commutative stochastic games we are interested in the convergence of the value of n stage games as n goes to infinity and the existence of the uniform value in stochastic games with a general set of states and finite sets of actions where the transition is commutative this means that playing an action profile a1 followed by an action profile a2 leads to the same distribution on states as playing first the action profile a2 and then a1 for example absorbing games can be reformulated as commutative stochastic games when there is only one player and the transition function is deterministic we show that the existence of a uniform value in pure strategies implies the existence of 0 optimal strategies in the framework of two player stochastic games we study a class of games where the set of states is m and the transition is deterministic and 1 lipschitz for the l1 norm and prove that these games have a uniform value a similar proof shows the existence of an equilibrium in the nonzero sum case these results remain true if one co

prebuckling and buckling of unsymmetrically laminated composite panels with stringer run outs a meshless approach is developed and used to predict buckling loads of discretely assembled composite panels made from skin and stiffeners particular emphasis is given to stringer run outs within a stiffened panel where abrupt eccentricity can trigger very large transverse displacements of the skin in front of the run out tip and perturb the internal in plane loads distribution the effect of load eccentricity is included in the formulation the final set of nonlinear equations is obtained by combining von karman s formulation for moderately large deflections in plates with an extended timoshenko approach for small initial perturbations solutions are calculated by means of a rayleigh ritzmethod in conjunctionwith agalerkin technique orthogonal eigenfunctions are employed to expand the variables of interest in generalized fourier series an iterative algorithm is proposed to calculate buckling loads limits of applicability convergence of results and further potential exploitations are discussed numerical results are compared with those from finite element analysis and other numerical approaches

on stationary equilibria of a single controller stochastic game we consider a two person general sum rational data undiscounted stochastic game in which one player player ii controls the transition probabilities we show that the set of stationary equilibrium points is the union of a finite number of sets such that every element of each of these sets can be constructed from a finite number of extreme equilibrium strategies for player i and from a finite number of pseudo extreme equilibrium strategies for player ii these extreme and pseudo extreme strategies can themselves be constructed by finite but inefficient algorithms analogous results can also be established in the more straightforward case of discounted single controller games

tame functions are semismooth superlinear convergence of the newton method for nonsmooth equations requires a semismoothness assumption in this work we prove that locally lipschitz functions definable in an o minimal structure in particular semialgebraic or globally subanalytic functions are semismooth semialgebraic or more generally globally subanalytic mappings present the special interest of being order semismooth where is a positive parameter as an application of this new estimate we prove that the error at the kth step of the newton method behaves like o 2 1 gamma k

a matrix game solution of the single controller stochastic game we consider a stochastic game on finitely many states with limiting average payoff further we assume that the law of motion depends on the actions of one player only say the minimizer we show that these games have the following properties a the value of the stochastic game for each state s is the same as the value of the matrix game whose rows and columns are the pure stationary strategies of the players and whose entries are the corresponding payoffs b these matrix games have a common optimal strategy for the maximizer which in turn yields his optimal stationary strategy in the stochastic game c if the value of a stochastic subgame obtained by deleting a column or a row in a particular state coincides with the value of the original game at that state then it coincides at all states d if all actions of the minimizer at each state are essential for optimal play then in the transient states under optimal play the minimizer has only one action in such a case the original game can be solve

risk sensitive control of finite state machines on an infinite horizon i in this paper we consider robust and risk sensitive control of discrete time finite state systems on an infinite horizon the solution of the state feedback robust control problem is characterized in terms of the value of an average cost dynamic game the risk sensitive stochastic optimal control problem is solved using the policy iteration algorithm and the optimal rate is expressed in terms of the value of a stochastic dynamic game with average cost per unit time criterion by taking a small noise limit a deterministic dynamic game which is closely related to the robust control problem is obtained

the value of repeated games with an informed controller we consider the general model of zero sum repeated games or stochastic games with signals and assume that one of the players is fully informed and controls the transitions of the state variable we prove the existence of the uniform value generalizing several results of the literature a preliminary existence result is obtained for a particular class of stochastic games played with pure strategies

