Related papers: Open determinacy for class games
The object of this study are countably infinite games with perfect information that allow players to choose among arbitrarily many moves in a turn; in particular, we focus on the generalisations of the finite board games of Hex and…
Schmidt's game is a powerful tool for studying properties of certain sets which arise in Diophantine approximation theory, number theory, and dynamics. Recently, many new results have been proven using this game. In this paper we address…
In two-player games on graphs, the players move a token through a graph to produce an infinite path, which determines the winner of the game. Such games are central in formal methods since they model the interaction between a…
In previous work on higher-order games, we accounted for finite games of unbounded length by working with continuous outcome functions, which carry implicit game trees. In this work we make such trees explicit. We use concepts from…
A famous result in game theory known as Zermelo's theorem says that "in chess either White can force a win, or Black can force a win, or both sides can force at least a draw". The present paper extends this result to the class of all…
A traditional assumption in game theory is that players are opaque to one another---if a player changes strategies, then this change in strategies does not affect the choice of other players' strategies. In many situations this is an…
In this paper we study the selection principle of closed discrete selection, first researched by Tkachuk in [13] and strengthened by Clontz, Holshouser in [3], in set-open topologies on the space of continuous real-valued functions.…
We propose a unifying additive theory for standard conventions in Combinatorial Game Theory, including normal-, mis\`ere- and scoring-play, studied by Berlekamp, Conway, Dorbec, Ettinger, Guy, Larsson, Milley, Neto, Nowakowski, Renault,…
We study a simple example of a sequential game illustrating problems connected with making rational decisions that are universal for social sciences. The set of chooser's optimal decisions that manifest his preferences in case of a constant…
Game-theoretic characterizations of selection principles provide a powerful framework for analyzing covering properties through strategic interactions. For a Tychonoff space $X$ and a non-trivial metrizable arc-connected topological group…
Coherent sets of almost desirable gambles and credal sets are known to be equivalent models. That is, there exists a bijection between the two collections of sets preserving the usual operations, e.g. conditioning. Such a correspondence is…
Two selection games from the literature, $G_c(\mathcal O,\mathcal O)$ and $G_1(\mathcal O_{zd},\mathcal O)$, are known to characterize countable dimension among certain spaces. This paper studies their perfect- and limited-information…
A traditional assumption in game theory is that players are opaque to one another -- if a player changes strategies, then this change in strategies does not affect the choice of other players' strategies. In many situations this is an…
We prove that the class of all ordinals Ord is not weakly compact with respect to definable classes. Specifically, in any model of ZFC, the definable tree property fails for Ord, in that there is a definable Ord tree with no definable…
Given a dynamic ordinal game, we deem a strategy sequentially rational if there exist a Bernoulli utility function and a conditional probability system with respect to which the strategy is a maximizer. We establish a complete class theorem…
Combinatorial Game Theory is a branch of mathematics and theoretical computer science that studies sequential 2-player games with perfect information. Normal play is the convention where a player who cannot move loses. Here, we generalize…
We prove that the determinacy of Gale-Stewart games whose winning sets are infinitary rational relations accepted by 2-tape B\"uchi automata is equivalent to the determinacy of (effective) analytic Gale-Stewart games which is known to be a…
The forcing theorem is the most fundamental result about set forcing, stating that the forcing relation for any set forcing is definable and that the truth lemma holds, that is everything that holds in a generic extension is forced by a…
The categories of open learners (due to Fong, Spivak and Tuy\'eras) and open games (due to the present author, Ghani, Winschel and Zahn) bear a very striking and unexpected similarity. The purpose of this short note is to prove that there…
In an impartial combinatorial game, both players have the same options in the game and all its subpositions. The classical Sprague-Grundy Theory was developed for short impartial games, where players have a finite number of options, there…