eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2005-06-01
5011
1
26
10.4230/DagSemProc.05011.1
article
05011 Abstracts Collection – Computing and Markets
Lehmann, Daniel
Müller, Rudolf
Sandholm, Tuomas
From 03.01.05 to 07.01.05, the
Dagstuhl Seminar 05011``Computing and Markets'' was held
in the International Conference and Research Center (IBFI),
Schloss Dagstuhl.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol05011/DagSemProc.05011.1/DagSemProc.05011.1.pdf
Algorithms
complexity
game theory
social choice
auctions
equilibrium
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2005-06-01
5011
1
0
10.4230/DagSemProc.05011.2
article
05011 Executive Summary – Computing and Markets
Lehmann, Daniel
Müller, Rudolf
Sandholm, Tuomas
The seminar Computing and Markets facilitated a very fruitful
interaction between economists and computer scientists, which
intensified the understanding of the other disciplines' tool sets.
The seminar helped to pave the way to a unified theory of markets
that takes into account both the economic and the computational
issues---and their deep interaction.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol05011/DagSemProc.05011.2/DagSemProc.05011.2.pdf
Algorithms
complexity
game theory
social choice
auctions
equilibrium
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2005-06-01
5011
1
31
10.4230/DagSemProc.05011.3
article
A Contract and Balancing Mechanism for Sharing Capacity in a Communication Network
Anderson, Edward
Kelly, Frank
Steinberg, Richard
We propose a method for determining how much to charge users of a communication network when they share bandwidth. Our approach can be employed either when a network owner wishes to sell bandwidth for a specified period of time to a number of different users, or when users cooperate to build a network to be shared among themselves. We show how a Contract and Balancing Mechanism can be defined to mediate between rapidly fluctuating prices and the longer time scales over which bandwidth contracts might be traded. An important property of the process is that it avoids introducing perverse incentives for a capacity provider to increase congestion.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol05011/DagSemProc.05011.3/DagSemProc.05011.3.pdf
compact representation of games
congestion games
local-effect games
action-graph gamescomputational markets; auctions; bidding strategiesNegotiatio
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2005-06-01
5011
1
10
10.4230/DagSemProc.05011.4
article
A Network Approach to Bayes-Nash Incentive Compatible Mechanisms
Müller, Rudolf
Perea, Andres
Wolf, Sascha
This paper provides a characterization of Bayes-Nash incentive compatible mechanisms in settings where agents have one-dimensional or multi-dimensional types, quasi-linear utility functions and interdependent valuations. The characterization is derived in terms of conditions for the underlying allocation function.
We do this by making a link to network theory and building complete directed graphs for agents type spaces. We show that an allocation rule is Bayes-Nash incentive compatible if and only if these graphs have no negative, finite cycles.
In the case of one-dimensional types and given certain properties for agents valuation functions, we show that this condition reduces to the absence of negative 2-cycles. In the case of multi-dimensional types and given a linearity requirement on the valuation functions, we show that this condition reduces to the absence of negative 2-cycles and an integratebility condition on the valuation functions.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol05011/DagSemProc.05011.4/DagSemProc.05011.4.pdf
compact representation of games
congestion games
local-effect games
action-graph gamescomputational markets; auctions; bidding strategiesNegotiatio
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2005-06-01
5011
1
2
10.4230/DagSemProc.05011.5
article
Automated Mechanism Design
Sandholm, Tuomas
Mechanisms design has traditionally been a manual endeavor. In 2002, Conitzer and Sandholm introduced the automated mechanism design (AMD) approach, where the mechanism is computationally created for the specific problem instance at hand. This has several advantages: 1) it can yield better mechanisms than the ones known to date, 2) it applies beyond the problem classes studied manually to date, 3) it can circumvent seminal economic impossibility results that hold for classes of problems but not all instances, and 4) it shifts the burden of design from man to machine. In this talk I will overview our results on AMD to date. I will cover problem representations and the computational complexity of different variants of the design problem. Initial applications include revenue-maximizing combinatorial auctions and (combinatorial) public goods problems. Algorithms for AMD will be discussed. To reduce the computational complexity of designing optimal combinatorial auctions, I introduce an incentive compatible, individually rational subfamily called Virtual Valuations Combinatorial Auctions. The auction mechanism's revenue can be boosted (started, for example, from the VCG) by hill-climbing in this subspace. I will also present computational complexity and communication complexity results that motivate multi-stage and non-truth-promoting mechanisms. Finally, I present our first steps toward automatically designing multi-stage mechanisms.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol05011/DagSemProc.05011.5/DagSemProc.05011.5.pdf
Automated mechanism design
mechanism design
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2005-06-01
5011
1
8
10.4230/DagSemProc.05011.6
article
Computing Nash Equilibria of Action-Graph Games
Leyton-Brown, Kevin
Bhat, Navin A.R.
