1,849 research outputs found
Equilibria in Sequential Allocation
Sequential allocation is a simple mechanism for sharing multiple indivisible
items. We study strategic behavior in sequential allocation. In particular, we
consider Nash dynamics, as well as the computation and Pareto optimality of
pure equilibria, and Stackelberg strategies. We first demonstrate that, even
for two agents, better responses can cycle. We then present a linear-time
algorithm that returns a profile (which we call the "bluff profile") that is in
pure Nash equilibrium. Interestingly, the outcome of the bluff profile is the
same as that of the truthful profile and the profile is in pure Nash
equilibrium for \emph{all} cardinal utilities consistent with the ordinal
preferences. We show that the outcome of the bluff profile is Pareto optimal
with respect to pairwise comparisons. In contrast, we show that an assignment
may not be Pareto optimal with respect to pairwise comparisons even if it is a
result of a preference profile that is in pure Nash equilibrium for all
utilities consistent with ordinal preferences. Finally, we present a dynamic
program to compute an optimal Stackelberg strategy for two agents, where the
second agent has a constant number of distinct values for the items
Fallback Bargaining
Fallback bargaining is a bargaining procedure under which bargainers begin by indicating their preference rankings over all alternatives. They then fall back, in lockstep, to less and less preferred alternatives - starting with first choices, then adding second choices, and so on - until an alternative is found on which all bargainers agree. This common agreement, which becomes the outcome of the procedure, may be different if a decision rule other than unanimity is used.BARGAINING ; SOCIAL CHOICE ; NASH EQUILIBRIUM
PTAS for Minimax Approval Voting
We consider Approval Voting systems where each voter decides on a subset to
candidates he/she approves. We focus on the optimization problem of finding the
committee of fixed size k minimizing the maximal Hamming distance from a vote.
In this paper we give a PTAS for this problem and hence resolve the open
question raised by Carragianis et al. [AAAI'10]. The result is obtained by
adapting the techniques developed by Li et al. [JACM'02] originally used for
the less constrained Closest String problem. The technique relies on extracting
information and structural properties of constant size subsets of votes.Comment: 15 pages, 1 figur
Dividing the Indivisible: Procedures for Allocating Cabinet Ministries to Political Parties in a Parliamentary System
Political parties in Northern Ireland recently used a divisor method of apportionment to choose, in sequence, ten cabinet ministries. If the parties have complete information about each others' preferences, we show that it may not be rational for them to act sincerely by choosing their most-preferred ministry that is available. One consequence of acting sophisticatedly is that the resulting allocation may not be Pareto-optimal, making all the parties worse off. Another is nonmonotonicty-choosing earlier may hurt rather than help a party. We introduce a mechanism that combines sequential choices with a structured form of trading that results in sincere choices for two parties. Although there are difficulties in extending this mechanism to more than two parties, other approaches are explored, such as permitting parties to making consecutive choices not prescribed by an apportionment method. But certain problems, such as eliminating envy, remain.APPORTIONMENT METHODS; CABINETS; SEQUENTIAL ALLOCATION; MECHANISM DESIGN; FAIRNESS
Resolving Social Issues in a Merger: A Fair-Division Approach
One of the most elusive ingredients in the success of a deal is what deal makers euphemistically refer to as "Social issues" - how power, position, and status will be allocated among the merging companies' executives. A failure to resolve these issues often leads to the destruction of shareholder wealth and portrayal of top executives as petty corporates chieftains, unable to subordinate their selfish interests to the goal of promoting shareholder well-being.MERGERS ; EFFICIENCY ; EQUITY
Voter Sovereignty and Election Outcomes
APPROVAL VOTING; ELECTIONS; CONDORCET WINNER/LOSER; NASH EQUILIBRIUM.
Going from Theory to Practice: The Mixed Success of Approval Voting
Approval voting (AV) is a voting system in which voters can vote for, or approve of, as many candidates as they like in multicandidate elections. In 1987 and 1988, four scientific and engineering societies, collectively comprising several hundred thousand members, used AV for the first time. Since then, about half a dozen other societies have adopted AV. Usually its adoption was seriously debated, but other times pragmatic or political considerations proved decisive in its selection. While AV has an ancient pedigree, its recent history is the focus of this paper. Ballot data from some of the societies that adopted AV are used to compare theoretical results with experience, including the nature of voting under AV and the kinds of candidates that are elected. Although the use of AV is generally considered to have been successful in the societies-living up to the rhetoric of its proponents-AV has been a controversial reform. AV is not currently used in any public elections, despite efforts to institute it, so its success should be judged as mixed. The chief reason for its nonadoption in public elections, and by some societies, seems to be a lack of key "insider" support.APPROVAL VOTING; ELECTIONS; PROFESSIONAL SOCIETIES; CONDORCET CANDIDATE.
Kingmakers and Leaders in Coalition Formation
Assume that players strictly rank each other as coalition partners. We propose a procedure whereby they âfall backâ 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 common to them, or kingmakers, determine which fallback coalition will form. The players(s) who are the first to be acceptable to all other members of a fallback coalition are the leader(s) of that coalition. The effects of different preference assumptionsâparticularly, different kinds of single-peakednessâand of player weights on the number of coherent coalitions, their connectedness, and which players become kingmakers and leaders are investigated. The fallback procedure may be used (i) empirically to identify kingmakers and leaders or (ii) normatively to select them.Coalition, Fallback Process, Kingmaker Leader, Cardinally Single-peaked, Ordinally Single-peaked
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