while classical model checking can be done in polynomial time for some temporal logic specification languages such as CTL, and polynomial space with LTL specifications, rational verification is much harder: the key decision problems for rational verification are 2EXPTIME-complete with LTL specifications, even when using explicit-state system representations. Against this background, our contributions in this paper are threefold. First, we show that the complexity of rational verification can be greatly reduced by restricting specifications to GR(1), a fragment of LTL that can represent a broad and practically useful class of response properties of reactive systems. In particular, we show that for a number of relevant settings, rational verification can be done in polynomial space and even in polynomial time. Second, we provide improved complexity results for rational verification when considering players' goals given by mean-payoff utility functions; arguably the most widely used approach for quantitative objectives in concurrent and multiagent systems. Finally, we consider the problem of computing outcomes that satisfy social welfare constraints. To this end, we consider both utilitarian and egalitarian social welfare and show that computing such outcomes is either PSPACE-complete or NP-complete.

cs.LO↗

arXiv2022

A Variational Approach For Price Formation Models In One Dimension

In this paper, we study a class of first-order mean-field games (MFGs) that model price formation. Using Poincar{é} Lemma, we eliminate one of the equations and obtain a variational problem for a single function. This variational problem offers an alternative approach for the numerical solution of the original MFGs system. We show a correspondence between solutions of the MFGs system and the variational problem. Moreover, we address the existence of solutions for the variational problem using the direct method in the calculus of variations. We end the paper with numerical results for a linear-quadratic model.

math.AP↗

arXiv2022

The Potential Method For Price-Formation Models

We consider the mean-field game price formation model introduced by Gomes and Saúde. In this MFG model, agents trade a commodity whose supply can be deterministic or stochastic. Agents maximize profit, taking into account current and future prices. The balance between supply and demand determines the price. We introduce a potential function that converts the MFG into a convex variational problem. This variational formulation is particularly suitable for machine learning approaches. Here, we use a recurrent neural network to solve this problem. In the last section of the paper, we compare our results with known analytical solutions.

math.NA↗

arXiv2021

A duality approach to a price formation MFG model

We study the connection between the Aubry-Mather theory and a mean-field game (MFG) price-formation model. We introduce a framework for Mather measures that is suited for constrained time-dependent problems in R. Then, we propose a variational problem on a space of measures, from which we obtain a duality relation involving the MFG problem examined in [36].

math.AP↗

arXiv2021

Rational Verification for Probabilistic Systems

Rational verification is the problem of determining which temporal logic properties will hold in a multi-agent system, under the assumption that agents in the system act rationally, by choosing strategies that collectively form a game-theoretic equilibrium. Previous work in this area has largely focussed on deterministic systems. In this paper, we develop the theory and algorithms for rational verification in probabilistic systems. We focus on concurrent stochastic games (CSGs), which can be used to model uncertainty and randomness in complex multi-agent environments. We study the rational verification problem for both non-cooperative games and cooperative games in the qualitative probabilistic setting. In the former case, we consider LTL properties satisfied by the Nash equilibria of the game and in the latter case LTL properties satisfied by the core. In both cases, we show that the problem is 2EXPTIME-complete, thus not harder than the much simpler verification problem of model checking LTL properties of systems modelled as Markov decision processes (MDPs).

cs.MA↗

arXiv2021

Equilibrium Design for Concurrent Games

In game theory, mechanism design is concerned with the design of incentives so that a desired outcome of the game can be achieved. In this paper, we study the design of incentives so that a desirable equilibrium is obtained, for instance, an equilibrium satisfying a given temporal logic property -- a problem that we call equilibrium design. We base our study on a framework where system specifications are represented as temporal logic formulae, games as quantitative concurrent game structures, and players' goals as mean-payoff objectives. In particular, we consider system specifications given by LTL and GR(1) formulae, and show that implementing a mechanism to ensure that a given temporal logic property is satisfied on some/every Nash equilibrium of the game, whenever such a mechanism exists, can be done in PSPACE for LTL properties and in NP/$Σ^{P}_{2}$ for GR(1) specifications. We also study the complexity of various related decision and optimisation problems, such as optimality and uniqueness of solutions, and show that the complexities of all such problems lie within the polynomial hierarchy. As an application, equilibrium design can be used as an alternative solution to the rational synthesis and verification problems for concurrent games with mean-payoff objectives whenever no solution exists, or as a technique to repair, whenever possible, concurrent games with undesirable rational outcomes (Nash equilibria) in an optimal way.

cs.GT↗

arXiv2021

Multi-Agent Reinforcement Learning with Temporal Logic Specifications

In this paper, we study the problem of learning to satisfy temporal logic specifications with a group of agents in an unknown environment, which may exhibit probabilistic behaviour. From a learning perspective these specifications provide a rich formal language with which to capture tasks or objectives, while from a logic and automated verification perspective the introduction of learning capabilities allows for practical applications in large, stochastic, unknown environments. The existing work in this area is, however, limited. Of the frameworks that consider full linear temporal logic or have correctness guarantees, all methods thus far consider only the case of a single temporal logic specification and a single agent. In order to overcome this limitation, we develop the first multi-agent reinforcement learning technique for temporal logic specifications, which is also novel in its ability to handle multiple specifications. We provide correctness and convergence guarantees for our main algorithm - ALMANAC (Automaton/Logic Multi-Agent Natural Actor-Critic) - even when using function approximation. Alongside our theoretical results, we further demonstrate the applicability of our technique via a set of preliminary experiments.

cs.AI↗

arXiv2020

Automated Temporal Equilibrium Analysis: Verification and Synthesis of Multi-Player Games

In the context of multi-agent systems, the rational verification problem is concerned with checking which temporal logic properties will hold in a system when its constituent agents are assumed to behave rationally and strategically in pursuit of individual objectives. Typically, those objectives are expressed as temporal logic formulae which the relevant agent desires to see satisfied. Unfortunately, rational verification is computationally complex, and requires specialised techniques in order to obtain practically useable implementations. In this paper, we present such a technique. This technique relies on a reduction of the rational verification problem to the solution of a collection of parity games. Our approach has been implemented in the Equilibrium Verification Environment (EVE) system. The EVE system takes as input a model of a concurrent/multi-agent system represented using the Simple Reactive Modules Language (SRML), where agent goals are represented as Linear Temporal Logic (LTL) formulae, together with a claim about the equilibrium behaviour of the system, also expressed as an LTL formula. EVE can then check whether the LTL claim holds on some (or every) computation of the system that could arise through agents choosing Nash equilibrium strategies; it can also check whether a system has a Nash equilibrium, and synthesise individual strategies for players in the multi-player game. After presenting our basic framework, we describe our new technique and prove its correctness. We then describe our implementation in the EVE system, and present experimental results which show that EVE performs favourably in comparison to other existing tools that support rational verification.

cs.LO↗