This talk will survey two graphical models which the authors have proposed
for compactly representing single-shot, finite-action games in which a large
number of agents contend for scarce resources.
The first model considered is Local-Effect Games (LEGs). These games often
(but not always) have pure-strategy Nash equilibria. Finding a potential
function is a good technique for finding such equilibria. We give a complete
characterization of which LEGs have potential functions and provide the
functions in each case; we also show a general case where pure-strategy
equilibria exist in the absence of potential functions.
Action-graph games (AGGs) are a fully expressive game representation which
can compactly express both strict and context-specific independence between
players' utility functions, and which generalize LEGs. We present algorithms
for computing both symmetric and arbitrary equilibria of AGGs, based on a
continuation method proposed by Govindan and Wilson. We analyze the worst-
case cost of computing the Jacobian of the payoff function, the exponential-
time bottleneck step of this algorithm, and in all cases achieve exponential
speedup. When the indegree of G is bounded by a constant and the game is
symmetric, the Jacobian can be computed in polynomial time.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol05011/DagSemProc.05011.6/DagSemProc.05011.6.pdf
compact representation of games
action-graph games
Nash equilibria
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2005-06-01
5011
1
21
10.4230/DagSemProc.05011.7
article
Congestion games with failures
Penn, Michal
Polukarov, Maria
Tennenholtz, Moshe
We introduce a new class of games, congestion games with
failures (CGFs), which extends the class of congestion games to
allow for facility failures. In a CGF agents share a common set of
facilities (service providers), where each service provider (SP)
may fail with some known probability. For reliability reasons, an
agent may choose a subset of the SPs in order to try and perform
his task. The cost of an agent for utilizing any SP is an
agent-specific function of the total number of agents using this
SP. A main feature of this setting is that the cost for an agent
for successful completion of his task is the minimum of the costs
of his successful attempts. We show that although congestion games
with failures do not admit a potential function, and thus are not
isomorphic to classic congestion games, they always possess a
pure-strategy Nash equilibrium. Moreover, an efficient algorithm
for the construction of pure-strategy Nash equilibrium profile is
presented. We also show that the SPs congestion experienced in
different Nash equilibria is (almost) unique. For the subclass of
symmetric CGFs we give a characterization of best and worst Nash
equilibria, present algorithms for their construction, and compare
the social disutilities of the agents at these points.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol05011/DagSemProc.05011.7/DagSemProc.05011.7.pdf
compact representation of games
congestion games
local-effect games
action-graph gamescomputational markets; auctions; bidding strategiesNegotiatio
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2005-06-01
5011
1
23
10.4230/DagSemProc.05011.8
article
Dominant Strategy Mechanisms with Multidimensional Types
Hongwei Gui
Müller, Rudolf
Vohra, Rakesh V.
This paper provides a characterization of dominant strategy
mechanisms with quasi-linear utilities and multi-dimensional types
for a variety of preference domains. These characterizations are
in terms of a monotonicity property on the underlying allocation
rule.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol05011/DagSemProc.05011.8/DagSemProc.05011.8.pdf
Dominant Strategy
Farkas Lemma,
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2005-06-01
5011
1
29
10.4230/DagSemProc.05011.9
article
Fair Payments for Efficient Allocations in Public Sector Combinatorial Auctions
Day, Robert
Raghavan, S.
Motivated by the increasing use of auctions by government
agencies, we consider the problem of fairly pricing public goods in a combinatorial
auction. A well-known problem with the incentive-compatible Vickrey-Clarke-Groves
(VCG) auction mechanism is that the resulting prices may not be in the core. Loosely
speaking, this means the payments of the winners could be so low, that there are losing
bidders who would have been willing to pay more than the payments of the winning bidders.
Clearly, this ``unfair'' outcome is unacceptable for a public-sector auction. Proxy-based
combinatorial auctions,
in which each bidder submits several package bids to a proxy, result in efficient outcomes
and bidder-Pareto-optimal core-payments by winners, thus offering a viable practical alternative
to address this problem.
