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WORKSHOP ON FAIR DIVISION

ISTANBUL TECHNICAL UNIVERSITY
ECONOMICS DEPARTMENT

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FEBRUARY 9, 2019



The Department of Economics at Istanbul Technical University is organizing an
International Workshop in Fair Division. The workshop will be held on February
9, 2019, at the Management Faculty of Istanbul Technical University. This
workshop aims to bring scholars in the area of Fair Division to present and
discuss their current research and to foster interaction and collaboration on
new research perspectives.

Fair Division is an active field of research that considers to allocate scarce
resources and to design social institutions. Recently, it has become a subject
of interdisciplinary research at the interface of Economics, Mathematics, and
Computer Science with successful real-life applications including divorce and
inheritance settlements, border settlements in international disputes,
allocation of mineral riches in the ocean bed, greenhouse gas reductions,
bandwidth and memory allocation in networks, cost sharing in communication
networks and many others.

Workshop Program


ABSTRACTS OF PRESENTATIONS

List of Speakers Institute Abstract Mustafa Oğuz Afacan Sabancı University A
Task-Allocation Problem Kemal Kıvanç Aköz Higher School of Economics Preemptive
versus Counter Offers Orhan Aygün Boğaziçi University Preserving Priorities in
the Case of the Re-Placement of Medical Residents in Turkey Emre Doğan Higher
School of Economics Population Monotonicity in Fair Division of Multiple
Indivisible Goods Sinan Ertemel Istanbul Technical University Ex-ante and
Ex-post Forms of Bankruptcy Rules for Risky Claims Emin Karagözoğlu Bilkent
University When the Going Gets Tough or Easy in Bargaining Rajnish Kumar Queen's
University Belfast Group Interactions in TU games: The k-lateral value Shiran
Rachmilevitch University of Haifa Pre-bargaining Investment and its Social Cost
David Thomas Seymour Istanbul Technical University Matching with Overlapping
Quotas under Weak Preferences

ORGANIZERS

SINAN ERTEMEL

Istanbul Technical University

DAVID THOMAS SEYMOUR

Istanbul Technical University

CONTACT WITH ORGANIZER

Assist. Prof. Dr. Sinan Ertemel

Office: D622

Phone: +90-212-2931300 (2059-16)

ertemels@itu.edu.tr



A TASK-ALLOCATION PROBLEM
MUSTAFA OĞUZ AFACAN (SABANCI UNIVERSITY)



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Abstract: We consider a task-allocation problem in which agents differ in terms
of their seniority and their experience with tasks. We introduce two mechanism
classes: the feasibility augmented serial dictatorship (FSD) and the minimally
reluctant efficient priority (MREP). The first class is efficient,
senior-optimal, and strategy-proof. However, a disadvantage of this class is
that a greater number of agents can be assigned to tasks that they unwillingly
perform — we call such tasks “unwillingly acceptable” — than what is actually
achievable. We say that a mechanism is minimally reluctant if it always
minimizes the number agents who are matched with their unwillingly acceptable
tasks. The second mechanism class is minimally reluctant, efficient, and
constrained senior-optimal — senior-optimal in the class of minimally reluctant
mechanisms. No minimally reluctant mechanism is strategy-proof, which implies
that no MREP mechanism is strategy-proof. Each MREP mechanism has a unique
equilibrium outcome that is equivalent to the truthtelling outcome of a
particular FSD mechanism. Hence, in equilibrium, each MREP mechanism is
efficient, senior-optimal, but not minimally reluctant. Nevertheless, no
mechanism is minimally reluctant in equilibrium either.

