Game Theory with Graphs

As you can imagine, you can pretty much represent anything that has any type of flow as a graph.  It might not a nice DAG, but it is a graph that allows different states.

A game can obviuosly be presented as a graph as well.  There are states, and based on a decision or strategy, one moves from one state to the next.  One thing that is different about a game is that two graphs are NOT the same if the way to arrived at a given node differs between the two graphs. 

For example, if it took one game 20 moves to get to a node ‘z’, and another game 3, then these two games are said to be unequal even though every move from ‘z’ onward is the same for both games.

Very important concept of game theory: history matters.  How can a fair-share methodology be accurate if history does not play a role?  How can I make a decision soley based on my current queue size without taking history into account?

 

Art Sedighi

 

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