A controller and a stopper game with degenerate variance control.
A note on the first occurrence of strings.
BSDEs with two reflecting barriers driven by a Brownian and a Poisson noise and related Dynkin game.
Caracterización de la función de valor de los juegos estocásticos continuos.
Se establece una caracterización de la función de valor de los juegos estocásticos continuos, similar a la contenida en [2] y [3] para juegos matriciales y en [4] para juegos estocásticos discretos. Tras la formulación del problema se señalan algunas propiedades de la función de valor. Más adelante se prueba que tales propiedades son suficientes para identificar el funcional que asigna a cada juego su valor.
Computing the Stackelberg/Nash equilibria using the extraproximal method: Convergence analysis and implementation details for Markov chains games
In this paper we present the extraproximal method for computing the Stackelberg/Nash equilibria in a class of ergodic controlled finite Markov chains games. We exemplify the original game formulation in terms of coupled nonlinear programming problems implementing the Lagrange principle. In addition, Tikhonov's regularization method is employed to ensure the convergence of the cost-functions to a Stackelberg/Nash equilibrium point. Then, we transform the problem into a system of equations in the...
Dynamic Programming Principle for tug-of-war games with noise
We consider a two-player zero-sum-game in a bounded open domain Ω described as follows: at a point x ∈ Ω, Players I and II play an ε-step tug-of-war game with probability α, and with probability β (α + β = 1), a random point in the ball of radius ε centered at x is chosen. Once the game position reaches the boundary, Player II pays Player I the amount given by a fixed payoff function F. We give a detailed proof of the fact that...
Dynamic Programming Principle for tug-of-war games with noise
We consider a two-player zero-sum-game in a bounded open domain Ω described as follows: at a point x ∈ Ω, Players I and II play an ε-step tug-of-war game with probability α, and with probability β (α + β = 1), a random point in the ball of radius ε centered at x is chosen. Once the game position reaches the boundary, Player II pays Player I the amount given by a fixed payoff function F. We give a detailed proof of the fact that the value functions of this game satisfy the Dynamic Programming Principle...
Dynamic Programming Principle for tug-of-war games with noise
We consider a two-player zero-sum-game in a bounded open domain Ω described as follows: at a point x ∈ Ω, Players I and II play an ε-step tug-of-war game with probability α, and with probability β (α + β = 1), a random point in the ball of radius ε centered at x is chosen. Once the game position reaches the boundary, Player II pays Player I the amount given by a fixed payoff function F. We give a detailed proof of the fact that...
Empirical approximation in Markov games under unbounded payoff: discounted and average criteria
This work deals with a class of discrete-time zero-sum Markov games whose state process evolves according to the equation where and represent the actions of player 1 and 2, respectively, and is a sequence of independent and identically distributed random variables with unknown distribution . Assuming possibly unbounded payoff, and using the empirical distribution to estimate , we introduce approximation schemes for the value of the game as well as for optimal strategies considering both,...
Equilibrium points of random generalized games.
Ergodicity and extremality of AMS sources and channels.
Existence of Nash equilibria in two-person stochastic games of resource extraction
This paper deals with two-person stochastic games of resource extraction under both the discounted and the mean payoff criterion. Under some concavity and additivity assumptions concerning the payoff and the transition probability function a stationary Nash equilibrium is shown to exist. The proof is based on Schauder-Tychonoff's fixed point theorem, applied to a suitable payoff vector space.
From repeated games to brownian games
Interval valued bimatrix games
Payoffs in (bimatrix) games are usually not known precisely, but it is often possible to determine lower and upper bounds on payoffs. Such interval valued bimatrix games are considered in this paper. There are many questions arising in this context. First, we discuss the problem of existence of an equilibrium being common for all instances of interval values. We show that this property is equivalent to solvability of a certain linear mixed integer system of equations and inequalities. Second, we...
Juegos estocásticos continuos: valor y estrategias óptimas.
El objeto de este trabajo es analizar los juegos estocásticos cuyo espacio de estados y de acciones son métricos compactos, con adecuadas condiciones de continuidad acerca de las funciones de pago y de transición. Tras describir el modelo e introducir las hipótesis de continuidad, se trata el problema con horizonte finito, a fin de probar que existe valor y estrategias óptimas para ambos jugadores, que puedan ser determinados recurrentemente. También se considera el caso de horizonte infinito en...
Markov stopping games with an absorbing state and total reward criterion
This work is concerned with discrete-time zero-sum games with Markov transitions on a denumerable space. At each decision time player II can stop the system paying a terminal reward to player I, or can let the system to continue its evolution. If the system is not halted, player I selects an action which affects the transitions and receives a running reward from player II. Assuming the existence of an absorbing state which is accessible from any other state, the performance of a pair of decision...
Modeling shortest path games with Petri nets: a Lyapunov based theory
In this paper we introduce a new modeling paradigm for shortest path games representation with Petri nets. Whereas previous works have restricted attention to tracking the net using Bellman's equation as a utility function, this work uses a Lyapunov-like function. In this sense, we change the traditional cost function by a trajectory-tracking function which is also an optimal cost-to-target function. This makes a significant difference in the conceptualization of the problem domain, allowing the...
Nash Equilibria in a class of Markov stopping games
This work concerns a class of discrete-time, zero-sum games with two players and Markov transitions on a denumerable space. At each decision time player II can stop the system paying a terminal reward to player I and, if the system is no halted, player I selects an action to drive the system and receives a running reward from player II. Measuring the performance of a pair of decision strategies by the total expected discounted reward, under standard continuity-compactness conditions it is shown...
Nash equilibrium payoffs for stochastic differential games with reflection
In this paper, we investigate Nash equilibrium payoffs for nonzero-sum stochastic differential games with reflection. We obtain an existence theorem and a characterization theorem of Nash equilibrium payoffs for nonzero-sum stochastic differential games with nonlinear cost functionals defined by doubly controlled reflected backward stochastic differential equations.
Nash -equilibria for stochastic games with total reward functions: an approach through Markov decision processes
The main objective of this paper is to find structural conditions under which a stochastic game between two players with total reward functions has an -equilibrium. To reach this goal, the results of Markov decision processes are used to find -optimal strategies for each player and then the correspondence of a better answer as well as a more general version of Kakutani’s Fixed Point Theorem to obtain the -equilibrium mentioned. Moreover, two examples to illustrate the theory developed are presented....