This paper confronts two critical issues facing the proxy-auction. First, motivated to
minimize a bidder's ability to benefit through strategic manipulation (through collusive
agreement or unilateral action), we demonstrate the strength of a mechanism that minimizes
total payments among all possible proxy auction outcomes, narrowing the previously broad
solution concept. Secondly, we address the computational difficulties of achieving these outcomes
with a constraint-generation approach, promising to broaden the range of applications for which the
proxy-auction achieves a comfortably rapid solution.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol05011/DagSemProc.05011.9/DagSemProc.05011.9.pdf
auctions
core
bidder-Pareto-optimal
constraint generation
VCG payments
proxy auctions
combinatorial auctions
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2005-06-01
5011
1
2
10.4230/DagSemProc.05011.10
article
Fundamentals in Discrete Convex Analysis
Murota, Kazuo
This talk describes fundamental properties of M-convex and L-convex functions that play the central roles in discrete convex analysis.
These concepts were originally introduced in combinatorial optimization, but turned out to be relevant in economics.
Emphasis is put on discrete duality and conjugacy respect to the Legendre-Fenchel transformation.
Monograph information:
http://www.misojiro.t.u-tokyo.ac.jp/~murota/mybooks.html#DCAsiam2003
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol05011/DagSemProc.05011.10/DagSemProc.05011.10.pdf
gross substitute
discrete convex functions
M-convex function
Fenchel-Legendre transformation
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2005-06-01
5011
1
6
10.4230/DagSemProc.05011.11
article
Local-Effect Games
Leyton-Brown, Kevin
Tennenholtz, Moshe
This talk will survey two graphical models which the authors have proposed
for compactly representing single-shot, finite-action games in which a large
number of agents contend for scarce resources.
The first model considered is Local-Effect Games (LEGs). These games often
(but not always) have pure-strategy Nash equilibria. Finding a potential
function is a good technique for finding such equilibria. We give a complete
characterization of which LEGs have potential functions and provide the
functions in each case; we also show a general case where pure-strategy
equilibria exist in the absence of potential functions.
Action-graph games (AGGs) are a fully expressive game representation which
can compactly express both strict and context-specific independence between
players' utility functions, and which generalize LEGs. We present algorithms
for computing both symmetric and arbitrary equilibria of AGGs, based on a
continuation method proposed by Govindan and Wilson. We analyze the worst-
case cost of computing the Jacobian of the payoff function, the exponential-
time bottleneck step of this algorithm, and in all cases achieve exponential
speedup. When the indegree of G is bounded by a constant and the game is
symmetric, the Jacobian can be computed in polynomial time.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol05011/DagSemProc.05011.11/DagSemProc.05011.11.pdf
compact representation of games
congestion games
local-effect
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2005-06-01
5011
1
0
10.4230/DagSemProc.05011.12
article
Overcoming Free Riding in Multi-Party Computations
Smordinsky, Rann
Tennenholtz, Moshe
This paper addresses the question of multi party computation in a model with asymmetric information. Each agent has a private value (secret), but in contrast to standard models, the agent incurs a cost when retrieving the secret. There is a social choice function
the agents would like to compute and implement. All agents would like to perform a joint computation, which input is their vector
of secrets. However, agents would like to free-ride on others contribution.
A mechanism which elicits players secrets and performs the desired computation defines a game. A mechanism is `appropriate if it (weakly) implements the social choice function for all
secret vectors. namely, if there exists an equilibrium in which it is able to elicit (sufficiently many) agents secrets and perform
the computation, for all possible secret vectors. We show that `appropriate mechanisms approach agents sequentially and that
they have low communication complexity.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol05011/DagSemProc.05011.12/DagSemProc.05011.12.pdf
compact representation of games
congestion games
local-effect games
action-graph gamescomputational markets; auctions; bidding strategiesNegotiatio
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2005-06-01
5011
1
5
10.4230/DagSemProc.05011.13
article
Reference-Dependent Preferences in Multi-Issue Bargaining
Gimpel, Henner
Game theoretic bargaining models usually assume parties to have exogenously given preferences from the beginning of a negotiation on. Preferences in these models do not depend on the history of offers made during a negotiation. This paper argues that preferences are based on issue-wise reference points changing during the bargaining process as result of the counterpartys offers.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol05011/DagSemProc.05011.13/DagSemProc.05011.13.pdf
compact representation of games
congestion games
local-effect games
action-graph gamescomputational markets; auctions; bidding strategiesNegotiatio
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2005-06-01
5011
1
9
10.4230/DagSemProc.05011.14
article
Self-Confirming Price Prediction for Bidding in Simultaneous Ascending Auctions
Osepayshvili, Anna
Wellman, Michael
Reeves, Daniel
MacKie-Mason, Jeffrey
Simultaneous, separate ascending auctions are ubiquitous, even when agents have preferences over combinations of goods, from which arises the emph{exposure problem}. Little is known about
strategies that perform well when the exposure problem is important. We present a new family of bidding strategies for this situation, in which agents form and utilize various amounts of
information from predictions of the distribution of final prices.