approximate nonlinear analysis method for debonding of skin stringer composite assemblies doi 10 2514 1 31914 a nonlinear approach is developed and used to predict crack initiation in discretely assembled composite panels made from skin and stringers particular emphasis is given to stringer run outs within a stiffened panel for the optimization of novel composite wing configurations the nonlinear structural behavior is obtained by means of the von karman formulation for moderately large deflections in plates three dimensional assemblies are schematized and the effect of eccentricity is included in the simulation solutions are calculated by means of a rayleigh ritz approach based on galerkin s orthogonal eigenfunctions and a linear elastic fracture mechanics based model is used to simulate the crack initiation in the critical regions numerical results obtained by means of the present method are validated against tests reported in the literature and compared with advanced nonlinear finite element analysis limits of applicability and further potential exploitations are discussed a validation study showed fairly good correlation with reported experimental data

the value of markov chain games with lack of information on one side we consider a two player zero sum game given by a markov chain over a finite set of states and a family of matrix games indexed by states the sequence of states follows the markov chain at the beginning of each stage only player 1 is informed of the current state then the corresponding matrix game is played and the actions chosen are observed by both players before proceeding to the next stage we call such a game a markov chain game with lack of information on one side this model generalizes the model of aumann and maschler of zero sum repeated games with lack of information on one side which corresponds to the case where the transition matrix of the markov chain is the identity matrix we generalize the proof of aumann and maschler and from the definition and the study of appropriate nonrevealing auxiliary games with infinitely many stages show the existence of the uniform value an important difference with aumann and maschler s model is that here the notions for player 1 of using the information and revealing a relevant information are distinct

zero sum absorbing games with incomplete information on one side asymptotic analysis we prove the existence of the limit of the values of finitely repeated resp discounted absorbing games with incomplete information on one side as the number of repetitions goes to infinity resp the discount factor goes to zero the main tool is the study of the shapley operator for which the value of the lambda discounted game is a fixed point and of its derivative with respect to lambda

from max plus algebra to nonexpansive mappings a nonlinear theory for discrete event systems discrete event systems provide a useful abstraction for modelling a wide variety of systems digital circuits communication networks manufacturing plants etc their dynamics stability equilibrium states cyclical behaviour asymptotic average delays are of vital importance to system designers however in marked contrast to continuous dynamical systems there has been little systematic mathematical theory that designers can draw upon in this paper we survey the development of such a theory based on the dynamics of maps which are nonexpansive in the l norm this has its origins in linear algebra over the max plus semiring but extends to a nonlinear theory that encompasses a variety of problems arising in other mathematical disciplines we concentrate on the mathematical aspects and set out several open problems

a formula for the value of a stochastic game in 1953 lloyd shapley defined the model of stochastic games which were the first general dynamic model of a game to be defined and proved that competitive stochastic games have a discounted value in 1982 jean francois mertens and abraham neyman proved that competitive stochastic games admit a robust solution concept the value which is equal to the limit of the discounted values as the discount rate goes to 0 both contributions were published in pnas in the present paper we provide a tractable formula for the value of competitive stochastic games

the value of markov chain games with incomplete information on both sides we consider zero sum repeated games with incomplete information on both sides where the states privately observed by each player follow independent markov chains it generalizes the model introduced by aumann and maschler in the sixties and solved by mertens and zamir in the seventies where the private states of the players were fixed it also includes the model introduced in renault 19 renault j 2006 the value of markov chain games with lack of information on one side math oper res 31 3 490 512 of markov chain repeated games with lack of information on one side where only one player privately observes the sequence of states we prove here that the limit value exists and we obtain a characterization via the mertens zamir system where the nonrevealing value function plugged in the system is now defined as the limit value of an auxiliary nonrevealing dynamic game this nonrevealing game is defined by restricting the players not to reveal any information on the limit behavior of their

