Related papers: Weak covering properties and infinite games
Taking matrix as a synonym for a numerical function on the Cartesian product of two (in general, infinite) sets, a simple purely algebraic "reciprocity property" says that the set of rows spans a finite-dim space iff the set of columns does…
We characterize various Menger/Rothberger related properties by means of ultrafilter convergence, and discuss their behavior with respect to products.
A natural partial ordering exists on the set of all weighted games and, more broadly, on all linear games. We describe several properties of the partially ordered sets formed by these games and utilize this perspective to enumerate proper…
We introduce the category of optiongraphs and option-preserving maps as a model to study impartial combinatorial games. Outcomes, remoteness, and extended nim-values are preserved under option-preserving maps. We show that the four…
By resorting to the vector space structure of finite games, skew-symmetric games (SSGs) are proposed and investigated as a natural subspace of finite games. First of all, for two player games, it is shown that the skew-symmetric games form…
Here, we study the existence and the convergence of solutions for the vanishing discount MFG problem with a quadratic Hamiltonian. We give conditions under which the discounted problem has a unique classical solution and prove convergence…
Kuhn's Theorem shows that extensive games with perfect recall can equivalently be analyzed using mixed or behavioral strategies, as long as players are expected utility maximizers. This note constructs an example that illustrate the limits…
In order to better understand reasoning involved in analyzing infinite games in extensive form, we performed experiments in the proof assistant Coq that are reported here.
In this paper, we defined two new games - the mildly Menger game and the compact-clopen game. In a zero-dimensional space, the Menger game is equivalent to the mildly Menger game and the compact-open game is equivalent to the compact-clopen…
We present a selection principle $S_1(\mathcal{O},\mathcal{H})$ that characterizes the $G_{\delta}$-diagonal property. We also present a topological game induced by this selection principle and we study the relations between this game and…
We consider the problem of constructing a weakly-continuous mapping extending continuous mapping defined on a dense set of a topological space to the entire space. Theorem on necessary and sufficient conditions for the existence of such an…
Let $H$ be a Hilbert space. We investigate the properties of weak limit points of iterates of random projections onto $K\geq 2$ closed convex sets in $H$ and the parallel properties of weak limit points of residuals of random greedy…
Optimizing strategic decisions (a.k.a. computing equilibrium) is key to the success of many non-cooperative multi-agent applications. However, in many real-world situations, we may face the exact opposite of this game-theoretic problem --…
We consider infinite-state Attacker-Defender games with reachability objectives. The results of the paper are twofold. Firstly we prove a new language-theoretic result for weighted automata on infinite words and show its encoding into the…
We introduce quantum XOR games, a model of two-player one-round games that extends the model of XOR games by allowing the referee's questions to the players to be quantum states. We give examples showing that quantum XOR games exhibit a…
We study properties of quantum strategies, which are complete specifications of a given party's actions in any multiple-round interaction involving the exchange of quantum information with one or more other parties. In particular, we focus…
In a mean field game of controls, a large population of identical players seek to minimize a cost that depends on the joint distribution of the states of the players and their controls. We first consider the classes of mean field games of…
Simple games cover voting systems in which a single alternative, such as a bill or an amendment, is pitted against the status quo. A simple game or a yes-no voting system is a set of rules that specifies exactly which collections of ``yea''…
We study games of chance (e.g., pokers, dices, horse races) in the form of agents' first-order posterior beliefs about game outcomes. We ask for any profile of agents' posterior beliefs, is there a game that can generate these beliefs? We…
Understanding invertibility in restricted mis\`ere play has been challenging; in particular, the possibility of non-conjugate inverses posed difficulties. Advances have been made in a few specific universes, but a general theorem was…