Sequential games with random priority. (English) Zbl 0745.62080

The paper formulates and solves the following two-person zero-sum sequential game, that involves a stopping criterion: There are \(N\) random variables: \(X_ 1, \dots , X_ N\); each player, based on some indirect information, selects a time instant \(t,\;1 \leq t \leq N\), which signals his desire to accept an unknown realization \(x_ t\) of \(X_ t\). When only one player selects the time instant \(t\), then he receives the realization \(x_ t\). If both players select the same \(t\), then a lottery decides who should receive \(x_ t\), and the one who loses in this lottery gets another chance to pick a time instant \(t'\), \(t< t' \leq N\), and once he makes his choice the game ends. The payoff function depends on the realizations received by the players, the expected value of which one player wishes to minimize and the other one to maximize.
For this game, the author obtains a saddle-point solution by constructing a normal form, and establishes some properties of the corresponding equilibrium strategies. The paper ends with two numerical examples.
Reviewer: T.Basar (Urbana)


62L15 Optimal stopping in statistics
91A35 Decision theory for games
91A15 Stochastic games, stochastic differential games
91A05 2-person games
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