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...

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...

Is there a division among n players of a cake using n-1 parallel vertical cuts, or of a pie using n radial cuts, that is envy-free (each player thinks he or she receives a largest piece and so does not envy another player) and undominated (there is no other allocation as good for all players and...

Power sharing is modeled as a duel over some prize. Each of two players may either share the prize in some ratio or fire at the other player—either in sequence or simultaneously—and eliminate it with a specified probability. If one player eliminates the other without being eliminated itself,...