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Game Logic is an excellent setting to study proofs-about-programs via the interpretation of those proofs as programs, because constructive proofs for games correspond to effective winning strategies to follow in response to the opponent's…

Ludics is peculiar in the panorama of game semantics: we first have the definition of interaction-composition and then we have semantical types, as a set of strategies which "behave well" and react in the same way to a set of tests. The…

Finding, counting, or determining the existence of Nash equilibria, where players must play optimally given each others' actions, are known to be computational intractable problems. We ask whether weakening optimality to the requirement…

It is known that there are uncoupled learning heuristics leading to Nash equilibrium in all finite games. Why should players use such learning heuristics and where could they come from? We show that there is no uncoupled learning heuristic…

We establish finite-time last-iterate guarantees for vanilla stochastic gradient descent in co-coercive games under noisy feedback. This is a broad class of games that is more general than strongly monotone games, allows for multiple Nash…

We refine HO/N game semantics with an additional notion of pointer (mu-pointers) and extend it to first-order classical logic with completeness results. We use a Church style extension of Parigot's lambda-mu-calculus to represent proofs of…

Under the uncoupled learning setup, the last-iterate convergence guarantee towards Nash equilibrium is shown to be impossible in many games. This work studies the last-iterate convergence guarantee in general games toward rationalizability,…

The successes of reinforcement learning in recent years are underpinned by the characterization of suitable reward functions. However, in settings where such rewards are non-intuitive, difficult to define, or otherwise error-prone in their…

Consider a game where Alice generates an integer and Bob wins if he can factor that integer. Traditional game theory tells us that Bob will always win this game even though in practice Alice will win given our usual assumptions about the…

We consider two-player games with imperfect information and the synthesis of a randomized strategy for one player that ensures the objective is satisfied almost-surely (i.e., with probability 1), regardless of the strategy of the other…

We introduce the notion of logical A-games for a fairly general class of algebras A of real truth-values. This concept generalizes the Boolean games of Harrenstein et al. as well as the recently defined Lukasiewicz games of Marchioni and…

We propose a simple yet rich model to extend the notions of Nash equilibria and correlated equilibria of strategic games to the quantum setting, in which we then study the relations between classical and quantum equilibria. Unlike the…

We consider the celebrated Blackwell Approachability Theorem for two-player games with vector payoffs. We show that Blackwell's result is equivalent, via efficient reductions, to the existence of "no-regret" algorithms for Online Linear…

Infinitely repeated games can support cooperative outcomes that are not equilibria in the one-shot game. The idea is to make sure that any gains from deviating will be offset by retaliation in future rounds. However, this model of…

Many learning algorithms are known to converge to an equilibrium for specific classes of games if the same learning algorithm is adopted by all agents. However, when the agents are self-interested, a natural question is whether agents have…

Inverse reinforcement learning (IRL) aims to infer a reward from expert demonstrations, motivated by the idea that the reward, rather than the policy, is the most succinct and transferable description of a task [Ng et al., 2000]. However,…

Recent work (Xu et al., 2020) has suggested that numeral systems in different languages are shaped by a functional need for efficient communication in an information-theoretic sense. Here we take a learning-theoretic approach and show how…

In this article, we investigate the arithmetical hierarchy from the perspective of realizability theory. An experimental observation in classical computability theory is that the notion of degrees of unsolvability for natural arithmetical…

Consider concurrent, infinite duration, two-player win/lose games played on graphs. If the winning condition satisfies some simple requirement, the existence of Player 1 winning (finite-memory) strategies is equivalent to the existence of…

Imitation learning in a high-dimensional environment is challenging. Most inverse reinforcement learning (IRL) methods fail to outperform the demonstrator in such a high-dimensional environment, e.g., Atari domain. To address this…