Léonard Brice

Léonard Brice

theoretical computer science and game theory

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About Me

I am a researcher in theoretical computer science, currently post-doc at Institute of Science and Technology Austria, in the group lead by Thomas A. Henzinger. I hold a Master's degree from ENS Paris-Saclay (France), and a PhD from Université libre de Bruxelles (Belgium), realised under the supervision of Jean-François Raskin and Marie van den Bogaard. My research focuses on game theory, with applications to formal verification and synthesis of reactive systems, secure protocols, and more generally multi-agent systems.

Pronouns: He/him

Reach out to me in: French (native), English, Spanish/Castilian, Dutch, German

Research & Publications

My research focuses on games. Games are a convenient abstract model for the interaction of several agents with different objectives. In computer science, they are typically used to model the interaction between a computer-controlled system and its environment: if one wishes to program the system so that it enforces some property whatever happens in the environment, that challenge amounts to searching for a winning strategy in the corresponding game. I usually more sophisticated settings, with more than two players, in order to model multi-agent systems.

My PhD thesis: L. Brice, Equilibria in Multiplayer Graph Games: An Algorithmic Study (ULB)

Team-versus-one games

Recently, my work focus on settings in which a team of players, for example representing a decentralised computer-controlled system, competes against an environment. Those players are limited in how they can communicate, and in particular, in settings in which randomised strategies are necessary to maximise their chances (think of rock-paper-scissors), they cannot resort to a common private source of randomness. This contrasts, for example, with the semantics of logics such as Probabilistic (or Randomised) Alternating Temporal Logic (PATL, RATL), in which one can express the fact that a given coalition can enforce a given specification, but implicitely assuming that they can randomise jointly, which amounts to merging them into a single player. We defined an extension of those logics, Individually Randomised Alternating Temporal Logic (IRATL), and showed that a fragment of it, in concurrent graph games, is decidable in PSPACE. We also proposed a formalism called dicey games, to capture setting in which players may resort to sources of randomness that are shared, but only among a given subset of the team. We studied such games in a one-shot setting.

Equilibria

When studying multiplayer games, where the players' objectives may overlap, a natural question is to ask whether there exists a stable situation, where no player has an incentive to deviate. Such situations are called equilibria.

Nash equilibria

The most classical notion of equilibrium is the Nash equilibrium, where no player can improve their outcome by changing their own strategy, if the other players keep their strategies unchanged. Nash equilibria were extensively studied in the literature. However, I contributed to this line of work with results about the complexity of Nash equilibria in energy and in discounted-sum games (MFCS 2023). More recently, we studied the complexity of stationary Nash equilibria in stochastic games, by proposing a new approximation algorithm (FSTTCS 2025).

Subgame-perfect equilibria

An significant part of my PhD focused on a refinement of Nash equilibria, called subgame-perfect equilibria (SPEs). Those are defined as Nash equilibria with the additional requirement that the strategies that the players plan to follow, after any possible history of the game, must also form a Nash equilibrium: the players are then not allowed to threaten each other with irrational behaviour. With J.-F. Raskin and M. van den Bogaard, we defined the negotiation function (LMCS 2023), a conceptual and algorithmic tool to characterise the set of SPE outcomes in a game. That lead to results about the complexity of SPEs in parity games (CSL 2022) and mean-payoff games (ICALP 2022). We also studied related rational verification problems in those games, as well as in energy and discounted-sum games (MFCS 2023).

Strong secure equilibria

With my PhD advisors and in collaboration with M. Sassolas and G. Scerri, we studied possible applications of game theory to the design of secure communication protocols. In that context, we introduced a new notion of equilibrium, called strong secure equilibrium (CSF 2025). A strong secure equilibrium is a strategy profile from which no coalition of players can deviate in a way that decreases the payoff of another player, without decreasing the payoff of any player in the coalition. We studied the complexity of those problems in multiplayer games with payoffs defined with a parity condition, or with an external parity automaton.

Risk-sensitive equilibria

In collaboration with T. Henzinger and K. Thejaswini, we studied a new notion of equilibrium, called risk-sensitive equilibrium (MFCS 2025). This concept is relevant in stochastic games, or when players are allowed to use randomised strategies. In such situation, one usually considers the expected payoff of a player, but that does not capture the risk that the player is willing to take. Risk-sensitive equilibria are defined from a partition of players, assuming that some are pessimists, and some optimists; they are strategy profiles from which no pessimist (resp. optimist) can deviate and improve the least (resp. greatest) payoff they get with positive probability.

Others

Robbins' problem

Robbins' problem is a famous open problem, one of the variants of the secretary problem. We used a Markov decision process approach to compute numerically better values than those formerly known (in Principles of Verification: Cycling the Probabilistic Landscape).

Some other open problems I am interested in:

Teaching

I have been teaching assistant of the following courses:

Contact

You have questions on my works, or you want to start a collaboration? Feel free to reach out!