The predictor strategies we define differ in their choice of method for generating the initial (pre-auction) prediction. We explore several methods, but focus on emph{self-confirming} predictions. An agents prediction of characteristics of the
distribution of closing prices is self-confirming if, when all agents follow the same predictor bidding strategy, the final price distributions that actually result are consistent with the
utilized characteristics of the prediction.
We extensively analyze an auction environment with five goods, and five agents who each can choose from 53 different bidding strategies (resulting in over 4.2 million distinct strategy combinations). We find that the self-confirming distribution
predictor is a highly stable, pure-strategy Nash equilibrium. We have been unable to find any other Nash strategies in this environment.
In limited experiments in other environments the self-confirming distribution predictor consistently performs well, but is not generally a pure-strategy Nash equilibrium.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol05011/DagSemProc.05011.14/DagSemProc.05011.14.pdf
compact representation of games
congestion games
local-effect games
action-graph gamescomputational markets; auctions; bidding strategies
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2005-06-01
5011
1
12
10.4230/DagSemProc.05011.15
article
Selfish Routing of Splittable Flow with Respect to Maximum Congestion
Feldmann, Rainer
We study the problem of selfishly routing
splittable traffic with respect to maximum congestion through a shared
network.
Our model naturally combines features of the two best studied
models in the context of selfish routing: The KP-model \cite{KP99} and the
Wardrop-model \cite{War52}.
We are given a network with source nodes $s_i$, sink
nodes $t_i$, $1 \leq i \leq k$, $m$ edges,
and a latency function for each edge. Traffics of rate
$r_i$ are destined from $s_i$ to $t_i$.
Traffics are splittable and each piece of traffic tries to route in
such a way that it minimizes its private latency.
In the absence of a central regulation, Nash Equilibria represent
stable states of such a system. In a Nash Equilibrium, no
piece of traffic can decrease its private latency by
unilaterally changing its route. The increased social cost due to
the lack of central regulation is defined in terms of the
coordination ratio, i.e. the worst
possible ratio of the social cost of a traffic flow at Nash
Equilibrium and the social cost of a global optimal traffic flow.
In this paper,
we show that in the above model pure Nash Equilibria always exist.
Then, we analyze the coordination ratio of single-commodity networks with
linear latency functions.
Our main result is a tight upper bound of $\frac{4}{3} m$, where $m$
is the number of edges of the network, for the coordination ratio of
single-commodity networks with linear latency functions.
On our way to our main result we analyze the coordination ratio of
single-hop networks and show a tight upper bound of
$m+\Theta(\sqrt{m})$. A more sophisticated analysis yields an upper
bound of $\frac{4}{3}m$ for the coordination ratio of multi-hop networks,
which is then used to derive the main result for arbitrary
single-commodity linear networks.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol05011/DagSemProc.05011.15/DagSemProc.05011.15.pdf
selfish routing
coordination ratio
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2005-06-01
5011
1
17
10.4230/DagSemProc.05011.16
article
Sequences of Take-It-or-Leave-It Offers: Near-Optimal Auctions Without Full Valuation Revelation
Sandholm, Tuomas
Gilpin, Andrew
We introduce take-it-or-leave-it auctions (TLAs) as an allocation
mechanism that allows buyers to retain much of their private valuation
information, yet generates close-to-optimal expected utility for the
seller. We show that if each buyer receives at most one offer, each
buyers dominant strategy is to act truthfully. In more general TLAs,
the buyers optimal strategies are more intricate, and we derive the
perfect Bayesian equilibrium for the game. We develop algorithms for
finding the equilibrium and also for optimizing the offers so as to
maximize the sellers expected utility. In several example settings we
show that the sellers expected utility already is close to optimal
for a small number of offers. As the number of buyers increases, the
sellers expected utility increases, and becomes increasingly (but not
monotonically) more competitive with Myersons expected utility
maximizing auction.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol05011/DagSemProc.05011.16/DagSemProc.05011.16.pdf
compact representation of games
congestion games
local-effect games
action-graph gamescomputational markets; auctions; bidding strategiesNegotiatio
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2005-06-01
5011
1
16
