Omniscience and omnipotence: How they may help - or hurt - in a game

The concepts of omniscience and omnipotence are defined in 2 ? 2 ordinal games, and implications for the optimal play of these games, when one player is omniscient or omnipotent and the other player is aware of his omniscience or omnipotence, are derived. Intuitively, omniscience allows a player to predict the strategy choice of an opponent in advance of play, and omnipotence allows a player, after initial strategy choices are made, to continue to move after the other player is forced to stop. Omniscience and its awareness by an opponent may hurt both players, but this problem can always be rectified if the other player is omniscient. This pathology can also be rectified if at least one of the two players is omnipotent, which can override the effects of omniscience. In some games, one player's omnipotence ? versus the other's ? helps him, whereas in other games the outcome induced does not depend on which player is omnipotent. Deducing whether a player is superior (omniscient or omnipotent) from the nature of his game playing alone raises several problems, however, suggesting the difficulty of devising tests for detecting superior ability in games
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DOI 10.1080/00201748208601963
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References found in this work BETA

Prisoners' Dilemma is a Newcomb Problem.David K. Lewis - 1979 - Philosophy and Public Affairs 8 (3):235-240.
The God of Philosophers.Anthony Kenny - 1979 - Oxford: Oxford University Press.
What an Omnipotent Agent Can Do.Gary Rosenkrantz & Joshua Hoffman - 1980 - International Journal for Philosophy of Religion 11 (1):1 - 19.

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Limited-Move Equilibria in 2 X 2 Games.Frank C. Zagare - 1984 - Theory and Decision 16 (1):1.
Staying Power in Sequential Games.Steven J. Brams & Marek P. Hessel - 1983 - Theory and Decision 15 (3):279-302.

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