Stochastic revision opportunities in Markov decision problems

The worst-case payoff in games with stochastic revision opportunities

“…Second, when the scope is limited to particular types of SAR game, the Theorem is translated to case-specific conditions that may be more applicable and easier to verify. To demonstrate this, we examine in Section 4 two models of two-player games where only one of the players is asynchronous in a manner previously studied by Tsodikovich and Lehrer [2019]. Applying Theorem 1, we obtain concrete and simple conditions on the inter-revision timings for which the asynchronous game is more favorable than the simultaneous-move game (such as Corollary 1).…”

“…Whenever player 2 cannot revise his action, he is forced to repeat the pure action he chose in the previous stage ("strict-revision process", see Tsodikovich and Lehrer [2019]). We set two different levels of information for players.…”

“…These games are examined in Section 4. Their single-decision maker version was analyzed in Tsodikovich and Lehrer [2019].…”

“…To exemplify our main result we consider a two-player game with complete information where one plays synchronously (with a revision opportunity at each stage) while the other plays asynchronously and has revision opportunities only at certain randomly chosen stages ("strict-revision process", as in Tsodikovich and Lehrer [2019]). A deterministic version of this model was explored by Wen [2002] (see also Takahashi and Wen [2003]) and largely inspired this paper.…”