10.4230/DagSemProc.05011.17
article
Spiteful Bidding in Sealed-Bid Auctions
Brandt, Felix
Sandholm, Tuomas
Shoham, Yoav
We study the bidding behavior of spiteful agents who, contrary to
the common assumption of self-interest, maximize the weighted
difference of their own profit and their competitors' profit. This
assumption is motivated by inherent spitefulness, or, for example,
by competitive scenarios such as in closed markets where the loss of
a competitor will likely result in future gains for oneself. We
derive symmetric Bayes Nash equilibria for spiteful agents in
first-price and second-price sealed-bid auctions. In first-price
auctions, bidders become "more truthful" the more spiteful they
are. Surprisingly, the equilibrium strategy in second-price
auctions does not depend on the number of bidders. Based on these
equilibria, we compare revenue in both auction types. It turns out
that expected revenue in second-price auctions is higher than
expected revenue in first-price auctions whenever agents have the
slightest interest in reducing others' profit as long as they still
care for their own profit. In other words, revenue equivalence only
holds for auctions in which all agents are either self-interested or
completely malicious.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol05011/DagSemProc.05011.17/DagSemProc.05011.17.pdf
Auctions
Externalities
Spite
Revenue
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2005-06-01
5011
1
0
10.4230/DagSemProc.05011.18
article
The PageRank Axioms
Altman, Alon
This talk introduces the first graph-theoretic,
ordinal representation theorem for the PageRank
algorithm, bridging the gap between page ranking
algorithms and the formal theory of social choice.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol05011/DagSemProc.05011.18/DagSemProc.05011.18.pdf
pagerank
social choice
ranking system
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2005-06-01
5011
1
12
10.4230/DagSemProc.05011.19
article
The Price of Anarchy for Polynomial Social Cost
Gairing, Martin
Lücking, Thomas
Mavronicolas, Marios
Monien, Burkhard
In this work, we consider an interesting variant
of the well-studied KP model [KP99] for selfish
routing that reflects some influence from the much
older Wardrop [War52]. In the new model, user
traffics are still unsplittable, while social cost
is now the expectation of the sum, over all links,
of a certain polynomial evaluated at the total
latency incurred by all users choosing the link;
we call it polynomial social cost. The polynomials
that we consider have non-negative coefficients.
We are interested in evaluating Nash equilibria in
this model, and we use the Price of Anarchy as our
evaluation measure. We prove the Fully Mixed Nash
Equilibrium Conjecture for identical users and two
links, and establish an approximate version of the
conjecture for arbitrary many links. Moreover, we
give upper bounds on the Price of Anarchy.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol05011/DagSemProc.05011.19/DagSemProc.05011.19.pdf
selfish routing
KP-model
price of anarchy
fully mixed Nash Equilibrium
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2005-06-01
5011
1
29
10.4230/DagSemProc.05011.20
article
The Value of Correlation in Strategic Form Games
Ashlagi, Itai
Monderer, Dov
Tennenholtz, Moshe
Every game in strategic form can be extended by adding a correlation device.
Any Equilibrium in such an extended game is called a correlated equilibrium (Aumann 1974).
Aumann showed that there exist games, where the agents surplus in
a correlated equilibrium is greater than their surplus in every equilibrium.
This suggests the study of two major measures for the value of correlation:
1. The ratio between the maximal surplus obtained in an correlated equilibrium to the maximal surplus obtained in equilibrium.
We refer to this ratio as the mediation value.
2. The ratio between the optimal surplus to the maximal surplus obtained in correlated equilibrium.
We refer to this ratio as the enforcement value.
In this work we initiate the study of the mediation value and of the enforcement value,
providing several general results on the value of correlation as captured by these concepts.
We also present a set of results for the more specialized case of congestion games,
a class of games that received a lot attention in the recent computer science and e-commerce communities.
Indeed, while much work in computer science has been devoted to the study of the ratio between the surplus in optimal strategies to the surplus in the worst Nash equilibrium (the so called "price of anarchy") for congestion games, our work presents and initiates the study of two other complementary measures.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol05011/DagSemProc.05011.20/DagSemProc.05011.20.pdf
Correlation
mediation
enforcement
equilibrium
mediator