urn models replicator processes and random genetic drift to understand the relative importance of natural selection and random genetic drift in finite but growing populations the asymptotic behavior of a class of generalized polya urns is studied using the method of ordinary differential equation ode of particular interest is the replicator process two balls individuals are chosen from an urn the population at random with replacement and balls of the same colors strategies are added or removed according to probabilities that depend only on the colors of the chosen balls under the assumption that the expected number of balls being added always exceeds the expected number of balls being removed whenever balls are in the urn the probability of nonextinction is shown to be positive on the event of nonextinction three results are proven i the number of balls increases asymptotically at a linear rate ii the distribution x n of strategies at the nth update is a noisy cauchy euler approximation to the mean limit ode of the process and iii the limit set of x n is almost surely a connected internally chain recurrent set for the mean limit ode under a stronger set of assumptions it is shown that for any attractor of the mean limit ode there is a positive probability that the limit set for x n lies in this attractor theoretical and numerical estimates for the probabilities of nonextinction and convergence to an attractor suggest that random genetic drift is more likely to overcome natural selection in small populations for which pairwise interactions lead to highly variable outcomes and is less likely to overcome natural selection in large populations with the potential for rapid growth

multilevel large deviations and interacting diffusions let n be a sequence of random variables with values in a topological space which satisfy the large deviation principle for eachm and eachn let m n denote the empirical measure associated withm independent copies of n as a main result we show that m n also satisfies the large deviation principle asm n we derive several representations of the associated rate function these results are then applied to empirical measure processes m n t m 1 i 1n in t 0 t t where 1n mn t is a system of weakly interacting diffusions with noise intensity 1 n this is a continuation of our previous work on the mckean vlasov limit and related hierarchical models 4 5

some properties of wkb series we investigate some properties of the wkb series for arbitrary analytic potentials and then specifically for potentials xn n even where more explicit formulae for the wkb terms are derived our main new results are i we find the explicit functional form for the general wkb terms k where one has only to solve a general recursion relation for the rational coefficients ii we give a systematic algorithm for an essential simplification of the integrated wkb terms k dx that enter the energy eigenvalue equation and iii we derive almost explicit formulae for the wkb terms for the energy eigenvalues of the homogeneous power law potentials v x xn where n is even

stochastic stability in spatial games we discuss similarities and differences between systems of interacting players maximizing their individual payoffs and particles minimizing their interaction energy long run behavior of stochastic dynamics of spatial games with multiple nash equilibria is analyzed in particular we construct an example of a spatial game with three strategies where stochastic stability of nash equilibria depends on the number of players and the kind of dynamics

evolutionary stability for large populations and backward induction it has been shown hart 2002 that the backward induction or subgame perfect equilibrium of a perfect information game is the unique stable outcome for dynamic models consisting of selection and mutation when the mutation rate is low and the populations are large under the assumption that the expected number of mutations per generation is bounded away from zero here it is shown that one can dispense with this last condition in particular it follows that the backward induction equilibrium is evolutionarily stable for large populations

evolutionary games in economics evolutionary games are introduced as models for repeated anonymous strategic interaction actions or behaviors which are more fit given the current distribution of behaviors tend over time to displace less fit behaviors cone fields characterize the continuous time processes compatible with a given fitness or payoff function for large classes of dynamics it is shown that all stable steady states are nash equilibria and that all nash equilibria are steady states the biologists evolutionarily stable strategy condition is shown to be less closely related to the dynamic equilibria economic examples and a literature survey are also provided copyright 1991 by the econometric society

deterministic approximation of stochastic evolution in games this paper provides deterministic approximation results for stochastic processes that arise when finite populations recurrently play finite games the processes are markov chains and the approximation is defined in continuous time as a system of ordinary differential equations of the type studied in evolutionary game theory we establish precise connections between the long run behavior of the discrete stochastic process for large populations and its deterministic flow approximation in particular we provide probabilistic bounds on exit times from and visitation rates to neighborhoods of attractors to the deterministic flow we sharpen these results in the special case of ergodic processes

a lyapunov like characterization of asymptotic controllability it is shown that a control system in bf r n is asymptotically controllable to the origin if and only if there exists a positive definite continuous functional of the states whose derivative can be made negative by appropriate choices of controls

