Related papers: Evolutionary stability in quantum games
We use co-evolutionary genetic algorithms to model the players' learning process in several Cournot models, and evaluate them in terms of their convergence to the Nash Equilibrium. The "social-learning" versions of the two co-evolutionary…
In this paper, we examine the Nash equilibrium convergence properties of no-regret learning in general N-player games. For concreteness, we focus on the archetypal follow the regularized leader (FTRL) family of algorithms, and we consider…
To verify the robustness of a program or protocol, it is common in the computer science community to rely on the theoretical framework of game theory. In particular, if one seeks to enforce a desired property, or specification, despite an…
$S$ equilibrium synthesizes a century of game-theoretic modeling. $S$-beliefs determine choices as in the refinement literature and level-$k$, without anchoring on Nash equilibrium or imposing ad hoc belief formation. $S$-choices allow for…
Most of atoms and molecule found in nature are capable of evolving towards and staying at their ground states, the lowest energy states. This paper offers a global optimization approach to understand the ground state as the equilibrium…
Over the past few decades, many works have studied the evolutionary dynamics of continuous games. However, previous works have primarily focused on two-player games with pairwise interactions. Indeed, group interactions rather than pairwise…
For any two-by-two game $\G$, we define a new two-player game $\G^Q$. The definition is motivated by a vision of players in game $\G$ communicating via quantum technology according to a certain standard protocol originally introduced by…
This paper proposes a co-evolutionary model of directed graphs and three opinions, i.e., conservative$(+)$, neutral$(\odot)$ and liberal$(-)$. Agents update both opinions and social relationships with bias. We find that an emergent game…
Green Security Games have become a popular way to model scenarios involving the protection of natural resources, such as wildlife. Sensors (e.g. drones equipped with cameras) have also begun to play a role in these scenarios by providing…
Secure equilibrium is a refinement of Nash equilibrium, which provides some security to the players against deviations when a player changes his strategy to another best response strategy. The concept of secure equilibrium is specifically…
A fundamental problem with the Nash equilibrium concept is the existence of certain "structurally deficient" equilibria that (i) lack fundamental robustness properties, and (ii) are difficult to analyze. The notion of a "regular" Nash…
We propose a simple yet rich model to extend the notions of Nash equilibria and correlated equilibria of strategic games to the quantum setting, in which we then study the relations between classical and quantum equilibria. Unlike the…
One of the best examples of traditional analysis of evolutionary stable strategies (ESS) is provided by the so called Dove-Hawk model. In this paper we present several enhancements to the model aimed at describing the evolution of…
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,…
Complex change is often described as "evolutionary" in economics, policy, and technology, yet most system dynamics models remain constrained to fixed state spaces and equilibrium-seeking behavior. This paper argues that evolutionary…
We analyze the stability of a nonlinear dynamical model describing the noncooperative strategic interactions among the agents of a finite collection of populations. Each agent selects one strategy at a time and revises it repeatedly…
This paper is concerned with complexity theoretic aspects of a general formulation of quantum game theory that models strategic interactions among rational agents that process and exchange quantum information. In particular, we prove that…
Methods of exploring Nash equilibrium in quantum games are studied. Analytical conditions of the existence, the uniqueness or the multiplicity of the equilibria are found.
We discuss a population of sequences subject to mutations and frequency-dependent selection, where the fitness of a sequence depends on the composition of the entire population. This type of dynamics is crucial to understand the evolution…
In this paper, we show that different types of evolutionary game dynamics are, in principle, special cases of a dynamical system model based on our previously reported framework of generalized growth transforms. The framework shows that…