Online research in philosophy

This paper analyzes criteria of fair division of a set of indivisible items among people whose revealed preferences are limited to rankings of the items and for whom no side payments are allowed. The criteria include refinements of Pareto optimality and envy-freeness as well as dominance-freeness, evenness of shares, and two criteria based on equally-spaced surrogate utilities, referred to as maxsum and equimax. Maxsum maximizes a measure of aggregate utility or welfare, whereas equimax lexicographically maximizes persons' utilities from smallest to (...) largest. The paper analyzes conflicts among the criteria along with possibilities and pitfalls of achieving fair division in a variety of circumstances. (shrink)

A cornerstone of game theory is backward induction, whereby players reason backward from the end of a game in extensive form to the beginning in order to determine what choices are rational at each stage of play. Truels, or three-person duels, are used to illustrate how the outcome can depend on (1) the evenness/oddness of the number of rounds (the parity problem) and (2) uncertainty about the endpoint of the game (the uncertainty problem). Since there is no known endpoint in (...) the latter case, an extension of the idea of backward induction is used to determine the possible outcomes. The parity problem highlights the lack of robustness of backward induction, but it poses no conflict between foundational principles. On the other hand, two conflicting views of the future underlie the uncertainty problem, depending on whether the number of rounds is bounded (the players invariably shoot from the start) or unbounded (they may all cooperate and never shoot, despite the fact that the truel will end with certainty and therefore be effectively bounded). Some real-life examples, in which destructive behavior sometimes occurred and sometimes did not, are used to illustrate these differences, and some ethical implications of the analysis are discussed. (shrink)

Issues that arise in using game theory to model national security problems are discussed, including positing nation-states as players, assuming that their decision makers act rationally and possess complete information, and modeling certain conflicts as two-person games. A generic two-person game called the Conflict Game, which captures strategic features of such variable-sum games as Chicken and Prisoners'' Dilemma, is then analyzed. Unlike these classical games, however, the Conflict Game is a two-stage game in which each player can threaten to retaliate (...) — and carry out this threat in the second stage — if its opponent chose noncooperation in the first stage.Conditions for the existence of different pure-strategy Nash equilibria, or stable outcomes, are found, and these results are extended to situations in which the players can select mixed strategies (i.e., make probabilistic threats or choices). Although the Conflict Game sheds light on the rational foundations underlying arms races, nuclear deterrence, and other strategic situations, more detailed assumptions are required to tie this generic game to specific conflicts. (shrink)

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)