asymptotic controllability implies feedback stabilization it is shown that every asymptotically controllable system can be globally stabilized by means of some discontinuous feedback law the stabilizing strategy is based on pointwise optimization of a smoothed version of a control lyapunov function iteratively sending trajectories into smaller and smaller neighborhoods of a desired equilibrium a major technical problem and one of the contributions of the present paper concerns the precise meaning of solution when using a discontinuous controller

some asymptotic theory for the bootstrap efron s bootstrap method of distribution approximation is shown to be asymptotically valid in a large number of situations including t statistics the empirical and quantile processes and von mises functionals some counter examples are also given to show that the approximation does not always succeed

wkb approach applied to 1d time dependent nonlinear hamiltonian oscillators we present a simple wkb like approach to obtain approximate analytic solutions to a certain class of time dependent nonlinear 1d hamiltonian oscillators the case of homogeneous power law potentials is solved explicitly in a closed form in the leading order the accuracy of the approximation is surprisingly good and we illustrate it in the case of the quartic oscillator

effects of strategy migration direction and noise in the evolutionary spatial prisoner s dilemma spatial games are crucial for understanding patterns of cooperation in nature and to some extent society they are known to be more sensitive to local symmetries than e g spin models this paper concerns the evolution of the prisoner s dilemma game on regular lattices with three different types of neighborhoods char22 the von neumann moore and kagom e types we investigate two kinds of dynamics for the players to update their strategies that can be unconditional cooperator or defector depending on the payoff difference an individual can adopt the strategy of a random neighbor a voter model like dynamics vmld or impose its strategy on a random neighbor i e invasion process like dynamics ipld in particular we focus on the effects of noise in combination with the strategy dynamics on the evolution of cooperation we find that vmld compared to ipld better supports the spreading and sustaining of cooperation we see that noise has nontrivial effects on the evolution of cooperation maximum cooperation density can be realized either at a medium noise level in the limit of zero noise or in both these regions the temptation to defect and the local interaction structure determine the outcome especially in the low noise limit the local interaction plays a crucial role in determining the fate of cooperators we elucidate these both by numerical simulations and mean field cluster approximation methods

integration of large deviation kernels and applications to large deviations for evolutionary games we investigate large deviation properties for systems of probability kernels and these kernels when integrated with respect to a system of measures that also satisfy the large deviation principle the results of our analysis are then used to demonstrate the large deviation property and derive rate functions for systems of measures derived from the distributions of evolutionary game processes

statistical dynamics of the royal road genetic algorithm abstract metastability is a common phenomenon many evolutionary processes both natural and artificial alternate between periods of stasis and brief periods of rapid change in their behavior in this paper an analytical model for the dynamics of a mutation only genetic algorithm ga is introduced that identifies a new and general mechanism causing metastability in evolutionary dynamics the ga s population dynamics is described in terms of flows in the space of fitness distributions the trajectories through fitness distribution space are derived in closed form in the limit of infinite populations we then show how finite populations induce metastability even in regions where fitness does not exhibit a local optimum in particular the model predicts the occurrence of fitness epochs periods of stasis in population fitness distributions at finite population size and identifies the locations of these fitness epochs with the flow s hyperbolic fixed points this enables exact predictions of the metastable fitness distributions during the fitness epochs as well as giving insight into the nature of the periods of stasis and the innovations between them all these results are obtained as closed form expressions in terms of the ga s parameters an analysis of the jacobian matrices in the neighborhood of an epoch s metastable fitness distribution allows for the calculation of its stable and unstable manifold dimensions and so reveals the state space s topological structure more general quantitative features of the dynamics fitness fluctuation amplitudes epoch stability and speed of the innovations are also determined from the jacobian eigenvalues the analysis shows how quantitative predictions for a range of dynamical behaviors that are specific to the finite population dynamics can be derived from the solution of the infinite population dynamics the theoretical predictions are shown to agree very well with statistics from ga simulations we also discuss the connections of our results with those from population genetics and molecular evolution theory

the evolution of conventions the author shows how a group of individuals can learn to play a coordination game without any common knowledge and with only a small amount of rationality the game is repeated many times by different players each player chooses an optimal reply based on incomplete information about what other players have done in the past occasionally they make mistakes when the likelihood of mistakes is very small typically one coordination equilibrium will be played almost all of the time over the long run this stochastically stable equilibrium can be computed analytically using a general theorem the author proves on perturbed markov processes copyright 1993 by the econometric society

