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In many repeated auction settings, participants care not only about how frequently they win but also how their winnings are distributed over time. This problem arises in various practical domains where avoiding congested demand is crucial,…

We present tropical games, a generalization of combinatorial min-max games based on tropical algebras. Our model breaks the traditional symmetry of rational zero-sum games where players have exactly opposed goals (min vs. max), is more…

Shortest-path games are two-player zero-sum games played on a graph equipped with integer weights. One player, that we call Min, wants to reach a target set of states while minimising the total weight, and the other one has an antagonistic…

Consider the following one-player game. Take a well-formed sequence of opening and closing brackets. As a move, the player can pair any opening bracket with any closing bracket to its right, erasing them. The goal is to re-pair (erase) the…

In this work, we establish the first separation between computation with bounded and unbounded space, for problems with short outputs (i.e., working memory can be exponentially larger than output size), both in the classical and the quantum…

Understanding the properties of games played under computational constraints remains challenging. For example, how do we expect rational (but computationally bounded) players to play games with a prohibitively large number of states, such…

Computing lower and upper bounds on the competitive ratio of online algorithms is a challenging question: For a minimization combinatorial problem, proving a competitive ratio for a given algorithm leads to an upper bound. However computing…

While game theory is widely used to model strategic interactions, a natural question is where do the game representations come from? One answer is to learn the representations from data. If one wants to learn both the payoffs and the…

There are two well-known sufficient conditions for Nash equilibrium in two-player games: mutual knowledge of rationality (MKR) and mutual knowledge of conjectures. MKR assumes that the concept of rationality is mutually known. In contrast,…

In an iterated game between two players, there is much interest in characterizing the set of feasible payoffs for both players when one player uses a fixed strategy and the other player is free to switch. Such characterizations have led to…

In two-player zero-sum games, the learning dynamic based on optimistic Hedge achieves one of the best-known regret upper bounds among strongly-uncoupled learning dynamics. With an appropriately chosen learning rate, the social and…

Adversarial self-play in two-player games has delivered impressive results when used with reinforcement learning algorithms that combine deep neural networks and tree search. Algorithms like AlphaZero and Expert Iteration learn tabula-rasa,…

Courcelle's Theorem states that every problem definable in Monadic Second-Order logic can be solved in linear time on structures of bounded treewidth, for example, by constructing a tree automaton that recognizes or rejects a tree…

Natural selection drives species to develop brains, with sizes that increase with the complexity of the tasks to be tackled. Our goal is to investigate the balance between the metabolic costs of larger brains compared to the advantage they…

In the experts problem, on each of $T$ days, an agent needs to follow the advice of one of $n$ ``experts''. After each day, the loss associated with each expert's advice is revealed. A fundamental result in learning theory says that the…

We consider {\em bidding games}, a class of two-player zero-sum {\em graph games}. The game proceeds as follows. Both players have bounded budgets. A token is placed on a vertex of a graph, in each turn the players simultaneously submit…

Our paper studies the setting of players using no-regret algorithms in various two-player games. We address whether having stronger regret guarantees or playing against an opponent with weaker regret guarantees yields higher utilities for…

The growing use of machine learning models in consequential settings has highlighted an important and seemingly irreconcilable tension between transparency and vulnerability to gaming. While this has sparked sizable debate in legal…

Within the framework of Game Theory, contests study decision-making in those situations or conflicts when rewards depend on the relative rank between contenders rather than their absolute performance. By relying on the formalism of Tullock…

We study 2-player zero-sum concurrent (i.e., simultaneous move) stochastic B\"uchi games and Transience games on countable graphs. Two players, Max and Min, seek respectively to maximize and minimize the probability of satisfying the game…