Barbanel, Brams, and Stromquist (2009) asked whether there exists a two-person moving-knife procedure that yields an envy-free, undominated, and equitable allocation of a pie. We present two procedures: One yields an envy-free, almost undominated, and almost equitable allocation, whereas the...

Players are assumed to rank each other as coalition partners. Two processes of coalition formation are defined and illustrated: i) Fallback (FB): Players seek coalition partners by descending lower and lower in their preference rankings until some majority coalition, all of whose members...

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 the ordering,...

Assume that players strictly rank each other as coalition partners. We propose a procedure whereby they fall back on their preferences, yielding internally compatible, or coherent, majority coalition(s), which we call fallback coalitions. If there is more than one fallback coalition, the players...

In this unusual book, first published by The MIT Press in 1980 and now updated with a new chapter, Steven Brams applies the mathematical theory of games to the Hebrew Bible. Brams's thesis is that God and the human biblical characters acted rationally—that is, given their preferences and their...

In the much-studied Centipede Game, which resembles the Iterated Prisoners' Dilemma, two players successively choose between (1) cooperating, by continuing play, or (2) defecting and terminating play. The subgame-perfect Nash equilibrium implies that play terminates on the first move, even...

Assume that players strictly rank each other as coalition partners. We propose a procedure whereby they “fall back” on their preferences, yielding internally compatible, or coherent, majority coalition(s), which we call fallback coalitions. If there is more than one fallback coalition, the...

We study the problem of dissolving a partnership when agents have unequal endowments. Agents bid on the price of the entire partnership. The highest bidder is awarded the partnership and buys out her partners' shares at a per-unit price that is a function of the two highest bids. We show that...

We analyze a class of proportional cake-cutting algorithms that use a minimal number of cuts (n-1 if there are n players) to divide a cake that the players value along one dimension. While these algorithms may not produce an envy-free or efficient allocation--as these terms are used in the...

Assume that players strictly rank each other as coalition partners. We propose a procedure whereby they “fall back” on their preferences, yielding internally compatible, or coherent, majority coalition(s), which we call fallback coalitions. If there is more than one fallback coalition, the...