Displaying similar documents to “A game model referring to the control of independent discrete time stochastic processes”

Deterministic Markov Nash equilibria for potential discrete-time stochastic games

Alejandra Fonseca-Morales (2022)

Kybernetika

Similarity:

In this paper, we study the problem of finding deterministic (also known as feedback or closed-loop) Markov Nash equilibria for a class of discrete-time stochastic games. In order to establish our results, we develop a potential game approach based on the dynamic programming technique. The identified potential stochastic games have Borel state and action spaces and possibly unbounded nondifferentiable cost-per-stage functions. In particular, the team (or coordination) stochastic games...

Differential games of partial information forward-backward doubly SDE and applications

Eddie C. M. Hui, Hua Xiao (2014)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

This paper addresses a new differential game problem with forward-backward doubly stochastic differential equations. There are two distinguishing features. One is that our game systems are initial coupled, rather than terminal coupled. The other is that the admissible control is required to be adapted to a subset of the information generated by the underlying Brownian motions. We establish a necessary condition and a sufficient condition for an equilibrium point of nonzero-sum games...

Weak infinitesimal operators and stochastic differential games.

Ramón Ardanuy, A. Alcalá (1992)

Stochastica

Similarity:

This article considers the problem of finding the optimal strategies in stochastic differential games with two players, using the weak infinitesimal operator of process xi the solution of d(xi) = f(xi,t,u,u)dt + sigma(xi,t,u,u)dW. For two-person zero-sum stochastic games we formulate the minimax solution; analogously, we perform the solution for coordination and non-cooperative stochastic differential games.

A note on 'Big Match'

Jean-Michel Coulomb (2010)

ESAIM: Probability and Statistics

Similarity:

We present a very simple proof of the existence of the value for 'Big Match' first shown by Blackwell and Ferguson (1968).

Existence of Nash equilibria in two-person stochastic games of resource extraction

P. Szajowski (2006)

Banach Center Publications

Similarity:

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.

On approximations of nonzero-sum uniformly continuous ergodic stochastic games

Andrzej Nowak (1999)

Applicationes Mathematicae

Similarity:

We consider a class of uniformly ergodic nonzero-sum stochastic games with the expected average payoff criterion, a separable metric state space and compact metric action spaces. We assume that the payoff and transition probability functions are uniformly continuous. Our aim is to prove the existence of stationary ε-equilibria for that class of ergodic stochastic games. This theorem extends to a much wider class of stochastic games a result proven recently by Bielecki [2].

A Separation Theorem for Expected Value and Feared Value Discrete Time Control

Pierre Bernhard (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We show how the use of a parallel between the ordinary (+, X) and the (max, +) algebras, Maslov measures that exploit this parallel, and more specifically their specialization to probabilities and the corresponding cost measures of Quadrat, offer a completely parallel treatment of stochastic and minimax control of disturbed nonlinear discrete time systems with partial information. This paper is based upon, and improves, the discrete time part of the earlier paper [9]. ...

Discrete stochastic processes, replicator and Fokker-Planck equations of coevolutionary dynamics in finite and infinite populations

Jens Christian Claussen (2008)

Banach Center Publications

Similarity:

Finite-size fluctuations in coevolutionary dynamics arise in models of biological as well as of social and economic systems. This brief tutorial review surveys a systematic approach starting from a stochastic process discrete both in time and state. The limit N → ∞ of an infinite population can be considered explicitly, generally leading to a replicator-type equation in zero order, and to a Fokker-Planck-type equation in first order in 1/√N. Consequences and relations to some previous...

Nash equilibrium payoffs for stochastic differential games with reflection

Qian Lin (2013)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

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.

Interplay of simple stochastic games as models for the economy

Garibaldi, Ubaldo, Radivojević, Tijana, Scalas, Enrico

Similarity:

Using the interplay among three simple exchange games, one may give a satisfactory representation of a conservative economic system where total wealth and number of agents do not change in time. With these games it is possible to investigate the emergence of statistical equilibrium in a simple pure-exchange environment. The exchange dynamics is composed of three mechanisms: a decentralized interaction, which mimics the pair-wise exchange of wealth between two economic agents, a failure...

Stochastic differential games involving impulse controls

Feng Zhang (2011)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

A zero-sum stochastic differential game problem on infinite horizon with continuous and impulse controls is studied. We obtain the existence of the value of the game and characterize it as the unique viscosity solution of the associated system of quasi-variational inequalities. We also obtain a verification theorem which provides an optimal strategy of the game.

Sensitivity of computer support game algorithms of safe ship control

Józef Lisowski (2013)

International Journal of Applied Mathematics and Computer Science

Similarity:

The paper investigates the sensitivity of safe ship control to inaccurate data from the ARPA anti-collision radar system and to changes in the process control parameters. The system structure of safe ship control in collision situations and computer support programmes exploring information from the ARPA anti-collision radar are presented. Sensitivity characteristics of the multistage positional non-cooperative and cooperative game and kinematics optimization control algorithms are determined...