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PREEMPTIVE VERSUS COUNTER OFFERS (JOINT WITH NEJAT ANBARCI AND KANG RONG)
KEMAL KIVANÇ AKÖZ (HIGHER SCHOOL OF ECONOMICS)

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Abstract: We consider an ultimatum-game setup, which has two key non-standard
features: (1) The responder has an initial fallback position, which is her
private information (except for the benchmark complete-information case), and
(2) she can improve her initial fallback position further by means of costly
investment, which does not contribute to the joint surplus. There are two
sources of inefficiency in our model: disagreement and the deadweight-loss
investment. The proposer ends up either making a counter offer after finding out
the responder's type and her outside offer or a particular preemptive offer
before her investment and before the uncertainty of about her type is not
resolved (except for the incomplete-information case). Thus, any preemptive
offer aims for agreement before investment, which, if accepted, avoids the
inefficiency due to deadweight-loss investment; if rejected, it always leads to
inefficiency. A counter offer, however, always guarantees agreement, but only
after investment cost is incurred, and is thus inefficient. Along with the
complete-information case, we also consider the no- and noisy-information cases.
We find that in the complete-information case the unique offer is a preemptive
offer which always achieves efficiency by also leads to agreement, since the
responder's type is common knowledge. In the other cases, if the proposer's
(prior or posterior) belief about the responder's type is not precise enough, he
might prefer to wait until after the investment of the responder to make her a
counter offer. It turns out that more precise information reduces both types of
inefficiency by leading to preemptive offers which are accepted with higher
probability. We also show that our results are robust to various extensions such
as risk aversion by players, multiple offers by the proposer, continuum of
responder types, and type-dependent investment costs.

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PRESERVING PRIORITIES IN THE CASE OF THE RE-PLACEMENT OF MEDICAL RESIDENTS IN
TURKEY
ORHAN AYGÜN (BOĞAZIÇI UNIVERSITY)

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Abstract: In this paper, we analyze the re-placement mechanism used in the
Examination of Specialty in Medicine in Turkey, following the re-calculation of
the scores. We observe that the preservation of vested interests, together with
the limited capacities lead to violation of fairness. Furthermore, we show that
the current mechanism create redundant capacities at programs, even to those
doctors, who would not be accepted by the programs if the score calculation had
been correct in the beginning. In line with preventing the creation of those
unnecessary capacities, we define a new notion of fairness, capacity respecting
fairness (QRF), such that a candidate, who is ranked within the original
capacity of a program among the application pool is never rejected. We also
define QRF-Adjusted Modified Choice Function for programs, and show that it is
the choice function, which minimizes the deviation from the target capacities
whilst preserving the vested interests. Furthermore, we also show that the
QRF-Adjusted Modified Choice Function induced by the deferred acceptance
algorithm, is strategy-proof and minimizes the deviation of the outcome from the
target capacities of the programs.

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POPULATION MONOTONICITY IN FAIR DIVISION OF MULTIPLE INDIVISIBLE GOODS
EMRE DOĞAN (HIGHER SCHOOL OF ECONOMICS)

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Abstract: We consider the fair division of a set of indivisible goods where each
agent can receive more than one, and monetary transfers are allowed. We show in
case there are three (four) or more goods that no solution is simultaneously
efficient and population monotonic (PM) on the superadditive (subadditive)
Cartesian product preference domain. Moreover, the Shapley solution is not PM
even on the submodular domain. For the two-good case, Shapley solution and the
constrained egalitarian solution are PM on the subadditive preference domain. We
also define hybrid solutions that are efficient and PM on the entire monotone
preference domain. The hybrid Shapley solution and the hybrid constrained
egalitarian solution are two examples of such solutions.

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EX-ANTE AND EX-POST FORMS OF BANKRUPTCY RULES FOR RISKY CLAIMS
SINAN ERTEMEL (ISTANBUL TECHNICAL UNIVERSITY)

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Abstract: Bankruptcy rules are considered in a model where individual claims are
state contingent. A rule must allocate shares before uncertainty resolves.
Within a wide class, we characterize when does the rule have the ex-ante form in
terms of the way that the rule processes inherent uncertainty in the individual
claims. The key property is: No Penalty for Risk. It says that the rule does not
penalize an individual in a situation that differs from another only in terms of
this individual’s claim in that the former situation has a risky version of the
riskless claim in the latter situation. For the ex-post characterization, the
key property is: Indifference to Independence. It says that if individuals are
risk neutral then the rule makes the individual indifferent between any
bankruptcy problem and a corresponding one which is an independent combination
of gamble, with each gamble being a randomization over an “ex-post” problem
based on the statewise specification of the original problem and another problem
which has zero resource such that the probability on the first is equal to the
probability of realization of the state to which the “ex-post” problem
corresponds to. Finally, within the specified class, a comparative static result
is established which leads to the point that ex-ante rules may be normatively
more appealing on being proposed to individuals when the level of the resource
is low enough.

