Related papers: Game Theory and Topological Phase Transition
In this work, we introduce graphical modelsfor multi-player game theory, and give powerful algorithms for computing their Nash equilibria in certain cases. An n-player game is given by an undirected graph on n nodes and a set of n local…
Nash equilibrium is the most commonly-used notion of equilibrium in game theory. However, it suffers from numerous problems. Some are well known in the game theory community; for example, the Nash equilibrium of repeated prisoner's dilemma…
We realize an extensive numerical study of the Naming Game model with a noise term which accounts for perturbations. This model displays a non-equilibrium phase transition between an absorbing ordered consensus state, which occurs for small…
In the time since a merger of quantum mechanics and game theory was proposed formally in 1999, the two distinct perspectives apparent in this merger of applying quantum mechanics to game theory, referred to henceforth as the theory of…
We suggest to look at quantum measurement outcomes not through the lens of probability theory, but instead through decision theory. We introduce an original game-theoretical framework, model and algorithmic procedure where measurement…
The renormalization group has played an important role in the physics of the second half of the twentieth century both as a conceptual and a calculational tool. In particular it provided the key ideas for the construction of a qualitative…
We perform a detailed renormalization group analysis to study a (2+1)-dimensional quantum field theory that is composed of two interacting scalar bosons, which represent the order parameters for two continuous phase transitions. This sort…
Mating preferences of many biological species are not constant but season-dependent. Within the framework of evolutionary game theory this can be modeled with two finite opposite-sex populations playing against each other following the…
Economists were content with the concept of the Nash equilibrium as game theory's solution concept until Daskalakis, Goldberg, and Papadimitriou showed that finding a Nash equilibrium is most likely a computationally hard problem, a result…
We consider evolutionary games on a population whose underlying topology of interactions is determined by a binomial random graph $G(n,p)$. Our focus is on 2-player symmetric games with 2 strategies played between the incident members of…
The paper defines a non-cooperative simultaneous finite game to study coalition structure formation with intra and inter-coalition externalities. The novelty of the game is that the game definition embeds a \textit{coalition structure…
The class of weakly acyclic games, which includes potential games and dominance-solvable games, captures many practical application domains. In a weakly acyclic game, from any starting state, there is a sequence of better-response moves…
We find a series of topological phase transitions of increasing order, beyond the more standard second-order phase transition in a one-dimensional topological superconductor. The jumps in the order of the transitions depend on the range of…
We study the following game on a finite graph $G = (V, E)$. At the start, each edge is assigned an integer $n_e \ge 0$, $n = \sum_{e \in E} n_e$. In round $t$, $1 \le t \le n$, a uniformly random vertex $v \in V$ is chosen and one of the…
In a situation where each player has control over the transition probabilities of each subsystem, we game-theoretically analyze the optimization problem of minimizing both the partial entropy production of each subsystem and a penalty for…
The glass transition is considered as a phase transition in the system of topologically protected excitations in matter structure. The critical behavior of the system is considered both in statics and dynamics cases. It is shown in the…
Phase transitions, such as the freezing of water and the magnetisation of a ferromagnet upon lowering the ambient temperature, are familiar physical phenomena. Interestingly, such a collective change of behaviour at a phase transition is…
We examine the phase transition phenomenon for the Knapsack problem from both a computational and a human perspective. We first provide, via an empirical and a theoretical analysis, a characterization of the phenomenon in terms of two…
Topological phases are generally characterized by topological invariants denoted by integer numbers. However, different topological systems often require different topological invariants to measure, such as geometric phases, topological…
In this paper, a gentle introduction to Game Theory is presented in the form of basic concepts and examples. Minimax and Nash's theorem are introduced as the formal definitions for optimal strategies and equilibria in zero-sum and…