moderate deviations of minimum contrast estimators under contamination since statistical models are simplifications of reality it is important in estimation theory to study the behavior of estimators also under distributions slightly different from the proposed model in testing theory when dealing with test statistics where nuisance parameters are estimated knowledge of the behavior of the estimators of the nuisance parameters is needed under alternatives to evaluate the power in this paper the moderate deviation behavior of minimum contrast estimators is investigated not only under the supposed model but also under distributions close to the model a particular example is the multivariate maximum likelihood estimator determined within the proposed model the set up is quite general including for instance also discrete distributions the rate of convergence under alternatives is determined both when comparing the minimum contrast estimator with a natural parameter in the parameter space and when comparing it with the proposed true value in the parameter space it turns out that under the model the asymptotic optimality of the maximum likelihood estimator in the local sense continues to hold in the moderate deviation area

learning mutation and long run equilibria in games an evolutionary model with a finite number of players and with stochastic mutations is analyzed the expansion and contraction of strategies is linked to their current relative success but mutuation perturbing the system from its deterministic evolution are present as well the focus is on the long run implications of ongoing mutations which drastically reduce the set of equilibria for 2 by 2 symmetric games with two symmetric strict nash equilibria the risk dominant equilibrium is selected in particular if both strategies have equal security levels the pareto dominant nash equilibrium is selected in particular if both strategies have equal security levels the pareto dominant nash equilibrium is selected even though there is another strict nash equilibrium copyright 1993 by the econometric society

estimating with partial statistics the parameters of ergodic finite markov sources parameter estimation based on data emitted from a finite ergodic markov source is discussed this can be considered an extension of the memoryless case first an asymptotically optimal estimator is suggested for the case where the parametric model is completely known for an unknown parametric model e g unknown noise distribution with training sequences available a necessary condition is given for the existence of a universally optimum estimate a universal estimate is then suggested that is asymptotically nearly optimal the results hold under fairly mild regularity conditions

finite size effects and bounds for perceptron models ablncl in lhis paper we consider two main aspsln of the binary perccptron problem the maximal capacity when random paltem are stored model a and its generalhation ability model b we have extended previous numerical estimates of critical capacilies and studied thermal properties of systems of small sizes to lest recent replica predictions we have also considered some simpler versions of thest models the discrete spherical vemions can be salved exactly using gardner s replica calculation for the spherical model and are shown to give a rigorous upper bound and lower bound on the capacities of models a and b respectively iby vemions of models a and b are soivcd in detail and provide information which is useful for interpreting the bnile size eeeciects present in the numerical studies of models a and b

well posedness and maximum entropy approximation for the dynamics of quantitative traits abstract we study the fokker planck equation derived in the large system limit of the markovian process describing the dynamics of quantitative traits the fokker planck equation is posed on a bounded domain and its transport and diffusion coefficients vanish on the domain s boundary we first argue that despite this degeneracy the standard no flux boundary condition is valid we derive the weak formulation of the problem and prove the existence and uniqueness of its solutions by constructing the corresponding contraction semigroup on a suitable function space then we prove that for the parameter regime with high enough mutation rate the problem exhibits a positive spectral gap which implies exponential convergence to equilibrium next we provide a simple derivation of the so called dynamic maximum entropy dynmaxent method for approximation of observables moments of the fokker planck solution which can be interpreted as a nonlinear galerkin approximation the limited applicability of the dynmaxent method inspires us to introduce its modified version that is valid for the whole range of admissible parameters finally we present several numerical experiments to demonstrate the performance of both the original and modified dynmaxent methods we observe that in the parameter regimes where both methods are valid the modified one exhibits slightly better approximation properties compared to the original one

semiclassical analysis of wigner functions in this work we study the wigner functions which are the quantum analogues of the classical phase space density and show how a full rigorous semiclassical scheme for all orders of can be constructed for them without referring to the actual coordinate space wavefunctions from which the wigner functions are typically calculated we find such a picture by a careful analysis around the stationary points of the main quantization equation and apply this approach to the harmonic oscillator solving it for all orders of

