Sequential games with random priority

Abstract

The paper deals with a class of two-person zero-sum sequential games related to a partial observation of random variables X₁,X₂,...,X_N by the players. Each player, based on some indirect information, selects a moment t, l≤t≤N. In this way he communicates that he would like to accept an unknown realization x_t of X_t. When only one player selects the moment t then he obtains the required realization. If both players select the same moment t, then there is a lottery choosing either Player 1 or Player 2. The player chosen by the lottery obtains the realization x_t and the player thus deprived of the acceptance of x_t at t<N, may select any later realization. Each player can accept only one realization. Payoff functions of the players depend on the realizations chosen by them. The normal form of the game is constructed and a solution is given with the help of the help of the dynamic programming method. The results are illustrated by examples.

Keywords:

• sequential decisions
• zero-sum game
• secretary problem