Related papers: An analysis of Bennett's pebble game
Pebble transducers are nested two-way transducers which can drop marks (named "pebbles") on their input word. Such machines can compute functions whose output size is polynomial in the size of their input. They can be seen as simple…
We consider average-energy games, where the goal is to minimize the long-run average of the accumulated energy. While several results have been obtained on these games recently, decidability of average-energy games with a lower-bound…
For decades, researchers have sought to understand how the irreversibility of the surrounding world emerges from the seemingly time symmetric, fundamental laws of physics. Quantum mechanics conjectured a clue that final irreversibility is…
We introduce a game on graphs. By a theorem of Zermelo, each instance of the game on a finite graph is determined. While the general decision problem on which player has a winning strategy in a given instance of the game is unsolved, we…
Matrix games constitute a fundamental problem of game theory and describe a situation of two players with completely conflicting interests. We show how methods from statistical mechanics can be used to investigate the statistical properties…
This paper investigates a class of games with large strategy spaces, motivated by challenges in AI alignment and language games. We introduce the hidden game problem, where for each player, an unknown subset of strategies consistently…
In this note, we consider repeated play of a finite game using learning rules whose period-by-period behavior probabilities or empirical distributions converge to some notion of equilibria of the stage game. Our primary focus is on…
Mechanism design is a well-established game-theoretic paradigm for designing games to achieve desired outcomes. This paper addresses a closely related but distinct concept, equilibrium design. Unlike mechanism design, the designer's…
In this paper we introduce polytopal stochastic games, an extension of two-player, zero-sum, turn-based stochastic games, in which we may have uncertainty over the transition probabilities. In these games the uncertainty over the…
The class of totally balanced games is a class of transferable-utility coalitional games providing important models of cooperative behavior used in mathematical economics. They coincide with market games of Shapley and Shubik and every…
A body moves in a medium composed of noninteracting point particles; interaction of particles with the body is absolutely elastic. It is required to find the body's shape minimizing or maximizing resistance of the medium to its motion. This…
A simple and general formulation of the quantum game theory is presented, accommodating all possible strategies in the Hilbert space for the first time. The theory is solvable for the two strategy quantum game, which is shown to be…
The paper studies the convergence properties of (continuous) best-response dynamics from game theory. Despite their fundamental role in game theory, best-response dynamics are poorly understood in many games of interest due to the…
Colonel Blotto games with discrete strategy spaces effectively illustrate the intricate nature of multidimensional strategic reasoning. This paper studies the equilibrium set of such games where, in line with prior experimental work, the…
Betting games provide a natural setting to capture how information yields strategic advantage. The Kelly criterion for betting, long a cornerstone of portfolio theory and information theory, admits an interpretation in the limit of…
A class of discrete Bidding Combinatorial Games that generalize alternating normal play was introduced by Kant, Larsson, Rai, and Upasany (2022). The major questions concerning optimal outcomes were resolved. By generalizing standard game…
In the online (time-series) search problem, a player is presented with a sequence of prices which are revealed in an online manner. In the standard definition of the problem, for each revealed price, the player must decide irrevocably…
We show that two-dimensional billiard systems are Turing complete, in the sense that the halting of any Turing machine with a given input is equivalent to a certain bounded trajectory in this system entering a specified open set. Billiards…
The game of best choice (also known as the secretary problem) is a model for sequential decision making with a long history and many variations. The classical setup assumes that the sequence of candidate rankings are uniformly distributed.…
Dots-and-Boxes is a child's game which remains analytically unsolved. We implement and evolve artificial neural networks to play this game, evaluating them against simple heuristic players. Our networks do not evaluate or predict the final…