159 research outputs found
Manipulating Tournaments in Cup and Round Robin Competitions
In sports competitions, teams can manipulate the result by, for instance,
throwing games. We show that we can decide how to manipulate round robin and
cup competitions, two of the most popular types of sporting competitions in
polynomial time. In addition, we show that finding the minimal number of games
that need to be thrown to manipulate the result can also be determined in
polynomial time. Finally, we show that there are several different variations
of standard cup competitions where manipulation remains polynomial.Comment: Proceedings of Algorithmic Decision Theory, First International
Conference, ADT 2009, Venice, Italy, October 20-23, 200
Undominated Groves Mechanisms
The family of Groves mechanisms, which includes the well-known VCG mechanism (also
known as the Clarke mechanism), is a family of efficient and strategy-proof mechanisms.
Unfortunately, the Groves mechanisms are generally not budget balanced. That is, under
such mechanisms, payments may flow into or out of the system of the agents, resulting
in deficits or reduced utilities for the agents. We consider the following problem: within
the family of Groves mechanisms, we want to identify mechanisms that give the agents the
highest utilities, under the constraint that these mechanisms must never incur deficits.
We adopt a prior-free approach. We introduce two general measures for comparing
mechanisms in prior-free settings. We say that a non-deficit Groves mechanism M in-
dividually dominates another non-deficit Groves mechanism M′ if for every type profile,
every agent’s utility under M is no less than that under M′, and this holds with strict
inequality for at least one type profile and one agent. We say that a non-deficit Groves
mechanism M collectively dominates another non-deficit Groves mechanism M′ if for every
type profile, the agents’ total utility under M is no less than that under M′, and this holds
with strict inequality for at least one type profile. The above definitions induce two partial
orders on non-deficit Groves mechanisms. We study the maximal elements corresponding
to these two partial orders, which we call the individually undominated mechanisms and
the collectively undominated mechanisms, respectively
Coreness of Cooperative Games with Truncated Submodular Profit Functions
Coreness represents solution concepts related to core in cooperative games,
which captures the stability of players. Motivated by the scale effect in
social networks, economics and other scenario, we study the coreness of
cooperative game with truncated submodular profit functions. Specifically, the
profit function is defined by a truncation of a submodular function
: if and
otherwise, where is a given threshold. In this paper, we
study the core and three core-related concepts of truncated submodular profit
cooperative game. We first prove that whether core is empty can be decided in
polynomial time and an allocation in core also can be found in polynomial time
when core is not empty. When core is empty, we show hardness results and
approximation algorithms for computing other core-related concepts including
relative least-core value, absolute least-core value and least average
dissatisfaction value
Settling Some Open Problems on 2-Player Symmetric Nash Equilibria
Over the years, researchers have studied the complexity of several decision
versions of Nash equilibrium in (symmetric) two-player games (bimatrix games).
To the best of our knowledge, the last remaining open problem of this sort is
the following; it was stated by Papadimitriou in 2007: find a non-symmetric
Nash equilibrium (NE) in a symmetric game. We show that this problem is
NP-complete and the problem of counting the number of non-symmetric NE in a
symmetric game is #P-complete.
In 2005, Kannan and Theobald defined the "rank of a bimatrix game"
represented by matrices (A, B) to be rank(A+B) and asked whether a NE can be
computed in rank 1 games in polynomial time. Observe that the rank 0 case is
precisely the zero sum case, for which a polynomial time algorithm follows from
von Neumann's reduction of such games to linear programming. In 2011, Adsul et.
al. obtained an algorithm for rank 1 games; however, it does not solve the case
of symmetric rank 1 games. We resolve this problem
Verifiably Truthful Mechanisms
It is typically expected that if a mechanism is truthful, then the agents
would, indeed, truthfully report their private information. But why would an
agent believe that the mechanism is truthful? We wish to design truthful
mechanisms, whose truthfulness can be verified efficiently (in the
computational sense). Our approach involves three steps: (i) specifying the
structure of mechanisms, (ii) constructing a verification algorithm, and (iii)
measuring the quality of verifiably truthful mechanisms. We demonstrate this
approach using a case study: approximate mechanism design without money for
facility location
Combinatorial Voter Control in Elections
Voter control problems model situations such as an external agent trying to
affect the result of an election by adding voters, for example by convincing
some voters to vote who would otherwise not attend the election. Traditionally,
voters are added one at a time, with the goal of making a distinguished
alternative win by adding a minimum number of voters. In this paper, we
initiate the study of combinatorial variants of control by adding voters: In
our setting, when we choose to add a voter~, we also have to add a whole
bundle of voters associated with . We study the computational
complexity of this problem for two of the most basic voting rules, namely the
Plurality rule and the Condorcet rule.Comment: An extended abstract appears in MFCS 201
Complexity of Manipulative Actions When Voting with Ties
Most of the computational study of election problems has assumed that each
voter's preferences are, or should be extended to, a total order. However in
practice voters may have preferences with ties. We study the complexity of
manipulative actions on elections where voters can have ties, extending the
definitions of the election systems (when necessary) to handle voters with
ties. We show that for natural election systems allowing ties can both increase
and decrease the complexity of manipulation and bribery, and we state a general
result on the effect of voters with ties on the complexity of control.Comment: A version of this paper will appear in ADT-201
Towards a Dichotomy of Finding Possible Winners in Elections Based on Scoring Rules
Abstract. To make a joint decision, agents (or voters) are often required to provide their preferences as linear orders. To determine a winner, the given linear orders can be aggregated according to a voting protocol. However, in realistic settings, the voters may often only provide partial orders. This directly leads to the POSSIBLE WINNER problem that asks, given a set of partial votes, if a distinguished candidate can still become a winner. In this work, we consider the computational complexity of POSSIBLE WINNER for the broad class of voting protocols defined by scoring rules. A scoring rule provides a score value for every position which a candidate can have in a linear order. Prominent examples include plurality, k-approval, and Borda. Generalizing previous NP-hardness results for some special cases and providing new many-one reductions, we settle the computational complexity for all but one scoring rule. More precisely, for an unbounded number of candidates and unweighted voters, we show that POSSI-BLE WINNER is NP-complete for all pure scoring rules except plurality, veto, and the scoring rule defined by the scoring vector (2,1,..., 1, 0), while it is solvable in polynomial time for plurality and veto.
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