inertia in strategy switching transforms the strategy evolution a recent experimental study traulsen et al proc natl acad sci 107 2962 2010 shows that human strategy updating involves both direct payoff comparison and the cost of switching strategy which is equivalent to inertia however it remains largely unclear how such a predisposed inertia affects 2 2 games in a well mixed population of finite size to address this issue the inertia bonus strategy switching cost is added to the learner payoff in the fermi process we find how inertia quantitatively shapes the stationary distribution and that stochastic stability under inertia exhibits three regimes with each covering seven regions in the plane spanned by two inertia parameters we also obtain the extended 1 3 rule with inertia and the speed criterion with inertia these two findings hold for a population above two we illustrate the above results in the framework of the prisoner s dilemma game as inertia varies two intriguing stationary distributions emerge the probability of coexistence state is maximized or those of two full states are simultaneously peaked our results may provide useful insights into how the inertia of changing status quo acts on the strategy evolution and in particular the evolution of cooperation

cooperation and effective computability a common interest game is a game in which there exists a unique pair of payoffs which strictly pareto dominates all other payoffs we consider the undiscounted repeated game obtained by the infinite repetition of such a two player stage game we show that if supergame strategies are restricted to be computable within church s thesis the only pair of payoffs which survives any computable tremble with sufficiently large support is the pareto efficient pair the result is driven by the ability of the players to use the early stages of the game to communicate their intention to play cooperatively in the future

convergent learning algorithms for unknown reward games in this paper we address the problem of convergence to nash equilibria in games with rewards that are initially unknown and must be estimated over time from noisy observations these games arise in many real world applications whenever rewards for actions cannot be prespecified and must be learned online but standard results in game theory do not consider such settings for this problem we derive a multiagent version of mathcal q learning to estimate the reward functions using novel forms of the epsilon greedy learning policy using these mathcal q learning schemes to estimate reward functions we then provide conditions guaranteeing the convergence of adaptive play and the better reply processes to nash equilibria in potential games and games with more general forms of acyclicity and of regret matching to the set of correlated equilibria in generic games a secondary result is that we prove the strong ergoditicity of stochastic adaptive play and stochastic better reply processes in the ca

finite size effects in random energy models and in the problem of polymers in a random medium by the use of traveling wave equations we calculate the finite size corrections to the free energy of random energy models in their low temperature phases and in the neighborhood of the transition temperature we find that although the extensive part of the free energy does not show any critical behavior when the temperature approaches its transition value the finite size corrections signal the transition by becoming singular we obtain a scaling form for these finite size corrections valid in the limitn andt t c by considering a generalized random energy model in the limit of a very large number of steps we obtain results for the finite size corrections in the problem of a polymer in a random medium

the dynamics of a genetic algorithm for simple random ising systems abstract a formalism is presented for analysing genetic algorithms it is used to study a simple genetic algorithm consisting of selection mutation and crossover which is searching for the ground states of simple random ising spin systems a random field ideal paramagnet and a spin glass chain the formalism can also be applied to other population based search techniques and to biological models of micro evolution to make the problem tractable it is assumed that the population dynamics can be described by a few macroscopic order parameters and that the remaining microscopic degrees of freedom can be averaged out the macroscopic quantities that are used are the cumulants of the distribution of fitnesses or energies in the population a statistical mechanics model is presented which describes the population configuration in terms of the cumulants this is used to derive equations of motion for the cumulants predictions of the theory are compared with experiments and are shown to predict the average time to convergence and the average fitness of the final population accurately a simplified version of the equations is produced by keeping only leading nonlinear terms and truncating the cumulant expansion this is shown to give a novel description of the role of genetic operators in search e g it is argued that an important role of crossover is to reduce the skewness of the population

