Related papers: Value-based distance between the information struc…

We define the distance between two information structures as the largest possible difference in value across all zero-sum games. We provide a tractable characterization of distance and use it to discuss the relation between the value of…

We revisit the question of modeling incomplete information among 2 Bayesian players, following an ex-ante approach based on values of zero-sum games. $K$ being the finite set of possible parameters, an information structure is defined as a…

Mertens [In Proceedings of the International Congress of Mathematicians (Berkeley, Calif., 1986) (1987) 1528-1577 Amer. Math. Soc.] proposed two general conjectures about repeated games: the first one is that, in any two-person zero-sum…

Two information structures are said to be close if, with high probability, there is approximate common knowledge that interim beliefs are close under the two information structures. We define an "almost common knowledge topology" reflecting…

In a zero-sum stochastic game with signals, at each stage, two adversary players take decisions and receive a stage payoff determined by these decisions and a variable called state. The state follows a Markov chain, that is controlled by…

We define a real-valued distance metric $wd$ on the space $\mathcal{C}$ of short combinatorial games in canonical form. We demonstrate the existence of Cauchy sequences informed by sidling sequences, find limit points, and investigate the…

We study continuity properties of stochastic game problems with respect to various topologies on information structures, defined as probability measures characterizing a game. We will establish continuity properties of the value function…

While Kolmogorov complexity is the accepted absolute measure of information content in an individual finite object, a similarly absolute notion is needed for the information distance between two individual objects, for example, two…

In this paper, we present a conceptual model game to examine the dynamics of asymmetric interactions in games with imperfect information. The game involves two agents with starkly contrasting capabilities: one agent can take actions but has…

We consider a two-player zero-sum stochastic differential game in which one of the players has a private information on the game. Both players observe each other, so that the non-informed player can try to guess his missing information. Our…

Recently, in [K.R. Apt and S. Simon: Well-founded extensive games with perfect information, TARK21], we studied well-founded games, a natural extension of finite extensive games with perfect information in which all plays are finite. We…

We develop a general framework for reasoning about distances between transition systems with quantitative information. Taking as starting point an arbitrary distance on system traces, we show how this leads to natural definitions of a…

In this paper we investigate a game of optimal stopping with incomplete information. There are two players of which only one is informed about the precise structure of the game. Observing the informed player the uninformed player is given…

We study zero-sum differential games with state constraints and one-sided information, where the informed player (Player 1) has a categorical payoff type unknown to the uninformed player (Player 2). The goal of Player 1 is to minimize his…

This paper considers an infinitely repeated three-player Bayesian game with lack of information on two sides, in which an informed player plays two zero-sum games simultaneously at each stage against two uninformed players. This is a…

We consider extensive games with perfect information with well-founded game trees and study the problems of existence and of characterization of the sets of subgame perfect equilibria in these games. We also provide such characterizations…

We study two-player zero-sum repeated games with incomplete information on one side, where the payoff function is tail measurable (and not necessarily the long-run average payoff). We show that the maxmin value equals the concavification of…

We describe and develop a close relationship between two problems that have customarily been regarded as distinct: that of maximizing entropy, and that of minimizing worst-case expected loss. Using a formulation grounded in the equilibrium…

The paper proposes a natural measure space of zero-sum perfect information games with upper semicontinuous payoffs. Each game is specified by the game tree, and by the assignment of the active player and of the capacity to each node of the…

We provide a formal definition of depth-limited games together with an accessible and rigorous explanation of the underlying concepts, both of which were previously missing in imperfect-information games. The definition works for an…