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We consider the problem of signal estimation in a generalized linear model (GLM). GLMs include many canonical problems in statistical estimation, such as linear regression, phase retrieval, and 1-bit compressed sensing. Recent work has…
In the last decade, stochastic models have shown to be very useful for quantitative modelling of social processes. Here, a configurational master equation for the description of behavioral changes by pair interactions of individuals is…
The partial monitoring (PM) framework provides a theoretical formulation of sequential learning problems with incomplete feedback. On each round, a learning agent plays an action while the environment simultaneously chooses an outcome. The…
In Hotelling's model of spatial competition, a unit mass of voters is distributed in the interval $[0,1]$ (with their location corresponding to their political persuasion), and each of $m$ candidates selects as a strategy his distinct…
Previous studies have shown that the topological properties of a complex network, such as heterogeneity and average degree, affect the evolutionary game dynamics on it. However, traditional numerical simulations are usually time-consuming…
We consider an n-player symmetric stochastic game with weak interaction between the players. Time is continuous and the horizon and the number of states are finite. We show that the value function of each of the players can be approximated…
This paper provides theoretical bounds for empirical game theoretical analysis of complex multi-agent interactions. We provide insights in the empirical meta game showing that a Nash equilibrium of the meta-game is an approximate Nash…
In this paper, we present a model of a game among teams. Each team consists of a homogeneous population of agents. Agents within a team are cooperative while the teams compete with other teams. The dynamics and the costs are coupled through…
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…
With the success of modern machine learning, it is becoming increasingly important to understand and control how learning algorithms interact. Unfortunately, negative results from game theory show there is little hope of understanding or…
Social networks have a scale-free property and community structure, and many problems in life have the characteristic of public goods, such as resource shortage. Due to different preferences of individuals, there exist individuals who adopt…
Population games model the evolution of strategic interactions among a large number of uniform agents. Due to the agents' uniformity and quantity, their aggregate strategic choices can be approximated by the solutions of a class of ordinary…
We study the evolution of cooperation in public goods games on the square lattice, focusing on the effects that are brought about by different sizes of groups where individuals collect their payoffs and search for potential strategy donors.…
Small Progress Measures is one of the classical parity game solving algorithms. For games with n vertices, m edges and d different priorities, the original algorithm computes the winning regions and a winning strategy for one of the players…
In this Letter, we introduce an aspiration-induced reconnection mechanism into the spatial public goods game. A player will reconnect to a randomly chosen player if its payoff acquired from the group centered on the neighbor does not exceed…
We investigate how the framework of mean-field games may be used to investigate strategic interactions in large heterogeneous populations. We consider strategic interactions in a population of players which may be partitioned into…
The basic problem in equilibrium statistical mechanics is to compute phase space average, in which Monte Carlo method plays a very important role. We begin with a review of nonlocal algorithms for Markov chain Monte Carlo simulation in…
The use of computers in statistical physics is common because the sheer number of equations that describe the behavior of an entire system particle by particle often makes it impossible to solve them exactly. Monte Carlo methods form a…
The framework of Mean-field Games (MFGs) is used for modelling the collective dynamics of large populations of non-cooperative decision-making agents. We formulate and analyze a kinetic MFG model for an interacting system of non-cooperative…
We study an evolutionary prisoner's dilemma game with two layered graphs, where the lower layer is the physical infrastructure on which the interactions are taking place and the upper layer represents the connections for the strategy…