0
votes
0answers
52 views

I'm looking for a formula to be applied on a game

I've been working on a game and I need to implement a feature, but I still haven't found a good formula for it. The problem is the following: Each team has X points, and all teams are able to ...
46
votes
8answers
11k views

Why do people lose in chess?

Zermelo's Theorem, when applied to chess, states: "either white can force a win, or black can force a win, or both sides can force at least a draw [1]" I do not get this. How can it be proven? ...
1
vote
1answer
70 views

What is the definition of “Winning Strategy” in an Ehrenfeucht-Fraïssé game?

I've read many descriptions and applications of a Winning Strategy, as much as many for a Strategy tout court, but when a formal, algebraic definition is called upon, I've found close to no input. I ...
7
votes
5answers
5k views

Help: rules of a game whose details I don't remember!

In a probability course, a game was introduced which a logical approach won't yield a strategy for winning, but a probabilistic one will. My problem is that I don't remember the details (the rules of ...
4
votes
1answer
62 views

Generlized Büchi Games and Closed under superset Muller Games

For a unique infinite play $p$ in a 2-Player game $G=(V_0,V_1,E)$. Let $$ \inf(p) \subseteq V_0 \cup V_1 $$ be the set of vertices which occur infinitly often in $p$. Generlized B├╝chi (GB) Games ...
1
vote
1answer
62 views

Question on the use of induction in the Electronic Mail Game

In Rubinstein's Electronic Mail Game, Player I and Player II's strategies take the form as $s_i : \mathbb{N} \to \{A,B\}$, $(i =1,2)$. Rubinstein shows that the pair of constant functions, $s_1(t_1) ...
0
votes
1answer
103 views

How to calculate Team Strength for future prediction?

You are given with $4$ players name, namely Player $A$, Player $B$, Player $C$ and Player $D$. These players are grouped into two teams with two players each. A Game is played between the two team.For ...
1
vote
2answers
342 views

common knowledge and concept of coarsening partition

Here is a proof of the equivalence between my definition and Aumann's for "common knowledge". I'm assuming some familiarity with set partitions. Aumann's definition is in terms of the ...
1
vote
1answer
460 views

Understanding common knowledge in logic and game theory

For $k = 2$, it is merely "first-order" knowledge. Each blue-eyed person knows that there is someone with blue eyes, but each blue eyed person does ''not'' know that the other blue-eyed person ...
8
votes
0answers
470 views

Irreversible chess [closed]

Suppose we play a chess-variant, where any finite number of pieces are allowed, and the board is as large as we wish, but only two kings in total. And there is no 50 move-rule, no castling and no ...
16
votes
3answers
2k views

Is chess Turing-complete?

Is there a set of rules that translates any program into a configuration of finite pieces on an infinite board, such that if black and white plays only legal moves, the game ends in finite time iff ...
2
votes
1answer
216 views

Nash equilibrium and common knowledge

If NE is a CK? It seems that yes since given all information about payoffs/strategies players can derive NE based on the procedures similar to that of in the common knowledge, but I'm not sure.
8
votes
1answer
334 views

Common knowledge as a fixed point

I read on a wikipedia page that from the modal logic formalization CK can be formulated as a fixed point. If it also holds for the set theory formalization? If it does, where I can find about it? ...