Any node can be the starting node and the game is finite (i.e no possible infinite loop). I need to show that for such game there exists a winning strategy for either verifier or the falsifier for every starting node.
How can I prove that if a game is finite, then it always has a winning strategy for every node in a graph.
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predicate-logic
game-theory
first-order-logic
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0Think about using induction on the depth of the graph. – 2017-01-25
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0My idea is to do it recursively. For every leaf nodes, either Verifier and falsifier has the winning strategy. Now for the nodes in n-1 level, we can say the node leading to winning node(in leaf) respective winner from leaf has the winning strategy. But I don't to how to formulate it or even if it is complete. – 2017-01-25
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0Can we be sure that draws are impossible ? – 2017-01-25
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0That's what I need to prove, and yes because the game is finite one has to win after n moves. – 2017-01-25