Population monotonic and strategy-proof mechanisms respecting welfare lower bounds

The significance of population monotonicity and welfare bounds is well-recognized in the fair division literature. We consider the welfare bounds that are central to the fair allocation literature, namely, the identical-preferences lower-bound, individual rationality, the stand-alone lower-bound, and k- fairness. We characterize population monotonic and incentive compatible mechanisms which allocate an object efficiently and respect a welfare lower bound chosen in the fair allocation problem of allocating a collectively owned indivisible good or bad when monetary transfers are possible and preferences are private information. © 2013 Elsevier B.V.Duygu Yengi

Groves mechanisms and welfare bounds in a variable population setting

In the problem of allocating indivisible goods when monetary transfers are possible, if prefer- ences are quasilinear, then the Groves mechanisms are the only mechanisms which assign indivisible goods in an e¢ cient way and induce the agents to report their true preferences. We characterize the class of Groves mechanisms that respect the identical-preferences lower-bound: each agent should be at least as well o¤ as in an hypothetical economy where all agents have the same preference as hers, no agent envies another, and the budget is balanced. We also study the implications on Groves mechanisms of imposing variable population axioms together with welfare bounds.Duygu Yenginhttp://sites.google.com/site/economicdesign2008

Characterizing welfare-egalitarian mechanisms with solidarity when valuations are private information

In the problem of assigning indivisible goods and monetary transfers, we characterize welfare-egalitarian mechanisms (that are decision-efficient and incentive compatible) with an axiom of solidarity under preference changes and a fair ranking axiom of order preservation. This result is in line with characterizations of egalitarian rules with solidarity in other economic models. We also show that we can replace order-preservation with egalitarian-equivalence or no-envy (on the subadditive domain) and still characterize the welfare-egalitarian class. However, if we weaken order preservation to symmetry, mechanisms that are not welfare-egalitarian exist. We also study upper bounds on deficit and welfare lower bounds that characterize subclasses of the welfare-egalitarian class.Duygu Yengi

No-envy and egalitarian-equivalence under multi-object-demand for heterogeneous objects

We study the problem of allocating heterogeneous indivisible tasks in a multi-object-demand model (i.e., each agent can be assigned multiple objects) where monetary transfers are allowed. Agents’ costs for performing tasks are their private information and depend on what other tasks they are obtained with. First, we show that when costs are unrestricted or superadditive, then there is no envy-free and egalitarian-equivalent mechanism that assigns the tasks efficiently. Then, we characterize the class of envy-free and egalitarian-equivalent Groves mechanisms when costs are subadditive. Finally, within this class, under a bounded-deficit condition, we identify the Pareto-dominant subclass. We show that the mechanisms in this subclass are not Pareto-dominated by any other Groves mechanism satisfying the same bounded-deficit condition.Duygu Yengi

Fixed-route traveling salesman games and the shapley value

http://www.kellogg.northwestern.edu/meds/games2008

Existence of equilibria in incomplete markets with non-ordered preferences

We consider a two-period exchange economy with a finite set of consumers, states of nature, independent assets and a single consumption good. We prove the existence of competitive equilibrium in incomplete markets, when consumption set is not assumed to be compact, set of assets is linearly independent, and individuals' preferences are not assumed to be complete or transitive. Our study therefore generalizes various results in the existing literature.Erkan Yalci

Welfare lower bounds and strategy-proofness in the queueing problem

Abstract not availableYoungsub Chuna, Duygu Yengi

Fair groves mechanisms

The original publication can be found at www.springerlink.comWe study allocation problems in which a costly task is to be assigned and money transfers are used to achieve fairness among agents. We consider a series of fairness notions (k-fairness for k epsilon {1, ... , n} where n is the number of agents) of decreasing restrictiveness that are based on Rawls' maximin equity criterion and impose welfare lower bounds. These fairness notions were introduced by Porter et al. (J Econ Theory 118:209-228, 2004) who also introduced two classes of Groves mechanisms that are 1-fair and 3-fair, respectively, and generate deficits that are bounded above. We show that these classes are the largest such classes of Groves mechanisms. We generalize these mechanisms for each k epsilon {2, ... , n} and show that the corresponding mechanisms generate the smallest deficit for each economy among all k-fair Groves mechanisms.Murat Atlamaz and Duygu Yengi

Coincidence of cooperative game theoretic solutions in the appointment problem

The fixed-route traveling salesman problem with appointments, simply the appointment problem, is concerned with the following situation. Starting from home, a traveler makes a scheduled visit to a group of sponsors and returns home. If a sponsor in the route cancels her appointment, the traveler returns home and waits for the next appointment. We are interested in finding a way of dividing the total traveling cost among sponsors in the appointment problem by applying solutions developed in the cooperative game theory. We show that the well-known solutions of the cooperative game theory, the Shapley value, the nucleolus (or the prenucleolus), and the τ -value, coincide under a mild condition on the traveling cost.Youngsub Chun, Nari Park, Duygu Yengi