1,612 research outputs found
Stationary Markov Perfect Equilibria in Discounted Stochastic Games
The existence of stationary Markov perfect equilibria in stochastic games is shown in several contexts under a general condition called "coarser transition kernels". These results include various earlier existence results on correlated equilibria, noisy stochastic games, stochastic games with mixtures of constant transition kernels as special cases. The minimality of the condition is illustrated. The results here also shed some new light on a recent example on the nonexistence of stationary equilibrium. The proofs are remarkably simple via establishing a new connection between stochastic games and conditional expectations of correspondences
Stationary Markov Perfect Equilibria in Discounted Stochastic Games
The existence of stationary Markov perfect equilibria in stochastic games is shown in several contexts under a general condition called "coarser transition kernels". These results include various earlier existence results on correlated equilibria, noisy stochastic games, stochastic games with mixtures of constant transition kernels as special cases. The minimality of the condition is illustrated. The results here also shed some new light on a recent example on the nonexistence of stationary equilibrium. The proofs are remarkably simple via establishing a new connection between stochastic games and conditional expectations of correspondences
Noisy Stochastic Games
This paper establishes existence of a stationary Markov perfect equilibrium in general stochastic games with noise a component of the state that is nonatomically distributed and not directly affected by the previous periods state and actions. Noise may be simply a payoff irrelevant public randomization device, delivering known results on existence of correlated equilibrium as a special case. More generally, noise can take the form of shocks that enter into players stage payoffs and the transition probability on states. The existence result is applied to a model of industry dynamics and to a model of dynamic partisan electoral competition.
Model and Reinforcement Learning for Markov Games with Risk Preferences
We motivate and propose a new model for non-cooperative Markov game which
considers the interactions of risk-aware players. This model characterizes the
time-consistent dynamic "risk" from both stochastic state transitions (inherent
to the game) and randomized mixed strategies (due to all other players). An
appropriate risk-aware equilibrium concept is proposed and the existence of
such equilibria is demonstrated in stationary strategies by an application of
Kakutani's fixed point theorem. We further propose a simulation-based
Q-learning type algorithm for risk-aware equilibrium computation. This
algorithm works with a special form of minimax risk measures which can
naturally be written as saddle-point stochastic optimization problems, and
covers many widely investigated risk measures. Finally, the almost sure
convergence of this simulation-based algorithm to an equilibrium is
demonstrated under some mild conditions. Our numerical experiments on a two
player queuing game validate the properties of our model and algorithm, and
demonstrate their worth and applicability in real life competitive
decision-making.Comment: 38 pages, 6 tables, 5 figure
Noisy Stochastic Games
This paper establishes existence of a stationary Markov perfect equilibrium in general stochastic games with noise—a component of the state that is nonatomically distributed and not directly affected by the previous period’s state and actions. Noise may be simply a payoff-irrelevant public randomization device, delivering known results on existence of correlated equilibrium as a special case. More generally, noise can take the form of shocks that enter into players’ stage payoffs and the transition probability on states. The existence result is applied to a model of industry dynamics and to a model of dynamic electoral competition.
Discounted Stochastic Games with Voluntary Transfers
This paper studies discounted stochastic games perfect or imperfect public monitoring and the opportunity to conduct voluntary monetary transfers. We show that for all discount factors every public perfect equilibrium payoff can be implemented with a simple class of equilibria that have a stationary structure on the equilibrium path and optimal penal codes with a stick and carrot structure. We develop algorithms that exactly compute or approximate the set of equilibrium payoffs and find simple equilibria that implement these payoffs.Stochastic games, Monetary transfers, Computation, Imperfect public monitoring, Public perfect equilibria
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