11,448 research outputs found
An Algorithmic Framework for Strategic Fair Division
We study the paradigmatic fair division problem of allocating a divisible
good among agents with heterogeneous preferences, commonly known as cake
cutting. Classical cake cutting protocols are susceptible to manipulation. Do
their strategic outcomes still guarantee fairness?
To address this question we adopt a novel algorithmic approach, by designing
a concrete computational framework for fair division---the class of Generalized
Cut and Choose (GCC) protocols}---and reasoning about the game-theoretic
properties of algorithms that operate in this model. The class of GCC protocols
includes the most important discrete cake cutting protocols, and turns out to
be compatible with the study of fair division among strategic agents. In
particular, GCC protocols are guaranteed to have approximate subgame perfect
Nash equilibria, or even exact equilibria if the protocol's tie-breaking rule
is flexible. We further observe that the (approximate) equilibria of
proportional GCC protocols---which guarantee each of the agents a
-fraction of the cake---must be (approximately) proportional. Finally, we
design a protocol in this framework with the property that its Nash equilibrium
allocations coincide with the set of (contiguous) envy-free allocations
A Multi-Game Framework for Harmonized LTE-U and WiFi Coexistence over Unlicensed Bands
The introduction of LTE over unlicensed bands (LTE-U) will enable LTE base
stations (BSs) to boost their capacity and offload their traffic by exploiting
the underused unlicensed bands. However, to reap the benefits of LTE-U, it is
necessary to address various new challenges associated with LTE-U and WiFi
coexistence. In particular, new resource management techniques must be
developed to optimize the usage of the network resources while handling the
interdependence between WiFi and LTE users and ensuring that WiFi users are not
jeopardized. To this end, in this paper, a new game theoretic tool, dubbed as
\emph{multi-game} framework is proposed as a promising approach for modeling
resource allocation problems in LTE-U. In such a framework, multiple,
co-existing and coupled games across heterogeneous channels can be formulated
to capture the specific characteristics of LTE-U. Such games can be of
different properties and types but their outcomes are largely interdependent.
After introducing the basics of the multi-game framework, two classes of
algorithms are outlined to achieve the new solution concepts of multi-games.
Simulation results are then conducted to show how such a multi-game can
effectively capture the specific properties of LTE-U and make of it a
"friendly" neighbor to WiFi.Comment: Accepted for publication at IEEE Wireless Communications Magazine,
Special Issue on LTE in Unlicensed Spectru
Monotonicity and Competitive Equilibrium in Cake-cutting
We study the monotonicity properties of solutions in the classic problem of
fair cake-cutting --- dividing a heterogeneous resource among agents with
different preferences. Resource- and population-monotonicity relate to
scenarios where the cake, or the number of participants who divide the cake,
changes. It is required that the utility of all participants change in the same
direction: either all of them are better-off (if there is more to share or
fewer to share among) or all are worse-off (if there is less to share or more
to share among).
We formally introduce these concepts to the cake-cutting problem and examine
whether they are satisfied by various common division rules. We prove that the
Nash-optimal rule, which maximizes the product of utilities, is
resource-monotonic and population-monotonic, in addition to being
Pareto-optimal, envy-free and satisfying a strong competitive-equilibrium
condition. Moreover, we prove that it is the only rule among a natural family
of welfare-maximizing rules that is both proportional and resource-monotonic.Comment: Revised versio
How efficiency shapes market impact
We develop a theory for the market impact of large trading orders, which we
call metaorders because they are typically split into small pieces and executed
incrementally. Market impact is empirically observed to be a concave function
of metaorder size, i.e., the impact per share of large metaorders is smaller
than that of small metaorders. We formulate a stylized model of an algorithmic
execution service and derive a fair pricing condition, which says that the
average transaction price of the metaorder is equal to the price after trading
is completed. We show that at equilibrium the distribution of trading volume
adjusts to reflect information, and dictates the shape of the impact function.
The resulting theory makes empirically testable predictions for the functional
form of both the temporary and permanent components of market impact. Based on
the commonly observed asymptotic distribution for the volume of large trades,
it says that market impact should increase asymptotically roughly as the square
root of metaorder size, with average permanent impact relaxing to about two
thirds of peak impact.Comment: 34 pages, 3 figure
The Sponge Cake Dilemma over the Nile: Achieving Fairness in Resource Allocation through Rawlsian Theory and Algorithms
This article examines water disputes through an integrated framework
combining normative and positive perspectives. John Rawls' theory of justice
provides moral guidance, upholding rights to reasonable access for all riparian
states. However, positive analysis using cake-cutting models reveals real-world
strategic constraints. While Rawls defines desired ends, cake-cutting offers
algorithmic means grounded in actual behaviors. The Nile River basin dispute
illustrates this synthesis. Rawls suggests inherent rights to water, but
unrestricted competition could enable monopoly. His principles alone cannot
prevent unfavorable outcomes, given limitations like self-interest. This is
where cake-cutting provides value despite biased claims. Its models identify
arrangements aligning with Rawlsian fairness while incorporating strategic
considerations. The article details the cake-cutting theory, reviews water
conflicts literature, examines the Nile case, explores cooperative vs.
non-cooperative games, and showcases algorithmic solutions. The integrated
framework assesses pathways for implementing Rawlsian ideals given real-world
dynamics. This novel synthesis of normative and positive lenses enriches the
study of water disputes and resource allocation more broadly.Comment: 31 pages, 7 Figure
Fair assignment of indivisible objects under ordinal preferences
We consider the discrete assignment problem in which agents express ordinal
preferences over objects and these objects are allocated to the agents in a
fair manner. We use the stochastic dominance relation between fractional or
randomized allocations to systematically define varying notions of
proportionality and envy-freeness for discrete assignments. The computational
complexity of checking whether a fair assignment exists is studied for these
fairness notions. We also characterize the conditions under which a fair
assignment is guaranteed to exist. For a number of fairness concepts,
polynomial-time algorithms are presented to check whether a fair assignment
exists. Our algorithmic results also extend to the case of unequal entitlements
of agents. Our NP-hardness result, which holds for several variants of
envy-freeness, answers an open question posed by Bouveret, Endriss, and Lang
(ECAI 2010). We also propose fairness concepts that always suggest a non-empty
set of assignments with meaningful fairness properties. Among these concepts,
optimal proportionality and optimal weak proportionality appear to be desirable
fairness concepts.Comment: extended version of a paper presented at AAMAS 201
Social Welfare in One-Sided Matching Mechanisms
We study the Price of Anarchy of mechanisms for the well-known problem of
one-sided matching, or house allocation, with respect to the social welfare
objective. We consider both ordinal mechanisms, where agents submit preference
lists over the items, and cardinal mechanisms, where agents may submit
numerical values for the items being allocated. We present a general lower
bound of on the Price of Anarchy, which applies to all
mechanisms. We show that two well-known mechanisms, Probabilistic Serial, and
Random Priority, achieve a matching upper bound. We extend our lower bound to
the Price of Stability of a large class of mechanisms that satisfy a common
proportionality property, and show stronger bounds on the Price of Anarchy of
all deterministic mechanisms
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