392 research outputs found
On Revenue Monotonicity in Combinatorial Auctions
Along with substantial progress made recently in designing near-optimal
mechanisms for multi-item auctions, interesting structural questions have also
been raised and studied. In particular, is it true that the seller can always
extract more revenue from a market where the buyers value the items higher than
another market? In this paper we obtain such a revenue monotonicity result in a
general setting. Precisely, consider the revenue-maximizing combinatorial
auction for items and buyers in the Bayesian setting, specified by a
valuation function and a set of independent item-type
distributions. Let denote the maximum revenue achievable under
by any incentive compatible mechanism. Intuitively, one would expect that
if distribution stochastically dominates .
Surprisingly, Hart and Reny (2012) showed that this is not always true even for
the simple case when is additive. A natural question arises: Are these
deviations contained within bounds? To what extent may the monotonicity
intuition still be valid? We present an {approximate monotonicity} theorem for
the class of fractionally subadditive (XOS) valuation functions , showing
that if stochastically dominates under
where is a universal constant. Previously, approximate monotonicity was
known only for the case : Babaioff et al. (2014) for the class of additive
valuations, and Rubinstein and Weinberg (2015) for all subaddtive valuation
functions.Comment: 10 page
The basic approval voting game
We survey results about Approval Voting obtained within the standard framework of game theory. Restricting the set of strategies to undominated and sincere ballots does not help to predict Approval Voting outcomes, which is also the case under strategic equilibrium concepts such as Nash equilibrium and its usual refinements. Strong Nash equilibrium in general does not exist but predicts the election of a Condorcet winner when one exists
Sequential Posted Price Mechanisms with Correlated Valuations
We study the revenue performance of sequential posted price mechanisms and
some natural extensions, for a general setting where the valuations of the
buyers are drawn from a correlated distribution. Sequential posted price
mechanisms are conceptually simple mechanisms that work by proposing a
take-it-or-leave-it offer to each buyer. We apply sequential posted price
mechanisms to single-parameter multi-unit settings in which each buyer demands
only one item and the mechanism can assign the service to at most k of the
buyers. For standard sequential posted price mechanisms, we prove that with the
valuation distribution having finite support, no sequential posted price
mechanism can extract a constant fraction of the optimal expected revenue, even
with unlimited supply. We extend this result to the the case of a continuous
valuation distribution when various standard assumptions hold simultaneously.
In fact, it turns out that the best fraction of the optimal revenue that is
extractable by a sequential posted price mechanism is proportional to ratio of
the highest and lowest possible valuation. We prove that for two simple
generalizations of these mechanisms, a better revenue performance can be
achieved: if the sequential posted price mechanism has for each buyer the
option of either proposing an offer or asking the buyer for its valuation, then
a Omega(1/max{1,d}) fraction of the optimal revenue can be extracted, where d
denotes the degree of dependence of the valuations, ranging from complete
independence (d=0) to arbitrary dependence (d=n-1). Moreover, when we
generalize the sequential posted price mechanisms further, such that the
mechanism has the ability to make a take-it-or-leave-it offer to the i-th buyer
that depends on the valuations of all buyers except i's, we prove that a
constant fraction (2-sqrt{e})/4~0.088 of the optimal revenue can be always be
extracted.Comment: 29 pages, To appear in WINE 201
Optimal Design of Robust Combinatorial Mechanisms for Substitutable Goods
In this paper we consider multidimensional mechanism design problem for
selling discrete substitutable items to a group of buyers. Previous work on
this problem mostly focus on stochastic description of valuations used by the
seller. However, in certain applications, no prior information regarding
buyers' preferences is known. To address this issue, we consider uncertain
valuations and formulate the problem in a robust optimization framework: the
objective is to minimize the maximum regret. For a special case of
revenue-maximizing pricing problem we present a solution method based on
mixed-integer linear programming formulation
Fixed Price Approximability of the Optimal Gain From Trade
Bilateral trade is a fundamental economic scenario comprising a strategically
acting buyer and seller, each holding valuations for the item, drawn from
publicly known distributions. A mechanism is supposed to facilitate trade
between these agents, if such trade is beneficial. It was recently shown that
the only mechanisms that are simultaneously DSIC, SBB, and ex-post IR, are
fixed price mechanisms, i.e., mechanisms that are parametrised by a price p,
and trade occurs if and only if the valuation of the buyer is at least p and
the valuation of the seller is at most p. The gain from trade is the increase
in welfare that results from applying a mechanism; here we study the gain from
trade achievable by fixed price mechanisms. We explore this question for both
the bilateral trade setting, and a double auction setting where there are
multiple buyers and sellers. We first identify a fixed price mechanism that
achieves a gain from trade of at least 2/r times the optimum, where r is the
probability that the seller's valuation does not exceed the buyer's valuation.
