Related papers: The Rock--Paper--Scissors Game
Several notions of game enjoy a Nash-like notion of equilibrium without guarantee of existence. There are different ways of weakening a definition of Nash-like equilibrium in order to guarantee the existence of a weakened equilibrium.…
This paper develops a novel methodology to study robust stability properties of Nash equilibrium points in dynamic games. Small-gain techniques in modern mathematical control theory are used for the first time to derive conditions…
Self-play is a technique for machine learning in multi-agent systems where a learning algorithm learns by interacting with copies of itself. Self-play is useful for generating large quantities of data for learning, but has the drawback that…
We develop a general game-theoretic framework for reasoning about strategic agents performing possibly costly computation. In this framework, many traditional game-theoretic results (such as the existence of a Nash equilibrium) no longer…
This paper investigates the geometrical properties of real world games (e.g. Tic-Tac-Toe, Go, StarCraft II). We hypothesise that their geometrical structure resemble a spinning top, with the upright axis representing transitive strength,…
We investigate the dynamics of Q-learning in a class of generalized Braess paradox games. These games represent an important class of network routing games where the associated stage-game Nash equilibria do not constitute social optima. We…
In this paper, Nash equilibrium seeking among a network of players is considered. Different from many existing works on Nash equilibrium seeking in non-cooperative games, the players considered in this paper cannot directly observe the…
In the evolutionary dynamics of a rock-paper-scissor (RPS) model, the effect of natural death plays a major role in determining the fate of the system. Coexistence, being an unstable fixed point of the model becomes very sensitive towards…
We study the network replicator equation and characterize its fixed points on arbitrary graph structures for $2 \times 2$ symmetric games. We show a relationship between the asymptotic behavior of the network replicator and the existence of…
We consider the existence and computational complexity of coalitional stability concepts based on social networks. Our concepts represent a natural and rich combinatorial generalization of a recent approach termed partition equilibrium. We…
We study the cyclic dominance of three species in two-dimensional constrained Newman-Watts networks with a four-state variant of the rock-paper-scissors game. By limiting the maximal connection distance $R_{max}$ in Newman-Watts networks…
In this study, we present models where participants strategically select their risk levels and earn corresponding rewards, mirroring real-world competition across various sectors. Our analysis starts with a normal form game involving two…
Game theory is a very profound study on distributed decision-making behavior and has been extensively developed by many scholars. However, many existing works rely on certain strict assumptions such as knowing the opponent's private…
Solving Nash equilibrium is the key challenge in normal-form games with large strategy spaces, where open-ended learning frameworks offer an efficient approach. In this work, we propose an innovative unified open-ended learning framework…
A cyclically dominating three-species ecosystem, modeled within the framework of rock-paper-scissor game, is studied in presence of natural death and an effect of the environment. The environmental impact is parameterized along with the…
Learning processes in games explain how players grapple with one another in seeking an equilibrium. We study a natural model of learning based on individual gradients in two-player continuous games. In such games, the arguably natural…
This paper introduces two fundamentally new concepts to game theory: multilateral Nash equilibria and families of games. Starting with non-cooperative games, we show how these notions together seamlessly integrate into and naturally extend…
Nash equilibria are crucial for understanding game behavior and systems in economics, physics, biology, and computer science. A significant application arises from the connection between Nash equilibria and optimization problems . However,…
We study several variants of the stochastic four-state rock-paper-scissors game or, equivalently, cyclic three-species predator-prey models with conserved total particle density, by means of Monte Carlo simulations on one- and…
This paper aims to reduce the communication and computation costs of the Nash equilibrium seeking strategy for the $N$-coalition noncooperative games proposed in [1]. The objective is achieved in two manners: 1. An interference graph is…