Stochastic games

Stochastic Games.

Introduction.-In a stochastic game the play proceeds by steps from position to position, according to transition probabilities controlled jointly by the two players. We shall assume a finite number, N, of positions, and finite numbers Mk, nk of choices at each position; nevertheless, the game may not be bounded in length. If, when at position k, the players choose their ith and jth alternatives...

Stochastic Games

In 1953, Lloyd Shapley contributed his paper "Stochastic games" to PNAS. In this paper, he defined the model of stochastic games, which were the first general dynamic model of a game to be defined, and proved that it admits a stationary equilibrium. In this Perspective, we summarize the historical context and the impact of Shapley's contribution.

Symmetric Incomplete Information Games as Stochastic Games

The purpose of this chapter is to show how games with incomplete information in fact reduce to stochastic games, as long as the information is symmetric among the players. The new state space corresponds to the beliefs on the space of unknown parameters.

Stochastic and Repeated Games

Stochastic Differential Portfolio Games

We study stochastic dynamic investment games in continuous time between two investors (players) who have available two different, but possibly correlated, investment opportunities. There is a single payoff function which depends on both investors’ wealth processes. One player chooses a dynamic portfolio strategy in order to maximize this expected payoff while his opponent is simultaneously choo...