the effect of increasing returns to scale in public goods investment on threshold values of cooperation under social exclusion mechanism abstract this paper establishes a stochastic evolutionary public goods game pgg model with exclusion type strategies in a well mixed and finite size population the effect of increasing returns to scale in public goods investment is considered we focus on the stochastic stable equilibrium sse of the evolutionary system by numerical experiments we observe that there are two types of sse in the system namely all individuals choosing defection all d state and the coexistence of cooperation and exclusion c e states and three types of phases namely choosing the all d state with probability one d phase choosing the c e states with probability one c e phase and choosing the all d and c e states with non zero probabilities c e d phase we study the combined effects of four parameters probability of exclusion success unit exclusion cost increasing returns to scale coefficient investment amplification factor on the phase selection of the system we get the boundary curves or surfaces for each pair or set of combined parameters thus conditions for the evolution of cooperative strategies depending on these parameters can be given notably we observe that in a well mixed population with exclusion type strategies the increasing returns to scale coefficient cannot change the parameter boundary between the c e phase and the c e d phase within our parameters corresponding simulation experiments are also carried out in a structured population and it is found that the increasing returns to scale effect can greatly reduce critical values of the amplification factor under which cooperation can emerge and the increase in the increasing returns to scale coefficient can induce the system to transfer directly from the d phase to the c e phase which is different from the well mixed situation this research can help us better understand the emergence of cooperation in the pgg with increasing returns to scale effect under social exclusion mechanism

a large deviation analysis of the maximum likelihood learning of markov tree structures the problem of maximum likelihood ml estimation of discrete tree structured distributions is considered chow and liu established that ml estimation reduces to the construction of a maximum weight spanning tree using the empirical mutual information quantities as the edge weights using the theory of large deviations we analyze the exponent associated with the error probability of the event that the ml estimate of the markov tree structure differs from the true tree structure given a set of independently drawn samples by exploiting the fact that the output of ml estimation is a tree we establish that the error exponent is equal to the exponential rate of decay of a single dominant crossover event we prove that in this dominant crossover event a non neighbor node pair replaces a true edge of the distribution that is along the path of edges in the true tree graph connecting the nodes in the non neighbor pair using ideas from euclidean information theory we then analyze the scenario of ml estimation in the very noisy learning regime and show that the error exponent can be approximated as a ratio which is interpreted as the signal to noise ratio snr for learning tree distributions we show via numerical experiments that in this regime our snr approximation is accurate

fast equilibrium selection by rational players living in a changing world we study a coordination game with randomly changing payoffs and small frictions in changing actions using only backwards induction we find that players must coordinate on the risk dominant equilibrium more precisely a continuum of fully rational players are randomly matched to play a symmetric 2 x 2 game the payoff matrix changes according to a random walk players observe these payoffs and the population distribution of actions as they evolve the game has frictions opportunities to change strategies arrive from independent random processes so that the players are locked into their actions for some time as the frictions disappear each player ignores what the others are doing and switches at her first opportunity to the risk dominant action history dependence emerges in some cases when frictions remain positive

asymptotic controllability and optimal control we consider a control problem where the state must approach asymptotically a target c while paying an integral cost with a non negative lagrangian l the dynamics f is just continuous and no assumptions are made on the zero level set of the lagrangian l through an inequality involving a positive number p 0 and a minimum restraint function u u x a special type of control lyapunov function we provide a condition implying that i the system is asymptotically controllable and ii the value function is bounded by u p 0 the result has significant consequences for the uniqueness issue of the corresponding hamilton jacobi equation furthermore it may be regarded as a first step in the direction of a feedback construction

how to decide how to decide how to modeling limited rationality it seems inconsistent to model boundedly rational action choice by assuming that the agent chooses the optimal decision procedure this criticism is not avoided by assuming that he chooses the optimal procedure to choose a procedure to to choose an action the author shows that properly interpreted this regress continued transfinitely generates a model representing the agent s perception of all his options including every way to refine his perceptions in this model the agent surely must choose the perceived best option hence it is not inconsistent to model limited rationality by assuming that the agent uses the optimal decision procedure copyright 1991 by the econometric society

evolution with state dependent mutations recent evolutionary models have introduced small mutation rates as a way of refining predictions of long run behavior we show that this refinement effect can only be obtained by restrictions on how the magnitude of the effect of mutation on evolution varies across states of the system in particular given any model of the effect of mutations any invariant distribution of the mutationless process is close to an invariant distribution of the process with appropriately chosen small mutation rates

