
A randomized strategy in the mirror game
Alice and Bob take turns (with Alice playing first) in declaring numbers...
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Completeness of Unbounded BestFirst Game Algorithms
In this article, we prove the completeness of the following game search ...
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Gradual learning supports cooperation in spatial prisoner's dilemma game
According to the standard imitation protocol, a less successful player a...
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StrategyStealing is NonConstructive
In many combinatorial games, one can prove that the first player wins un...
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A Note on Unbounded Polyhedra Derived from Convex Caps
The construction of an unbounded polyhedron from a "jagged” convex cap i...
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Monotonous betting strategies in warped casinos
Suppose that the outcomes of a roulette table are not entirely random, i...
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Blocking defector invasion by focusing on the most successful partner
According to the standard protocol of spatial public goods game, a coope...
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Granularity of wagers in games and the (im)possibility of savings
In a casino where arbitrarily small bets are admissible, any betting strategy M can be modified into a savings strategy that not only is successful on each casino sequence where M is (thus accumulating unbounded wealth inside the casino) but also saves an unbounded capital, by permanently and gradually withdrawing it from the game. Teutsch showed that this is no longer the case when a minimum wager is imposed by the casino, thus exemplifying a savings paradox where a player can win unbounded wealth inside the casino, but upon withdrawing a sufficiently large amount out of the game, he is forced into bankruptcy. We characterize the rate at which a variable minimum wager should shrink in order for saving strategies to succeed, subject to successful betting: if the minimum wager at stage s shrinks faster than 1/s, then savings are possible; otherwise Teutsch' savings paradox occurs.
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