a uniform tauberian theorem in dynamic programming we prove that in dynamic programming framework uniform convergence of v implies uniform convergence of vn and vice versa moreover both have the same limit

stochastic games with a single controller and incomplete information we study stochastic games with incomplete information on one side in which the transition is controlled by one of the players we prove that if the informed player also controls the transitions the game has a value whereas if the uninformed player controls the transitions the max min value as well as the min max value exist but they may differ we discuss the structure of the optimal strategies and provide extensions to the case of incom plete information on both sides

the real field with convergent generalized power series we construct a model complete and o minimal expansion of the field of real numbers in which each real function given on 0 1 by a series cnxn with 0 n and cn r n 1 is definable this expansion is polynomially bounded

the asymptotic value in finite stochastic games in 1976 bewley and kohlberg proved that the discounted values v of finite zero sum stochastic games have a limit as tends to 0 using the tarski seidenberg elimination theorem from real algebraic geometry this was a fundamental step in the development of the theory of stochastic games the current paper provides a new and direct proof for this result relying on the explicit description of asymptotically optimal strategies both approaches can be used to obtain the existence of the uniform value using the construction from mertens and neyman 1981

communicating zero sum product stochastic games abstract we study two classes of zero sum stochastic games with compact action sets and a finite product state space these two classes assume a communication property on the state spaces of the players for strongly communicating on one side games we prove the existence of the uniform value for weakly communicating on both sides games we prove that the asymptotic value and therefore the uniform value may fail to exist

blackwell optimality in markov decision processes with partial observation a blackwell epsilon optimal strategy in a markov decision process is a strategy that is epsilon optimal for every discount factor sufficiently close to 1 we prove the existence of blackwell epsilon optimal strategies in finite markov decision processes with partial observation

a tauberian theorem for nonexpansive operators and applications to zero sum stochastic games we prove a tauberian theorem for nonexpansive operators and apply it to the model of zero sum stochastic game under mild assumptions we prove that the value of the discounted game converges uniformly when goes to zero if and only if the value of the n stage game converges uniformly when n goes to infinity this generalizes the tauberian theorem of lehrer and sorin lehrer e sorin s 1992 a uniform tauberian theorem in dynamic programming math oper res 17 2 303 307 to the two player zero sum case we also provide the first example of a stochastic game with public signals on the state and perfect observation of actions with finite state space signal sets and action sets in which for some initial state known by both players the value of the discounted game and the value of the n stage game starting at that initial state converge to distinct limits

spectral theorem for convex monotone homogeneous maps and ergodic control we consider convex maps f rn rn that are monotone i e that preserve the product ordering of rn and nonexpansive for the sup norm this includes convex monotone maps that are additively homogeneous i e that commute with the addition of constants we show that the fixed point set of f when it is nonempty is isomorphic to a convex inf subsemilattice of rn whose dimension is at most equal to the number of strongly connected components of a critical graph defined from the tangent affine maps of f this yields in particular an uniqueness result for the bias vector of ergodic control problems this generalizes results obtained previously by lanery romanovsky and schweitzer and federgruen for ergodic control problems with finite state and action spaces which correspond to the special case of piecewise affine maps f we also show that the length of periodic orbits of f is bounded by the cyclicity of its critical graph which implies that the possible orbit lengths of f are exactly the orders of elements of the symmetric group on n letters

definable zero sum stochastic games definable zero sum stochastic games involve a finite number of states and action sets and reward and transition functions that are definable in an o minimal structure prominent examples of such games are finite semi algebraic or globally subanalytic stochastic games we prove that the shapley operator of any definable stochastic game with separable transition and reward functions is definable in the same structure definability in the same structure does not hold systematically we provide a counterexample of a stochastic game with semi algebraic data yielding a non semi algebraic but globally subanalytic shapley operator our definability results on shapley operators are used to prove that any separable definable game has a uniform value in the case of polynomially bounded structures we also provide convergence rates using an approximation procedure we actually establish that general zero sum games with separable definable transition functions have a uniform value these results highlight the key role played by the tame structure of transition functions as particular cases of our main results we obtain that stochastic games with polynomial transitions definable games with finite actions on one side and definable games with perfect information or switching controls have a uniform value applications to nonlinear maps arising in risk sensitive control and perron frobenius theory are also given

