Results 1  10
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20
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 ..."
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Cited by 406 (13 self)
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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 ..."
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Cited by 54 (0 self)
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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.
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. ..."
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Cited by 5 (0 self)
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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 ..."
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Cited by 4 (1 self)
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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
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 relate th ..."
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Cited by 4 (1 self)
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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...
Exact Sampling with Markov Chains
 Ph.D. Dissertation, M.I.T., http://dimacs.rutgers.edu/∼dbwilson
, 1996
"... Random sampling has found numerous applications in computer science, statistics, and physics. The most widely applicable method of random sampling is to use a Markov chain whose steady state distribution is the probability distribution ß from which we wish to sample. After the Markov chain has been ..."
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Cited by 3 (0 self)
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Random sampling has found numerous applications in computer science, statistics, and physics. The most widely applicable method of random sampling is to use a Markov chain whose steady state distribution is the probability distribution ß from which we wish to sample. After the Markov chain has been run for long enough, its state is approximately distributed according to ß. The principal problem with this approach is that it is often difficult to determine how long to run the Markov chain. In this thesis we present several algorithms that use Markov chains to return samples distributed exactly according to ß. The algorithms determine on their own how long to run the Markov chain. Two of the algorithms may be used with any Markov chain, but are useful only if the state space is not too large. Nonetheless, a spinoff of these two algorithms is a procedure for sampling random spanning trees of a directed graph that runs more quickly than the Aldous/Broder algorithm. Another of the exact sa...
Stochastic spatial models of hostpathogen and hostmutualist interactions
, 2006
"... Mutualists and pathogens, collectively called symbionts, are ubiquitous in plant communities. While some symbionts are highly hostspecific, others associate with multiple hosts. The outcomes of multispecies hostsymbiont interactions with different degrees of specificity are difficult to predict at ..."
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Cited by 3 (1 self)
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Mutualists and pathogens, collectively called symbionts, are ubiquitous in plant communities. While some symbionts are highly hostspecific, others associate with multiple hosts. The outcomes of multispecies hostsymbiont interactions with different degrees of specificity are difficult to predict at this point due to a lack of a general conceptual framework. Complicating our predictive power is the fact that plant populations are spatially explicit, and we know from past research that explicit space can profoundly alter plantplant interactions. We introduce a spatially explicit, stochastic model to investigate the role of explicit space and hostspecificity in multispecies hostsymbiont interactions. We find that in our model, pathogens can significantly alter the spatial structure of plant communities, promoting coexistence, whereas mutualists appear to have only a limited effect. Effects are more pronounced the more hostspecific symbionts are. 1. Introduction. The
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 ..."
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Cited by 3 (0 self)
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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.
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 ..."
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Cited by 2 (1 self)
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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.
A Spatial Model for the Abundance of Species
"... . The voter model, with mutations occurring at a positive rate # , has a unique equilibrium distribution. We investigate the logarithms of the relative abundance of species for these distributions in d # 2. We show that, as # # 0, the limiting distribution is right triangular in d = 2 and unifor ..."
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Cited by 1 (0 self)
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. The voter model, with mutations occurring at a positive rate # , has a unique equilibrium distribution. We investigate the logarithms of the relative abundance of species for these distributions in d # 2. We show that, as # # 0, the limiting distribution is right triangular in d = 2 and uniform in d # 3. We also obtain more detailed results for the histograms that biologists use to estimate the underlying density functions. 1. Introduction. In the seminal paper of Fisher, Corbet, and Williams (1943), field data collected at light traps on the number of individuals representing various butterfly and moth species was fitted to a log series distribution (f n = C #,n # n /n). Later, other investigators fit various species abundance data in a wide variety of settings to other distributions, including the lognormal (Preston (1948)) and negative binomial (Brian (1953)). More recently, various mathematical models have been proposed to derive these distributions. (See, e.g., May (1975...