Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 1 March 2021Accepted: 22 August 2021Published online: 04 January 2022Keywordssingular perturbation, stochastic differential game, Riccati equation, linear quadratic, zero sum, slow-fast, two scaleAMS Subject Headings34E13, 34D15, 93C70, 91A15Publication DataISSN (print): ...

This paper discusses, in both continuous time and discrete time, the issue of certainty equivalence in two-player zero-sum stochastic differential/dynamic games when the players have access to state information through a common noisy measurement channel. For the discrete-time case, the channel is also allowed to fail sporadically according to an independent Bernoulli process, leading to intermi...

In 1951, Dantzig [3] showed the equivalence of linear programming and two-person zero-sum games. However, in the description of his reduction from linear programming to zero-sum games, he noted that there was one case in which his reduction does not work. This also led to incomplete proofs of the relationship between the Minmax Theorem of game theory and the Strong Duality Theorem of linear pro...

1 Summary We discuss strategies in non-zero sum games of perfect information on graphs. The study of non-zero sum games on graphs is motivated by the advent of computational tasks on the worldwide web and related security requirements which have thrown up many interesting areas of interaction between game theory and computer science. For example, signing contracts on the web requires interactio...

After a brief survey of iterative algorithms for general stochastic games, we concentrate on finite-step algorithms for two special classes of stochastic games. They are Single-Controller Stochastic Games and Perfect Information Stochastic Games. In the case of single-controller games, the transition probabilities depend on the actions of the same player in all states. In perfect information st...

It is well known that the rock-paper-scissors game has no pure saddle point. We show that this holds more generally: A symmetric two-player zero-sum game has a pure saddle point if and only if it is not a generalized rock-paper-scissors game. Moreover, we show that every finite symmetric quasiconcave two-player zero-sum game has a pure saddle point. Further sufficient conditions for existence a...

We show that the value of a zero-sum Bayesian game is a Lipschitz continuous function of the players’common prior belief, with respect to the total variation metric on beliefs. This is unlike the case of general Bayesian games, where lower semi-continuity of Bayesian equilibrium (BE) payo¤s rests on the "almost uniform" convergence of conditional beliefs. We also show upper semi-continuity (USC...

There is limited formal mathematical analysis of one type of games — dynamic sequential games with large, or even infinitely large, planning horizons, from the point view of system controls. In this paper, we use a zero-sum game theoretical approach to address the disturbance attenuation analysis of state feedback Nash strategies for Dynamic Linear Quadratic Sequential Games (LQSGs) with uncert...