Related papers: Completeness of Unbounded Best-First Game Algorith…

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…

We describe an algorithm for computing best response strategies in a class of two-player infinite games of incomplete information, defined by payoffs piecewise linear in agents' types and actions, conditional on linear comparisons of…

This paper introduces a new paradigm for minimax game-tree search algo- rithms. MT is a memory-enhanced version of Pearls Test procedure. By changing the way MT is called, a number of best-first game-tree search algorithms can be simply and…

Solving complex planning problems has been a long-standing challenge in computer science. Learning-based subgoal search methods have shown promise in tackling these problems, but they often suffer from a lack of completeness guarantees,…

Two-player complete-information game trees are perhaps the simplest possible setting for studying general-sum games and the computational problem of finding equilibria. These games admit a simple bottom-up algorithm for finding subgame…

It is well-known that for infinitely repeated games, there are computable strategies that have best responses, but no computable best responses. These results were originally proved for either specific games (e.g., Prisoner's dilemma), or…

The Team-maxmin equilibrium prescribes the optimal strategies for a team of rational players sharing the same goal and without the capability of correlating their strategies in strategic games against an adversary. This solution concept can…

Infinite games where several players seek to coordinate under imperfect information are deemed to be undecidable, unless the information is hierarchically ordered among the players. We identify a class of games for which joint winning…

Several works have shown unconditional hardness (via integrality gaps) of computing equilibria using strong hierarchies of convex relaxations. Such results however only apply to the problem of computing equilibria that optimize a certain…

We consider games in which players search for a hidden prize, and they have asymmetric information about the prize location. We study the social payoff in equilibria of these games. We present sufficient conditions for the existence of an…

The rank of a bimatrix game is the matrix rank of the sum of the two payoff matrices. This paper comprehensively analyzes games of rank one, and shows the following: (1) For a game of rank r, the set of its Nash equilibria is the…

We study two-player zero-sum games over infinite-state graphs with boundedness conditions. Our first contribution is about the strategy complexity, i.e the memory required for winning strategies: we prove that over general infinite-state…

Here, we prove the existence of solutions to first-order mean-field games (MFGs) arising in optimal switching. First, we use the penalization method to construct approximate solutions. Then, we prove uniform estimates for the penalized…

We describe a new complete algorithm for computing Nash equilibrium in multiplayer general-sum games, based on a quadratically-constrained feasibility program formulation. We demonstrate that the algorithm runs significantly faster than the…

We introduce a new approach for computing optimal equilibria via learning in games. It applies to extensive-form settings with any number of players, including mechanism design, information design, and solution concepts such as correlated,…

We consider imperfect information stochastic games where we require the players to use pure (i.e. non randomised) strategies. We consider reachability, safety, B\"uchi and co-B\"uchi objectives, and investigate the existence of…

In this paper, we present exploitability descent, a new algorithm to compute approximate equilibria in two-player zero-sum extensive-form games with imperfect information, by direct policy optimization against worst-case opponents. We prove…

We present an algorithm for computing pure-strategy epsilon-perfect Bayesian equilibria in sequential auctions with continuous action and value spaces. Importantly, our algorithm includes a verification phase that computes an upper bound on…

The study of convex optimization has historically been concerned with worst-case convergence rates. The development of the Optimized Gradient Method (OGM), due to \citet{drori2012PerformanceOF,Kim2016optimal}, marked a major milestone in…

We study the conditions under which the iterated elimination of strictly dominated strategies is order independent and we identify a class of discontinuous games for which order does not matter. In this way, we answer the open problem…