qualitative determinacy and decidability of stochastic games with signals we consider two person zero sum stochastic games with signals a standard model of stochastic games with imperfect information the only source of information for the players consists of the signals they receive they cannot directly observe the state of the game nor the actions played by their opponent nor their own actions we are interested in the existence of almost surely winning or positively winning strategies under reachability safety buchi or co buchi winning objectives and the computation of these strategies when the game has finitely many states and actions we prove two qualitative determinacy results first in a reachability game either player 1 can achieve almost surely the reachability objective or player 2 can achieve surely the dual safety objective or both players have positively winning strategies second in a buchi game if player 1 cannot achieve almost surely the buchi objective then player 2 can ensure positively the dual co buchi objective we prove that players only need strategies with finite memory the number of memory states needed to win with finite memory strategies ranges from one corresponding to memoryless strategies to doubly exponential with matching upper and lower bounds together with the qualitative determinacy results we also provide fix point algorithms for deciding which player has an almost surely winning or a positively winning strategy and for computing an associated finite memory strategy complexity ranges from exptime to 2exptime with matching lower bounds our fix point algorithms also enjoy a better complexity in the cases where one of the players is better informed than their opponent our results hold even when players do not necessarily observe their own actions the adequate class of strategies in this case is mixed or general strategies they are equivalent behavioral strategies are too restrictive to guarantee determinacy it may happen that one of the players has a winning general strategy but none of them has a winning behavioral strategy on the other hand if a player can observe their actions then general mixed and behavioral strategies are equivalent finite memory strategies are sufficient for determinacy to hold provided that randomized memory updates are allowed

convergence of the 2d euler α to euler equations in the dirichlet case indifference to boundary layers abstract in this article we consider the euler system as a regularization of the incompressible euler equations in a smooth two dimensional bounded domain for the limiting euler system we consider the usual non penetration boundary condition while for the euler regularization we use velocity vanishing at the boundary we also assume that the initial velocities for the euler system approximate in a suitable sense as the regularization parameter 0 the initial velocity for the limiting euler system for small values of this situation leads to a boundary layer which is the main concern of this work our main result is that under appropriate regularity assumptions and despite the presence of this boundary layer the solutions of the euler system converge as 0 to the corresponding solution of the euler equations in l 2 in space uniformly in time we also present an example involving parallel flows in order to illustrate the indifference to the boundary layer of the 0 limit which underlies our work

a nonsmooth version of newton s method newton s method for solving a nonlinear equation of several variables is extended to a nonsmooth case by using the generalized jacobian instead of the derivative this extension includes the b derivative version of newton s method as a special case convergence theorems are proved under the condition of semismoothness it is shown that the gradient function of the augmented lagrangian forc2 nonlinear programming is semismooth thus the extended newton s method can be used in the augmented lagrangian method for solving nonlinear programs

generic uniqueness of the bias vector of finite stochastic games with perfect information mean payoff zero sum stochastic games can be studied by means of a nonlinear spectral problem when the state space is finite the latter consists in finding an eigenpair u solution of t u e u where t rn rn is the shapley or dynamic programming operator is a scalar e is the unit vector and u rn the scalar yields the mean payoff per time unit and the vector u called the bias allows one to determine optimal stationary strategies the existence of the eigenpair u is generally related to ergodicity conditions a basic issue is to understand for which classes of games the bias vector is unique up to an additive constant in this paper we consider perfect information zero sum stochastic games with finite state and action spaces thinking of the transition payments as variable parameters transition probabilities being fixed we show that the bias vector thought of as a function of the transition payments is generically unique up to an additive constant the proof uses techniques of max plus or tropical algebra and nonlinear perron frobenius theory as an application of our results we obtain a perturbation scheme allowing one to solve degenerate instances of stochastic games by policy iteration