natural models for evolution on networks evolutionary dynamics has been traditionally studied in the context of homogeneous populations mainly described by the moran process p moran random processes in genetics proceedings of the cambridge philosophical society 54 1 1958 60 71 recently this approach has been generalized in e lieberman c hauert m a nowak evolutionary dynamics on graphs nature 433 2005 312 316 by arranging individuals on the nodes of a network in general directed in this setting the existence of directed arcs enables the simulation of extreme phenomena where the fixation probability of a randomly placed mutant i e the probability that the offspring of the mutant eventually spread over the whole population is arbitrarily small or large on the other hand undirected networks i e undirected graphs seem to have a smoother behavior and thus it is more challenging to find suppressors amplifiers of selection that is graphs with smaller greater fixation probability than the complete graph i e the homogeneous population in this paper we focus on undirected graphs we present the first class of undirected graphs which act as suppressors of selection by achieving a fixation probability that is at most one half of that of the complete graph as the number of vertices increases moreover we provide some generic upper and lower bounds for the fixation probability of general undirected graphs as our main contribution we introduce the natural alternative of the model proposed in e lieberman c hauert m a nowak evolutionary dynamics on graphs nature 433 2005 312 316 in our new evolutionary model all individuals interact simultaneously and the result is a compromise between aggressive and non aggressive individuals we prove that our new model of mutual influences admits a potential function which guarantees the convergence of the system for any graph topology and any initial fitness vector of the individuals furthermore we prove fast convergence to the stable state for the case of the complete graph as well as we provide almost tight bounds on the limit fitness of the individuals apart from being important on its own this new evolutionary model appears to be useful also in the abstract modeling of control mechanisms over invading populations in networks we demonstrate this by introducing and analyzing two alternative control approaches for which we bound the time needed to stabilize to the healthy state of the system

theoretical comparison of bootstrap confidence intervals we develop a unified framework within which many commonly used bootstrap critical points and confidence intervals may be discussed and compared in all seven different bootstrap methods are examined each being usable in both parametric and nonparametric contexts emphasis is on the way in which the methods cope with first and second order departures from normality percentile t and accelerated bias correction emerge as the most promising of existing techniques certain other methods are shown to lead to serious errors in coverage and position of critical point an alternative approach based on shortest bootstrap confidence intervals is developed we also make several more technical contributions in particular we confirm efron s conjecture that accelerated bias correction is second order correct in a variety of multivariate circumstances and give a simple interpretation of the acceleration constant

extending the notion of rationality of selfish agents second order nash equilibria motivated by the increasing interest of the computer science community in the study and understanding of non cooperative systems we present a novel model for formalizing the rational behavior of agents with a more farsighted view of the consequences of their actions this approach yields a framework creating new equilibria which we call second order equilibria starting from a ground set of traditional ones by applying our approach to pure nash equilibria we define the set of second order pure nash equilibria and present their applications to the prisoner s dilemma game to an instance of braess s paradox in the wardrop model and to the kp model with identical machines

on the global convergence of stochastic fictitious play we establish global convergence results for stochastic fictitious play for four classes of games games with an interior ess zero sum games potential games and supermodular games we do so by appealing to techniques from stochastic approximation theory which relate the limit behavior of a stochastic process to the limit behavior of a differential equation defined by the expected motion of the process the key result in our analysis of supermodular games is that the relevant differential equation defines a strongly monotone dynamical system our analyses of the other cases combine lyapunov function arguments with a discrete choice theory result that the choice probabilities generated by any additive random utility model can be derived from a deterministic model based on payoff perturbations that depend nonlinearly on the vector of choice probabilities

exact wkb expansions for some potentials we find wkb expansions for the spectra of the three dimensional isotropic harmonic oscillator and eckart and morse potentials it is shown that for all these potentials the series are convergent and when summed yield the exact energy spectra these results support our working hypothesis that the wkb series for the energy spectra are convergent for all one dimensional solvable potentials and their sums yield the exact energies

delta method in large deviations and moderate deviations for estimators the delta method is a popular and elementary tool for deriving limiting distributions of transformed statistics while applications of asymptotic distributions do not allow one to obtain desirable accuracy of approximation for tail probabilities the large and moderate deviation theory can achieve this goal motivated by the delta method in weak convergence a general delta method in large deviations is proposed the new method can be widely applied to driving the moderate deviations of estimators and is illustrated by examples including the wilcoxon statistic the kaplan meier estimator the empirical quantile processes and the empirical copula function we also improve the existing moderate deviations results for m estimators and l statistics by the new method some applications of moderate deviations to statistical hypothesis testing are provided

