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{{Short description|Topological game in math}} In mathematics, the '''Banach game''' is a [[topological game]] introduced by [[Stefan Banach]] in 1935 in the second addendum to pr ...

In mathematics, the '''binary game''' is a [[topological game]] introduced by [[Stanisław Ulam]] in 1935 in an addendum to problem 4 ...See,<ref>{{cite journal|last1=Telgársky|first1=Rastislav|title=Topological Games: On the 50th Anniversary of the Banach-Mazur Game|journal=Rocky Mountain Jo ...

{{short description|Topological game}} ...k|last1=Choquet|first1=Gustave|title=Lectures on Analysis: Integration and topological vector spaces|date=1969|publisher=W. A. Benjamin|isbn=9780805369601|url=htt ...

In [[mathematics]], a '''D-space''' is a [[topological space]] where for every [[Neighbourhood (mathematics)|neighborhood]] assign ...ns an open neighborhood to each element in the set. More formally, given a topological space <math>X</math>. An open neighborhood assignment is a function <math>f ...

In mathematics, a '''Rothberger space''' is a [[topological space]] that satisfies a certain a basic [[selection principle]]. A Rothber === Topological game characterization === ...

...ambridge|authorlink1=József Beck}}</ref><ref name="pg14">{{Cite Positional Games 2014}}</ref>''' is a kind of a [[combinatorial game]] for two players. It i ...player who holds an entire winning-set wins. Other examples of positional games are [[Hex (board game)|Hex]] and the [[Shannon switching game]]. ...

...on E. Lemke|Lemke]] and [[J.T. Howson|Howson]] showed that, for two person games, computing a [[Nash equilibrium]] point is equivalent to an LCP. In 1968 [[ ...onal inequality|variational inequality theory]], [[fixed point theory]], [[topological degree theory]] and [[nonlinear analysis]]. ...

[[topological space]]s, especially [[function space]]s. Often, the Topological spaces having this covering property are called '''Menger spaces'''. ...

{{short description|Solution concept for non-cooperative games}} | citeseerx=10.1.1.295.4592}}</ref> for games with finite numbers of players and strategies. Later, Mertens<ref>{{cite jo ...

...makes connections to [[combinatorial game theory]] through the graph-based games of [[Sprouts (game)|Sprouts]] and Brussels Sprouts and their analysis using ...in which it was shown that the two-dimensional [[Closed manifold|compact]] topological surfaces can be completely described by their Euler characteristics and the ...

...case of locally finite graphs) as [[end (topology)|topological end]]s of [[topological space]]s associated with the graph. ...vens]], functions that describe evasion strategies for [[pursuit–evasion]] games on a graph <math>G</math>.<ref name=haven-end>The haven nomenclature, and t ...

{{Short description|Class of games in game theory}} '''Congestion games''' (CG) are a class of games in [[game theory]]. They represent situations which commonly occur in roads ...

| title = Simple realizability of complete abstract topological graphs in P * various properties of [[Nash equilibrium|Nash equilibria]] of multi-player games<ref name="gmvy15">{{citation ...

....|date=1952-02-01|title=Fixed-point and Minimax Theorems in Locally Convex Topological Linear Spaces|journal=Proceedings of the National Academy of Sciences|volum ...te=1986-01-01|title=The Existence of Equilibrium in Discontinuous Economic Games, I: Theory|journal=The Review of Economic Studies|volume=53|issue=1|pages=1 ...

...amics, and convergence towards equilibria can be considered as a driver of topological evolution. For example, Kasthurirathna and Piraveenan <ref>{{cite journal ...pressure on an initially random network which simulates a range of classic games, so that the network converges towards Nash equilibria while being allowed ...

{{defn|no=|[[Axiom of determinacy]] Certain games are determined, in other words one player has a winning strategy}} {{defn|no=|[[Axiom of projective determinacy]] Certain games given by projective set are determined, in other words one player has a win ...

...abeled <math>+\infty</math> and <math>-\infty</math> can be added to the [[topological space]] of the real numbers, producing the two-point [[compactification (ma ...int labeled <math>\infty</math>]] can be added to the complex plane as a [[topological space]] giving the [[one-point compactification]] of the complex plane. Whe ...

...duling and [[register allocation]] problems, the analysis of combinatorial games, and the proofs of other mathematical results including [[Brooks' theorem]] ...to determine optimal play in any single game or any [[disjunctive sum]] of games.<ref>E.g., see Section 1.1 of {{harvtxt|Nivasch|2006}}.</ref> ...

A less used presentation of the Möbius strip is as the topological quotient of a torus.<ref>Tony Phillips, ''[http://www.ams.org/mathmedia/arc ...ble manifold|orientable]]. In fact, the Möbius strip is the epitome of the topological phenomenon of [[Orientability|nonorientability]]. This is because two-dime ...

...//www.sciencedirect.com/science/article/abs/pii/S0899825606000169 |journal=Games and Economic Behavior |year=2006 |volume=56 |pages=61–86|doi=10.1016/j.geb. |chapter= Topological methods in cardinal utility theory ...