1. A GAME WITH OPTIMAL STOPPING OF RANDOM WALKS.
- Author
-
Mazalov, V.V. and Kochetov, E.A.
- Subjects
- *
PROBABILITY theory , *GAMES of chance , *EXPECTED returns - Abstract
A two-person game Γ is considered which is specified by the following random walks. Let x[SUBn] and y[SUBn] be independent symmetric random walks on the set E = {0, 1, . . . , K}. Assume they start from the states a and b respectively (1 ≦ a < b ≦ K - 1), are absorbed with probability 0.5 at points 0 and K, and are reflected to the points 1 and K - 1, respectively, with the same probability 0.5. Players I and II observe the random walks x[SUBn] and y[SUBn], respectively, and stop them at Markov times τ and σ being strategies of the game. Each player knows the values of K, a, and b but has no information about the behavior of the other player. The rules of the game are as follows. If x[SUB&tau] > y[SUBσ] then player II pays player I, say, $1; if x[SUBτ < y[SUBσ] then I pays II $1; and if x[SUB&tau] = y[SUBσ] then the outcome of the game is said to be a draw. The aim of each player is to maximize the expected value of his income. We find the equilibrium situation and the value of the game. [ABSTRACT FROM AUTHOR]
- Published
- 1998