Results 1  10
of
30
Exact Sampling with Coupled Markov Chains and Applications to Statistical Mechanics
, 1996
"... For many applications it is useful to sample from a finite set of objects in accordance with some particular distribution. One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain whose stationary distribution is the desired distribution on this set; after the Markov chain has ..."
Abstract

Cited by 439 (13 self)
 Add to MetaCart
For many applications it is useful to sample from a finite set of objects in accordance with some particular distribution. One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain whose stationary distribution is the desired distribution on this set; after the Markov chain has run for M steps, with M sufficiently large, the distribution governing the state of the chain approximates the desired distribution. Unfortunately it can be difficult to determine how large M needs to be. We describe a simple variant of this method that determines on its own when to stop, and that outputs samples in exact accordance with the desired distribution. The method uses couplings, which have also played a role in other sampling schemes; however, rather than running the coupled chains from the present into the future, one runs from a distant point in the past up until the present, where the distance into the past that one needs to go is determined during the running of the al...
Evolutionary games on graphs
, 2007
"... Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to ..."
Abstract

Cited by 60 (0 self)
 Add to MetaCart
Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in nonequilibrium statistical physics. This review gives a tutorialtype overview of the field for physicists. The first four sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fifth section surveys the topological complications implied by nonmeanfieldtype social network structures in general. The next three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner’s Dilemma, the Rock–Scissors–Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.
Ancestral processes with selection
 Theor. Popul. Biol
, 1997
"... In this paper, we show how to construct the genealogy of a sample of genes for a large class of models with selection and mutation. Each gene corresponds to a single locus at which there is no recombination. The genealogy of the sample is embedded in a graph which we call the ancestral selection gra ..."
Abstract

Cited by 22 (0 self)
 Add to MetaCart
In this paper, we show how to construct the genealogy of a sample of genes for a large class of models with selection and mutation. Each gene corresponds to a single locus at which there is no recombination. The genealogy of the sample is embedded in a graph which we call the ancestral selection graph. This graph contains all the information about the ancestry; it is the analogue of Kingman’s coalescent process which arises in the case with no selection. The ancestral selection graph can be easily simulated and we outline an algorithm for simulating samples. The main goal is to analyze the ancestral selection graph and to compare it to Kingman’s coalescent process. In the case of no mutation, we find that the distribution of the time to the most recent common ancestor does not depend on the selection coefficient and hence is the same as in the neutral case. When the mutation rate is positive, we give a procedure for computing the probability that two individuals in a sample are identical by descent and the Laplace transform of the time to the most recent common ancestor of a sample of two individuals; we evaluate the first two terms of their respective power series in terms of the selection coefficient. The probability of identity by descent depends on both the selection coefficient and the mutation rate and is different from the analogous expression in the neutral case. The Laplace transform does not have a linear correction term in the selection coefficient. We also provide a recursion formula that can be used to approximate the probability of a given sample by simulating backwards along the sample paths of the ancestral selection graph, a technique developed by Griffiths and Tavare (1994).] 1997 Academic Press 1.
Measurevalued branching diffusions: immigrations, excursions and limit theorems
 J. Math. Kyoto Univ
, 1995
"... Measurevalued branching diffusion processes (MBD processes) have been extensively studied concerning various problems such as ergodic behaviors [2],[17], sample path properties [4],[24], historical processes [5],[9], entrance laws [7] and so on. In the present paper we focus upon the immigration st ..."
Abstract

