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...

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,...

We study the problem of dissolving an equal-entitlement partnership when the objective is to minimize maximum regret. We initially focus on the family of linear-pricing mechanisms and derive regret-optimizing strategies. We also demonstrate that there exist linear-pricing mechanisms satisfying...

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...

We propose a procedure for dividing indivisible items between two players in which each player ranks the items from best to worst and has no information about the other player’s ranking. It ensures that each player receives a subset of items that it values more than the other player’s...

Three models are presented in which two players agree to share power in a particular ratio, but either player may subsequently “fire” at the other, as in a duel, to try to eliminate it. The players have positive probabilities of eliminating each other by firing. If neither is successful, the...

Democracy resolves conflicts in difficult games like Prisoners’ Dilemma and Chicken by stabilizing their cooperative outcomes. It does so by transforming these games into games in which voters are presented with a choice between a cooperative outcome and a Pareto-inferior noncooperative...

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...