# Questions tagged [infinite-games]

Infinite games. Combinatorial game theory for infinite two-player games of perfect information. Infinitary aspects of common recreational games. Open games, clopen games. Determinacy. Transfinite game values. Topological games.

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### Game on $[0;1]$ about repeating decimal

Two players play the following game. Before the beginning $"0."$ is written on the board. The first player writes any (finite) sequence of digits. The second one then writes only one digit. Then the ...
84 views

### history-based strategy versus position-based strategy

SUMMARY: suppose a game is played that is a walk on an infinite directed graph without blind points, where the two players each make one step alternatingly. Suppose that the pay-off of a play is ...
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### Can you help me find an optimal mixed strategy for this simple 2-person allocation game?

Consider the following simple 2-person game. Players 1 and 2 each have 100 dollar coins, with a barrier between them, hiding each other's moves. Each player must allocates his 100 coins into 3 piles:...
85 views

### How to win when placing colored dots on a plane against one opponent?

A‘s color is purple, B‘s color is green. They alternately set a dot in their color on a set 2D-plane. Whoever manages to construct a triangle in their own color without a dot in the other color ...
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### Do Hybrid games exist?

I'm new to game theory. So far, I know that we have games with finite strategy sets and games with continuous strategy sets. I was wondering if there are any games in which some players have finite ...
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### Coin Flipping Game — St. Petersburg Variant?

Suppose Alice and Bob are playing a game with a fair coin. Every time the coin comes up heads, the score (initially 0) increases by 1. If the coin comes up tails, the score decreases by 1. If the ...
### Reference Request: A Tychonoff space $X$ where the game $\mathrm{G}_1(\Omega,\Omega)$ is undetermined
Given a Tychonoff space $X$, let $\Omega$ be the set of all $\omega$-coverings of $X$, where by $\omega$-cover we mean a collection $\mathcal{U}$ of open sets of $X$ such that for any \$F\in[X]^{<\...