Stochastic games
LS Shapley - Proceedings of the national academy of …, 1953 - National Acad Sciences
Proceedings of the national academy of sciences, 1953•National Acad Sciences
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, respectively, then with probability sAj> 0 the game
stops, while with probability ph! the game moves to position 1. Define s= min s. k, i, j
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, respectively, then with probability sAj> 0 the game
stops, while with probability ph! the game moves to position 1. Define s= min s. k, i, j
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, respectively, then with probability sAj> 0 the game stops, while with probability ph! the game moves to position 1. Define s= min s. k, i, j
National Acad Sciences