3,467 research outputs found
Pareto-Optimal Allocation of Indivisible Goods with Connectivity Constraints
We study the problem of allocating indivisible items to agents with additive
valuations, under the additional constraint that bundles must be connected in
an underlying item graph. Previous work has considered the existence and
complexity of fair allocations. We study the problem of finding an allocation
that is Pareto-optimal. While it is easy to find an efficient allocation when
the underlying graph is a path or a star, the problem is NP-hard for many other
graph topologies, even for trees of bounded pathwidth or of maximum degree 3.
We show that on a path, there are instances where no Pareto-optimal allocation
satisfies envy-freeness up to one good, and that it is NP-hard to decide
whether such an allocation exists, even for binary valuations. We also show
that, for a path, it is NP-hard to find a Pareto-optimal allocation that
satisfies maximin share, but show that a moving-knife algorithm can find such
an allocation when agents have binary valuations that have a non-nested
interval structure.Comment: 21 pages, full version of paper at AAAI-201
Price Discrimination Through Communication
We study a seller's optimal mechanism for maximizing revenue when the buyer may present evidence relevant to the buyer's value, or when different types of buyer have a differential ability to communicate. We introduce a dynamic bargaining protocol in which the buyer first makes a sequence of concessions in a cheap talk phase, and then at a time determined by the seller, the buyer presents evidence to support his previous assertions, and then the seller makes a take-it-or-leave-it offer. Our main result is that the optimal mechanism can be implemented as a sequential equilibrium of our dynamic bargaining protocol. Unlike the optimal mechanism to which the seller can commit, the equilibrium of the bargaining protocol also provides incentives for the seller to behave as required. We thereby provide a natural procedure whereby the seller can optimally price discriminate on the basis of the buyer's evidence. JEL Code: C78, D82, D83.price discrimination, communication, bargaining, commitment, evidence, network flows
Price of Competition and Dueling Games
We study competition in a general framework introduced by Immorlica et al.
and answer their main open question. Immorlica et al. considered classic
optimization problems in terms of competition and introduced a general class of
games called dueling games. They model this competition as a zero-sum game,
where two players are competing for a user's satisfaction. In their main and
most natural game, the ranking duel, a user requests a webpage by submitting a
query and players output an ordering over all possible webpages based on the
submitted query. The user tends to choose the ordering which displays her
requested webpage in a higher rank. The goal of both players is to maximize the
probability that her ordering beats that of her opponent and gets the user's
attention. Immorlica et al. show this game directs both players to provide
suboptimal search results. However, they leave the following as their main open
question: "does competition between algorithms improve or degrade expected
performance?" In this paper, we resolve this question for the ranking duel and
a more general class of dueling games.
More precisely, we study the quality of orderings in a competition between
two players. This game is a zero-sum game, and thus any Nash equilibrium of the
game can be described by minimax strategies. Let the value of the user for an
ordering be a function of the position of her requested item in the
corresponding ordering, and the social welfare for an ordering be the expected
value of the corresponding ordering for the user. We propose the price of
competition which is the ratio of the social welfare for the worst minimax
strategy to the social welfare obtained by a social planner. We use this
criterion for analyzing the quality of orderings in the ranking duel. We prove
the quality of minimax results is surprisingly close to that of the optimum
solution
Long-lived collateralized assets and bubbles
When infinite-lived agents trade long-lived assets secured by durable goods, equilibrium exists without any additional debt constraints or uniform impatience conditions on agents' characteristics. Also, price bubbles are absent when physical endowments are uniformly bounded away from zero.Collateralized assets, Existence of equilibrium, Asset pricing bubbles.
Tropicalizing the simplex algorithm
We develop a tropical analog of the simplex algorithm for linear programming.
In particular, we obtain a combinatorial algorithm to perform one tropical
pivoting step, including the computation of reduced costs, in O(n(m+n)) time,
where m is the number of constraints and n is the dimension.Comment: v1: 35 pages, 7 figures, 4 algorithms; v2: improved presentation, 39
pages, 9 figures, 4 algorithm
Evaluating Projects and Assessing Sustainable Development in Imperfect Economies
We are interested in three related questions: (1) How should accounting prices be estimated? (2) How should we evaluate policy change in an imperfect economy? (3) How can we check whether intergenerational well-being will be sustained along a projected economic programme? We do not presume that the economy is convex, nor do we assume that the government optimizes on behalf of its citizens. We show that the same set of accounting prices should be used both for policy evaluation and for assessing whether or not intergenerational welfare along a given economic path will be sustained. We also show that a comprehensive measure of wealth, computed in terms of the accounting prices, can be used as an index for problems (2) and (3) above. The remainder of the paper is concerned with rules for estimating the accounting prices of several specific environmental natural resources, transacted in a few well known economic institutions.Sustainable development, Imperfect economies
All solution graphs in multidimensional screening
We study general discrete-types multidimensional screening without any noticeable restrictions on valuations, using instead epsilon-relaxation of the incentive-compatibility constraints. Any active (becoming equality) constraint can be perceived as "envy" arc from one type to another, so the set of active constraints is a digraph. We find that: (1) any solution has an in-rooted acyclic graph ("river"); (2) for any logically feasible river there exists a screening problem resulting in such river. Using these results, any solution is characterized both through its spanning-tree and through its Lagrange multipliers, that can help in finding solutions and their efficiency/distortion properties.incentive compatibility; multidimensional screening; second-degree price discrimination; non-linear pricing; graphs
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