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. (shrink)

This article examines deception possibilities for two players in simple three-person voting games. An example of one game vulnerable to (tacit) deception by two players is given and its implications discussed. The most unexpected findings of this study is that in those games vulnerable to deception by two players, the optimal strategy of one of them is always to announce his (true) preference order. Moreover, since the player whose optimal announcement is his true one is unable to induce a better (...) outcome for himself by misrepresenting his preference, while his partner can, this player will find that possessing a monopoly of information will not give him any special advantage. In fact, this analysis demonstrates that he may have incentives to share his information selectively with one or another of his opponents should he alone possess complete information at the outset. (shrink)