1,038 research outputs found
Simplicity-Expressiveness Tradeoffs in Mechanism Design
A fundamental result in mechanism design theory, the so-called revelation
principle, asserts that for many questions concerning the existence of
mechanisms with a given outcome one can restrict attention to truthful direct
revelation-mechanisms. In practice, however, many mechanism use a restricted
message space. This motivates the study of the tradeoffs involved in choosing
simplified mechanisms, which can sometimes bring benefits in precluding bad or
promoting good equilibria, and other times impose costs on welfare and revenue.
We study the simplicity-expressiveness tradeoff in two representative settings,
sponsored search auctions and combinatorial auctions, each being a canonical
example for complete information and incomplete information analysis,
respectively. We observe that the amount of information available to the agents
plays an important role for the tradeoff between simplicity and expressiveness
K-Implementation
This paper discusses an interested party who wishes to influence the behavior
of agents in a game (multi-agent interaction), which is not under his control.
The interested party cannot design a new game, cannot enforce agents' behavior,
cannot enforce payments by the agents, and cannot prohibit strategies available
to the agents. However, he can influence the outcome of the game by committing
to non-negative monetary transfers for the different strategy profiles that may
be selected by the agents. The interested party assumes that agents are
rational in the commonly agreed sense that they do not use dominated
strategies. Hence, a certain subset of outcomes is implemented in a given game
if by adding non-negative payments, rational players will necessarily produce
an outcome in this subset. Obviously, by making sufficiently big payments one
can implement any desirable outcome. The question is what is the cost of
implementation? In this paper we introduce the notion of k-implementation of a
desired set of strategy profiles, where k stands for the amount of payment that
need to be actually made in order to implement desirable outcomes. A major
point in k-implementation is that monetary offers need not necessarily
materialize when following desired behaviors. We define and study
k-implementation in the contexts of games with complete and incomplete
information. In the latter case we mainly focus on the VCG games. Our setting
is later extended to deal with mixed strategies using correlation devices.
Together, the paper introduces and studies the implementation of desirable
outcomes by a reliable party who cannot modify game rules (i.e. provide
protocols), complementing previous work in mechanism design, while making it
more applicable to many realistic CS settings
Bundling Equilibrium in Combinatorial auctions
This paper analyzes individually-rational ex post equilibrium in the VC
(Vickrey-Clarke) combinatorial auctions. If is a family of bundles of
goods, the organizer may restrict the participants by requiring them to submit
their bids only for bundles in . The -VC combinatorial auctions
(multi-good auctions) obtained in this way are known to be
individually-rational truth-telling mechanisms. In contrast, this paper deals
with non-restricted VC auctions, in which the buyers restrict themselves to
bids on bundles in , because it is rational for them to do so. That is,
it may be that when the buyers report their valuation of the bundles in
, they are in an equilibrium. We fully characterize those that
induce individually rational equilibrium in every VC auction, and we refer to
the associated equilibrium as a bundling equilibrium. The number of bundles in
represents the communication complexity of the equilibrium. A special
case of bundling equilibrium is partition-based equilibrium, in which
is a field, that is, it is generated by a partition. We analyze the tradeoff
between communication complexity and economic efficiency of bundling
equilibrium, focusing in particular on partition-based equilibrium
Simple Sequencing Problems with Interdependent Costs
In this paper we analyze sequencing situations under incomplete information where agents have interdependent costs. We first argue why Vickrey-Clarke-Groves (or VCG) mechanism fails to implement a simple sequencing problem in dominant strategies. Given this impossibility, we try to implement simple sequencing problems in ex-post equilibrium. We show that a simple sequencing problem is implementable if and only if the mechanism is a `generalized VCG mechanism'. We then show that for implementable n agent simple sequencing problems, with polynomial cost function of order (n-2) or less, one can achieve first best implementability. Moreover, for the class of simple sequencing problems with ``sufficiently well behaved'' cost function, this is the only class of first best implementable simple sequencing problems.Simple Sequencing Problems, Ex-post Equilibrium, First Best Implementability
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