Related papers: Multiplayer parallel repetition without dependency…

The designs of many large-scale systems today, from traffic routing environments to smart grids, rely on game-theoretic equilibrium concepts. However, as the size of an $N$-player game typically grows exponentially with $N$, standard game…

We consider 2-players, 2-values minimization games where the players' costs take on two values, $a,b$, $a<b$. The players play mixed strategies and their costs are evaluated by unimodal valuations. This broad class of valuations includes…

XOR games are the simplest model in which the nonlocal properties of entanglement manifest themselves. When there are two players, it is well known that the bias --- the maximum advantage over random play --- of entangled players can be at…

We study the behavior of the entangled value of two-player one-round projection games under parallel repetition. We show that for any projection game $G$ of entangled value 1-eps < 1, the value of the $k$-fold repetition of G goes to zero…

We show a parallel repetition theorem for the entangled value $\omega^*(G)$ of any two-player one-round game $G$ where the questions $(x,y) \in \mathcal{X}\times\mathcal{Y}$ to Alice and Bob are drawn from a product distribution on…

We consider two-player stochastic games played on a finite state space for an infinite number of rounds. The games are concurrent: in each round, the two players (player 1 and player 2) choose their moves independently and simultaneously;…

Multi-time-scale stochastic approximation is an iterative algorithm for finding the fixed point of a set of $N$ coupled operators given their noisy samples. It has been observed that due to the coupling between the decision variables and…

Two-player games on graphs is central in many problems in formal verification and program analysis such as synthesis and verification of open systems. In this work we consider solving recursive game graphs (or pushdown game graphs) that can…

We investigate a time-inconsistent, non-Markovian finite-player game in continuous time, where each player's objective functional depends non-linearly on the expected value of the state process. As a result, the classical Bellman optimality…

We present a systematic investigation of the quantum games, constructed using a novel repeated game protocol, when played repeatedly ad infinitum. We focus on establishing that such repeated games -- by virtue of inherent quantum-mechanical…

Subtraction games have a rich literature as normal-play combinatorial games (e.g., Berlekamp, Conway, and Guy, 1982). Recently, the theory has been extended to zero-sum scoring play (Cohensius et al. 2019). Here, we take the approach of…

We investigate the computation of equilibria in extensive-form games where ex ante correlation is possible, focusing on correlated equilibria requiring the least amount of communication between the players and the mediator. Motivated by the…

We investigate the convergence of symmetric stochastic differential games with interactions via control, where the volatility terms of both idiosyncratic and common noises are controlled. We apply the stochastic maximum principle, following…

Potential game is an emerging notion and framework for studying N-player games, especially with heterogeneous players. In this paper, we build an analytical framework for dynamic potential games. We prove that a game is a dynamic potential…

This paper proposes and studies a general form of dynamic $N$-player non-cooperative games called $\alpha$-potential games, where the change of a player's value function upon her unilateral deviation from her strategy is equal to the change…

Cooperative game theory has diverse applications in contemporary artificial intelligence, including domains like interpretable machine learning, resource allocation, and collaborative decision-making. However, specifying a cooperative game…

Selection in a time-periodic environment is modeled via the two-player replicator dynamics. For sufficiently fast environmental changes, this is reduced to a multi-player replicator dynamics in a constant environment. The two-player terms…

We consider one-round games between a classical verifier and two provers. One of the main questions in this area is the \emph{parallel repetition question}: If the game is played $\ell$ times in parallel, does the maximum winning…

While fictitious play is guaranteed to converge to Nash equilibrium in certain game classes, such as two-player zero-sum games, it is not guaranteed to converge in non-zero-sum and multiplayer games. We show that fictitious play in fact…

We examine online safe multi-agent reinforcement learning using constrained Markov games in which agents compete by maximizing their expected total rewards under a constraint on expected total utilities. Our focus is confined to an episodic…