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IpsumPanEst
IpsumPanEst
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All I ever found about this were natural language rules à la Asimov's three laws of robotics. The questions are straightforward questions:

  1. Is there a well-posed mathematical definition of game on a graph? If so, what is it?

  2. Is there a well defined category of games on graphs? If so, what is it?

But i'd love to hear some comments about issues involved in this question.

After some time working on a game on a graph, such as the timber game, or maker-breaker games, one can make $\textit{ad hoc}$ definitions, which usually involve defining a state space and player $1$ and player $2$ allowed moves by defining the stateto which states each can changeproceed in the state space, from a given state. Can this be formalized into categorical language in a way that encompasses all known games on graphs?

I'm looking for something along the lines of:

given an enriched graph category $\mathcal{Graph}_S$ (where $S$ is some extra structure on the graphs such as labeling, weights, etc...), the associated $S$-game structure on $G$ iscategory is the category $\mathcal{Game}_S$ whose objects are ....

All I ever found about this were natural language rules à la Asimov's three laws of robotics. The questions are straightforward questions:

  1. Is there a well-posed mathematical definition of game on a graph? If so, what is it?

  2. Is there a well defined category of games on graphs? If so, what is it?

But i'd love to hear some comments about issues involved in this question.

After some time working on a game on a graph, such as the timber game, or maker-breaker games, one can make $\textit{ad hoc}$ definitions, which usually involve defining a state space and player $1$ and player $2$ allowed moves by defining the state can change in state space. Can this be formalized into categorical language in a way that encompasses all known games on graphs?

I'm looking for something along the lines of:

given an enriched graph category $\mathcal{Graph}_S$ (where $S$ is some extra structure on the graphs such as labeling, weights, etc...), the associated $S$-game structure on $G$ is the category $\mathcal{Game}_S$ whose objects are ....

All I ever found about this were natural language rules à la Asimov's three laws of robotics. The questions are straightforward questions:

  1. Is there a well-posed mathematical definition of game on a graph? If so, what is it?

  2. Is there a well defined category of games on graphs? If so, what is it?

But i'd love to hear some comments about issues involved in this question.

After some time working on a game on a graph, such as the timber game, or maker-breaker games, one can make $\textit{ad hoc}$ definitions, which usually involve defining a state space and player $1$ and player $2$ allowed moves by defining to which states each can proceed in the state space, from a given state. Can this be formalized into categorical language in a way that encompasses all known games on graphs?

I'm looking for something along the lines of:

given an enriched graph category $\mathcal{Graph}_S$ (where $S$ is some extra structure on the graphs such as labeling, weights, etc...), the associated $S$-game category is the category $\mathcal{Game}_S$ whose objects are ....

Source Link
IpsumPanEst
IpsumPanEst
  • 11
  • 2

Is there a well-posed definition of game on a graph? Or a well defined category of games on graphs?

All I ever found about this were natural language rules à la Asimov's three laws of robotics. The questions are straightforward questions:

  1. Is there a well-posed mathematical definition of game on a graph? If so, what is it?

  2. Is there a well defined category of games on graphs? If so, what is it?

But i'd love to hear some comments about issues involved in this question.

After some time working on a game on a graph, such as the timber game, or maker-breaker games, one can make $\textit{ad hoc}$ definitions, which usually involve defining a state space and player $1$ and player $2$ allowed moves by defining the state can change in state space. Can this be formalized into categorical language in a way that encompasses all known games on graphs?

I'm looking for something along the lines of:

given an enriched graph category $\mathcal{Graph}_S$ (where $S$ is some extra structure on the graphs such as labeling, weights, etc...), the associated $S$-game structure on $G$ is the category $\mathcal{Game}_S$ whose objects are ....