the evolutionary game of pressure or interference resistance and collaboration in this paper we extend the framework of the evolutionary inspection game put forward recently by the author and coworkers to a large class of conflict interactions to address the pressure executed by the major player or principal on the large group of small players who can resist this pressure or collaborate with the major player we prove rigorous results on the convergence of various markov decision models of interacting small agents including evolutionary growth i e pairwise in groups and by coalition formation to a deterministic evolution on the distributions of the state spaces of small players paying main attention to situations with an infinite state space of small players we supply precise rates of convergence the theoretical results of the paper are applied to the analysis of the processes of inspection corruption cyber security counter terrorism banks and firms merging strategically enhanced preferential attachment and many other

large deviations of estimators the performance of a sequence of estimators t n of g theta can be measured by its inaccuracy rate lim inf n rightarrow infty n 1 log mathbb p theta t n g theta varepsilon for fixed varepsilon 0 optimality of consistent estimators operatorname wrt the inaccuracy rate is investigated it is shown that for exponential families in standard representation with a convex parameter space the maximum likelihood estimator is optimal if the parameter space is not convex which occurs for instance in curved exponential families in general no optimal estimator exists for the location problem the inaccuracy rate of m estimators is established if the underlying density is sufficiently smooth an optimal m estimator is obtained within the class of translation equivariant estimators tail behaviour of location estimators is studied a connection is made between gross error and inaccuracy rate optimality

stochastic stability analysis of evolutionary two player games on regular graphs abstract we study evolutionary two player games and identify stochastically stable equilibria of the network games restricted to infinite populations on regular graphs the players update their strategies according to four different rules birth death death birth imitation and pairwise comparison for prisoner s dilemma and snowdrift games respectively for two player games on regular graphs we show that there is a unique stochastically stable equilibrium for infinite populations for the prisoner s dilemma game if the benefit to cost ratio is larger than k 2 k is the degree of a regular graph the networked game has a higher fraction of cooperators than that for a well mixed population for the snowdrift game the fraction of cooperators in a regular graph would be higher than that of the well mixed population if the benefit to cost ratio is larger than 1 5 under certain conditions the lower graph connectivity can lead to the emergence of more cooperators finally some numerical simulation examples are given to demonstrate the theoretical results

pursuit evasion problems and viscosity solutions of isaacs equations the dirichlet problem for first order hamilton jacobi equations arising in differential games of pursuit and evasion is studied local and global sub and superoptimality principles are stated for respectively viscosity sub and supersolutions these results are applied to obtain a general existence theorem and to prove the existence of the value of the game the main application concerns the problem of stability terminability of a dynamical system with two competitive controls and the opposite one of evadability from a general closed set the approach used in this paper allows lyapunov functions satisfying the usual condition in the weak sense of viscosity solutions

on optimum parameter modulation estimation from a large deviations perspective we consider the problem of jointly optimum modulation and estimation of a real valued random parameter conveyed over an additive white gaussian noise awgn channel where the performance metric is the large deviations behavior of the estimator namely the exponential decay rate as a function of the observation time of the probability that the estimation error would exceed a certain threshold our basic result is in providing an exact characterization of the fastest achievable exponential decay rate among all possible modulator estimator transmitter receiver pairs where the modulator is limited only in the signal power but not in bandwidth this exponential rate turns out to be given by the reliability function of the awgn channel we also discuss several ways to achieve this optimum performance and one of them is based on quantization of the parameter followed by optimum channel coding and modulation which gives rise to a separation based transmitter if one views this setting from the perspective of joint source channel coding this is in spite of the fact that in general when error exponents are considered the source channel separation theorem does not hold true we also discuss several observations modifications and extensions of this result in several directions including other channels and the case of multidimensional parameter vectors one of our findings concerning the latter is that there is an abrupt threshold effect in the dimensionality of the parameter vector below a certain critical dimension the probability of excess estimation error may still decay exponentially but beyond this value it must converge to unity

global asymptotic controllability implies input to state stabilization the main problem addressed in this paper is the design of feedbacks for globally asymptotically controllable gac control affine systems that render the closed loop systems input to state stable iss with respect to actuator errors extensions for fully nonlinear gac systems with actuator errors are also discussed our controllers have the property that they tolerate small observation noise as well