Related papers: The Geometry of Zero-Determinant Strategies

Given a skew-symmetric matrix, the corresponding two-player symmetric zero-sum game is defined as follows: one player, the row player, chooses a row and the other player, the column player, chooses a column. The payoff of the row player is…

A simplified prisoner's game is studied on a square lattice when the players interacting with their neighbors can follow only two strategies: to cooperate (C) or to defect (D) unconditionally. The players updated in a random sequence have a…

How coperation between self-interested individuals evolve is a crucial problem, both in biology and in social sciences, that is far from being well understood. Evolutionary game theory is a useful approach to this issue. The simplest model…

We study a simple adaptive model in the framework of an N -player normal form game. The model consists of a repeated game where the players only know their own action space and their own payoff scored at each stage, not those of the other…

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…

Reward maximization, safe exploration, and intrinsic motivation are often studied as separate objectives in reinforcement learning (RL). We present a unified geometric framework, that views these goals as instances of a single optimization…

Nash equilibrium is a key concept in game theory fundamental for elucidating the equilibrium state of strategic interactions, finding applications in diverse fields such as economics, political science, and biology. However, the Nash…

Parity games play an important role for LTL synthesis as evidenced by recent breakthroughs on LTL synthesis, which rely in part on parity game solving. Yet state space explosion remains a major issue if we want to scale to larger systems or…

We study strategic games on weighted directed graphs, where the payoff of a player is defined as the sum of the weights on the edges from players who chose the same strategy augmented by a fixed non-negative bonus for picking a given…

We analyze a cooperative game, where the cooperative act is not based on the previous behaviour of the co-player, but on the similarity between the players. This system has been studied in a mean-field description recently [A. Traulsen and…

We investigate the spatial distribution and the global frequency of agents who can either cooperate or defect. The agent interaction is described by a deterministic, non-iterated prisoner's dilemma game, further each agent only locally…

In communication systems where users share common resources, users' selfish behavior usually results in suboptimal resource utilization. There have been extensive works that model communication systems with selfish users as one-shot games…

We investigate the repeated prisoner's dilemma game where both players alternately use reinforcement learning to obtain their optimal memory-one strategies. We theoretically solve the simultaneous Bellman optimality equations of…

We investigate symmetric equilibria of mutual reinforcement learning when both players alternately learn the optimal memory-two strategies against the opponent in the repeated prisoners' dilemma game. We provide a necessary condition for…

While discounted payoff games and classic games that reduce to them, like parity and mean-payoff games, are symmetric, their solutions are not. We have taken a fresh view on the constraints that optimal solutions need to satisfy, and…

Mechanisms such as auctions and pricing schemes are utilized to design strategic (noncooperative) games for networked systems. Although the participating players are selfish, these mechanisms ensure that the game outcome is optimal with…

Two-view correspondence pruning aims to identify reliable correspondences for camera pose estimation, serving as a fundamental step in many 3D vision tasks. Existing methods rely on geometric consistency to seek true correspondences…

We consider multi-dimensional payoff functions in partially observable Markov decision processes. We study the structure of the set of expected payoff vectors of all strategies (policies) and study what kind are needed to achieve a given…

We consider an autonomous navigation problem, whereby a traveler aims at traversing an environment in which an adversary tries to set an ambush. A two players zero sum game is introduced. Players' strategies are computed as random path…

Graph games and Markov decision processes (MDPs) are standard models in reactive synthesis and verification of probabilistic systems with nondeterminism. The class of $\omega$-regular winning conditions; e.g., safety, reachability,…