A theoretical analysis of the probability of nuclear war is developed that assumes a starting probability and an annual reduction factor. Whatever the starting probability is, a constant reduction factor leads to an eventual probability that is less than 1, whereas the eventual probability goes...

Ordinally single-peaked preferences are distinguished from cardinally single-peaked preferences, in which all players have a similar perception of distances in some one-dimensional ordering. While ordinal single-peakedness can lead to disconnected coalitions that have a ‘hole’ in...

In U.S. presidential elections, voters in noncompetitive states seem not to count—and so have zero voting power, according to the Banzhaf and other voting-power indices—because they cannot influence the outcome in their states. But because the electoral votes of these states are essential to...

We analyze a simple sequential algorithm (SA) for allocating indivisible items that are strictly ranked by n ≥ 2 players. It yields at least one Pareto-optimal allocation which, when n = 2, is envy-free unless no envy-free allocation exists. However, an SA allocation may not be maximin or...

An allocation of indivisible items among n ≥ 2 players is proportional if and only if each player receives a proportional subset—one that it thinks is worth at least 1/n of the total value of all the items. We show that a proportional allocation exists if and only if there is an allocation...

Assume it is known that one player in a 2 x 2 game can detect the strategy choice of its opponent with some probability before play commences. We formulate conditions under which the detector can, by credibly committing to a strategy of probabilistic tit-for-tat (based on its imperfect...

Many procedures have been suggested for the venerable problem of dividing a set of indivisible items between two players. We propose a new algorithm (AL), related to one proposed by Brams and Taylor (BT), which requires only that the players strictly rank items from best to worst. Unlike BT, in...

Game-theoretic models of deterrence and escalation, based on Chicken and Prisoners' Dilemma, are developed in which two players can initially choose any level of preemption in a crisis (Deterrence Game) or escalation in an arms race (Deescalation Game). The greater this level, the more likely an...

Arms-control inspection is modeled by two games, one played simultaneously and one sequentially, between an inspector (O) and an inspectee (E). In each game, E may choose to comply with or violate an arms-control agreement and O may choose to inspect, or not, for a possible violation by E....