Cited by 21 (12 self)
 Add to MetaCart
Measurevalued branching diffusion processes (MBD processes) have been extensively studied concerning various problems such as ergodic behaviors [2],[17], sample path properties [4],[24], historical processes [5],[9], entrance laws [7] and so on. In the present paper we focus upon the immigration structure of the MBD process and
Multiple scale analysis of spatial branching processes under the Palm distribution, Dissertation, Universität ErlangenNürnberg, http://www.mi.unierlangen.de/~winter/publikationen
, 1999
"... E l e c t r o n i ..."
Can Stable Social Groups be Maintained by Homophilous Imitation Alone
 Journal of Economic Behavior and Organization
, 2005
"... A central problem in the biological and social sciences concerns the conditions required for emergence and maintenance of cooperation among unrelated individuals. Most models and experiments have been pursued in a gametheoretic context and involve reward or punishment. Here we show that such payoff ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
A central problem in the biological and social sciences concerns the conditions required for emergence and maintenance of cooperation among unrelated individuals. Most models and experiments have been pursued in a gametheoretic context and involve reward or punishment. Here we show that such payoffs are unnecessary, and that stable social groups can sometimes be maintained provided simply that agents are more likely to imitate others who are like them (homophily). In contrast to other studies, to sustain multiple types we need not impose the restriction that agents also choose to make their opinions different from those in other groups.
Opinion Dynamics and Learning in Social Networks
, 2010
"... We provide an overview of recent research on belief and opinion dynamics in social networks. We discuss both Bayesian and nonBayesian models of social learning and focus on the implications of the form of learning (e.g., Bayesian vs. nonBayesian), the sources of information (e.g., observation vs. ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
We provide an overview of recent research on belief and opinion dynamics in social networks. We discuss both Bayesian and nonBayesian models of social learning and focus on the implications of the form of learning (e.g., Bayesian vs. nonBayesian), the sources of information (e.g., observation vs. communication), and the structure of social networks in which individuals are situated on three key questions: (1) whether social learning will lead to consensus, i.e., to agreement among individuals starting with different views; (2) whether social learning will effectively aggregate dispersed information and thus weed out incorrect beliefs; (3) whether media sources, prominent agents, politicians and the state will be able to manipulate beliefs and spread misinformation in a society.
The Axelrod model for the dissemination of culture revisited
, 1004
"... Abstract This article is concerned with the Axelrod model, a stochastic process which similarly to the voter model includes social influence, but unlike the voter model also accounts for homophily. Each vertex of the network of interactions is characterized by a set of cultural ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
Abstract This article is concerned with the Axelrod model, a stochastic process which similarly to the voter model includes social influence, but unlike the voter model also accounts for homophily. Each vertex of the network of interactions is characterized by a set of cultural
TIGHTNESS FOR THE INTERFACES OF ONEDIMENSIONAL VOTER MODELS
, 2006
"... Abstract. We show that for the voter model on {0, 1} Z corresponding to a random walk with kernel p(·) and starting from unanimity to the right and opposing unanimity to the left, a tight interface between 0’s and 1’s exists if p(·) has finite second moment but does not if p(·) fails to have finite ..."
Abstract

Cited by 5 (3 self)
 Add to MetaCart
Abstract. We show that for the voter model on {0, 1} Z corresponding to a random walk with kernel p(·) and starting from unanimity to the right and opposing unanimity to the left, a tight interface between 0’s and 1’s exists if p(·) has finite second moment but does not if p(·) fails to have finite moment of order α for some α < 2. 1.
Stochastic Strategy Adjustment in Coordination Games
, 1998
"... We explore a model of equilibrium selection in coordination games, where agents stochastically adjust their strategies to changes in their local environment. Instead of playing perturbed bestresponse, we assume that agents follow a rule of "switching to better strategies more likely". We ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
We explore a model of equilibrium selection in coordination games, where agents stochastically adjust their strategies to changes in their local environment. Instead of playing perturbed bestresponse, we assume that agents follow a rule of "switching to better strategies more likely". We relate this behavior to work of Rosenthal (1989) and Schlag (1998). Our main results are that both strict Nash equilibria of the coordination game correspond to stationary distributions of the process, hence evolution of play is not ergodic, but instead depends on initial conditions. However, coordination on the riskdominant equilibrium occurs with probability one whenever the initial share of agents playing the riskdominant strategy has at least some positive measure, how ever small, within the whole population. Journal of Economic Literature Classification: C72 Keywords: equilibrium selection, coordination game, evolution, strategy adjustment. This work has profited from several discussions w...