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WHEN THE GOING GETS TOUGH OR EASY IN BARGAINING
EMIN KARAGÖZOĞLU (BILKENT UNIVERSITY)

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Abstract: Same economic actors periodically bargain over the division of
resources. Labor-management, budget allocation, and contract negotiations are
some examples. For situations that involve (i) periodic negotiations (e.g.,
contract negotiations), (ii) multiple, competing reference points justified by
equity, precedents, or equality, and (iii) exogenously / stochastically varying
stakes, we ask the following questions: (a) Should economic actors bargain over
the whole pie or should they bargain over the amount of change with respect to
the old pie size? Is there a systematic difference in bargaining outcomes?
(i.e., does narrow or large bracketing make a difference?) and (b) Do subjective
entitlements and bargaining outcomes differ when negotiations are made over
losses rather than gains? In order to answer these questions, conduct a
laboratory experiment with a 2x2, between subjects design, where the size of a
bargaining pie stochastically changes. We observe systematic effects of our
manipulations on subjective entitlements and agreements. Most interestingly,
narrow bracketing leads to agreements even more asymmetric than what the induced
reference point implies; and it favors those players who were already favored by
the reference point present in the environment. We see that the treatment
manipulation first influences bargainers’ subjective entitlements, and then
transmitted to subjects’ first proposals, and then naturally influences
agreements. Importantly, the exposure to narrow-large bracketing is not
identical across subjects in the same pair.

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GROUP INTERACTIONS IN TU GAMES: THE K-LATERAL VALUE
RAJNISH KUMAR (QUEEN'S UNIVERSITY BELFAST)

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Abstract: In this paper we propose the k-lateral value that accounts for
simultaneous k-lateral group interactions among players. The Shapley like values
implicitly assume that players are independent in deciding to leave or join a
coalition. However in many real life situations, players are likely to be
influenced by their peers in making such decisions. Thus group interactions and
group contributions are also important in determining players’ shares in the
total resource they generate. The k-lateral value accounts for both
egalitarianism and marginal productivity of the players and thus it is a member
of the class of solidarity values. We give a couple of characterizations of the
k-lateral value with standard and intuitive axioms.

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PRE-BARGAINING INVESTMENT AND ITS SOCIAL COST
SHIRAN RACHMILEVITCH (UNIVERSITY OF HAIFA)

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Abstract: Two players play a symmetric game in which each player’s pure actions
are cooperate and don’t cooperate. The realized actions determine a bargaining
problem. The greater the number of cooperators (it can be zero, one, or two),
the greater is the available surplus in that problem. However, don’t cooperate
secures a high disagreement payoff, hence there is tradeoff between the two
actions. In the realized bargaining problem, payoffs are distributed according
to an exogenously given bargaining solution. I study the welfare-maximizing Nash
equilibrium of this game. The equilibrium cooperation probability
(alternatively, the equilibrium welfare) is decreasing in the bargaining
solution’s disagreement-sensitivity. Thus, to obtain a ranking of solutions in
terms of the cooperation/welfare they induce, it is enough to rank them in terms
of disagreement-sensitivity. I describe two classes of problems on which the
Nash and Kalai-Smorodinsky solutions are ranked in opposite ways.

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MATCHING WITH OVERLAPPING QUOTAS UNDER WEAK PREFERENCES
DAVID THOMAS SEYMOUR (ISTANBUL TECHNICAL UNIVERSITY)

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Abstract: We develop a framework for analyzing a school choice environment where
each student may simultaneously satisfy multiple quota criteria, such as race
and gender. In our environment, schools primarily care about filling as many
quota seats as possible and then care about maximizing student quality. Students
have weak preferences over their admitted status at a school, allowing students
to either prefer one admitted status to another or be indifferent between two
admitted statuses. By considering the sets of contracts that students are
indifferent between as the main object in the school's choice function, we
present a method for analyzing the overlapping quota problem. Our procedure can
be nested into a cumulative offer process and has appealing computational
properties.

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