This extends a previous result by McAfee. Subsequently, we improve this
approximation factor in an asymptotic sense, by showing that a more
sophisticated rule for setting the fixed price results in an expected gain from
trade within a factor O(log(1/r)) of the optimal gain from trade. This is
asymptotically the best approximation factor possible. Lastly, we extend our
study of fixed price mechanisms to the double auction setting defined by a set
of multiple i.i.d. unit demand buyers, and i.i.d. unit supply sellers. We
present a fixed price mechanism that achieves a gain from trade that achieves
for all epsilon > 0 a gain from trade of at least (1-epsilon) times the
expected optimal gain from trade with probability 1 - 2/e^{#T epsilon^2 /2},
where #T is the expected number of trades resulting from the double auction
Computing Stable Coalitions: Approximation Algorithms for Reward Sharing
Consider a setting where selfish agents are to be assigned to coalitions or
projects from a fixed set P. Each project k is characterized by a valuation
function; v_k(S) is the value generated by a set S of agents working on project
k. We study the following classic problem in this setting: "how should the
agents divide the value that they collectively create?". One traditional
approach in cooperative game theory is to study core stability with the
implicit assumption that there are infinite copies of one project, and agents
can partition themselves into any number of coalitions. In contrast, we
consider a model with a finite number of non-identical projects; this makes
computing both high-welfare solutions and core payments highly non-trivial.
The main contribution of this paper is a black-box mechanism that reduces the
problem of computing a near-optimal core stable solution to the purely
algorithmic problem of welfare maximization; we apply this to compute an
approximately core stable solution that extracts one-fourth of the optimal
social welfare for the class of subadditive valuations. We also show much
stronger results for several popular sub-classes: anonymous, fractionally
subadditive, and submodular valuations, as well as provide new approximation
algorithms for welfare maximization with anonymous functions. Finally, we
establish a connection between our setting and the well-studied simultaneous
auctions with item bidding; we adapt our results to compute approximate pure
Nash equilibria for these auctions.Comment: Under Revie
Bribeproof mechanisms for two-values domains
Schummer (Journal of Economic Theory 2000) introduced the concept of
bribeproof mechanism which, in a context where monetary transfer between agents
is possible, requires that manipulations through bribes are ruled out.
Unfortunately, in many domains, the only bribeproof mechanisms are the trivial
ones which return a fixed outcome.
This work presents one of the few constructions of non-trivial bribeproof
mechanisms for these quasi-linear environments. Though the suggested
construction applies to rather restricted domains, the results obtained are
tight: For several natural problems, the method yields the only possible
bribeproof mechanism and no such mechanism is possible on more general domains.Comment: Extended abstract accepted to SAGT 2016. This ArXiv version corrects
typos in the proofs of Theorem 7 and Claims 28-29 of prior ArXiv versio
Sequential Deliberation for Social Choice
In large scale collective decision making, social choice is a normative study
of how one ought to design a protocol for reaching consensus. However, in
instances where the underlying decision space is too large or complex for
ordinal voting, standard voting methods of social choice may be impractical.
How then can we design a mechanism - preferably decentralized, simple,
scalable, and not requiring any special knowledge of the decision space - to
reach consensus? We propose sequential deliberation as a natural solution to
this problem. In this iterative method, successive pairs of agents bargain over
the decision space using the previous decision as a disagreement alternative.
We describe the general method and analyze the quality of its outcome when the
space of preferences define a median graph. We show that sequential
deliberation finds a 1.208- approximation to the optimal social cost on such
graphs, coming very close to this value with only a small constant number of
agents sampled from the population. We also show lower bounds on simpler
classes of mechanisms to justify our design choices. We further show that
sequential deliberation is ex-post Pareto efficient and has truthful reporting
as an equilibrium of the induced extensive form game. We finally show that for
general metric spaces, the second moment of of the distribution of social cost
of the outcomes produced by sequential deliberation is also bounded
Structure of Extreme Correlated Equilibria: a Zero-Sum Example and its Implications
We exhibit the rich structure of the set of correlated equilibria by
analyzing the simplest of polynomial games: the mixed extension of matching
pennies. We show that while the correlated equilibrium set is convex and
compact, the structure of its extreme points can be quite complicated. In
finite games the ratio of extreme correlated to extreme Nash equilibria can be
greater than exponential in the size of the strategy spaces. In polynomial
games there can exist extreme correlated equilibria which are not finitely
supported; we construct a large family of examples using techniques from
ergodic theory. We show that in general the set of correlated equilibrium
distributions of a polynomial game cannot be described by conditions on
finitely many moments (means, covariances, etc.), in marked contrast to the set
of Nash equilibria which is always expressible in terms of finitely many
moments
Evolution of Cooperation and Coordination in a Dynamically Networked Society
Situations of conflict giving rise to social dilemmas are widespread in
society and game theory is one major way in which they can be investigated.
Starting from the observation that individuals in society interact through
networks of acquaintances, we model the co-evolution of the agents' strategies
and of the social network itself using two prototypical games, the Prisoner's
Dilemma and the Stag Hunt. Allowing agents to dismiss ties and establish new
ones, we find that cooperation and coordination can be achieved through the
self-organization of the social network, a result that is non-trivial,
especially in the Prisoner's Dilemma case. The evolution and stability of
cooperation implies the condensation of agents exploiting particular game
strategies into strong and stable clusters which are more densely connected,
even in the more difficult case of the Prisoner's Dilemma.Comment: 18 pages, 14 figures. to appea
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