In the distributed ontology alignment construction problem, two agents agree upon a meaningful subset of correspondences that map between their respective ontologies. However, an agent may be tempted to manipulate the negotiation in favour of a preferred alignment by misrepresenting the weight or confidence of the exchanged correspondences. Therefore such an agreement can only be meaningful if the agents can be incentivised to be honest when revealing information. We examine this problem and model it as a novel mechanism design problem on an edge-weighted bipartite graph, where each side of the graph represents each agent's private entities, and where each agent maintains a private set of valuations associated with its candidate correspondences. The objective is to find a matching (i.e. injective or one-to-one correspondences) that maximises the agents' social welfare. We study implementations in dominant strategies, and show that they should be solved optimally if truthful mechanisms are required. A decentralised version of the greedy allocation algorithm is then studied with a first-price payment rule, proving tight bounds on the Price of Anarchy and Stability.

1. Nan Zhi, Terry R. Payne, Piotr Krysta and Minming Li
Truthful Mechanisms for Multi Agent
Self-Interested Correspondence
Selection

2. The 18th International Semantic Web Conference, Auckland 2019Truthful Mechanisms for Multi Agent Self-Interested Correspondence Selection
Outline
•Explore the use of matchings when generating ontology alignments
• Contrast optimal with sub-optimal approaches
•Motivate the problem of finding decentralised alignments in service-
oriented scenarios
• Show that agents may behave strategically as alignment agreement becomes a game
• Explore the problem using game-theory and present salient results
•Explore a simple greedy algorithm from a Nash Equilibria perspective
• Show bounds on the Price of Anarchy
2

3. The 18th International Semantic Web Conference, Auckland 2019Truthful Mechanisms for Multi Agent Self-Interested Correspondence Selection
Open Systems, Ontologies and Alignment
•Different knowledge-based systems may assume different ontological
models
• Modelled implicitly, or explicitly by defining entities (classes, roles etc), typically using some
logical theory, i.e. an Ontology
• Need to identify and map corresponding entities across ontologies in a similar domain
•Alignment Systems align similar ontologies
3
Alignment
Correspondence

4. The 18th International Semantic Web Conference, Auckland 2019Truthful Mechanisms for Multi Agent Self-Interested Correspondence Selection
Finding the right correspondences
•Traditional alignment approaches
determine a similarity value
• between each of the concepts of the source
ontology…
• ….and those in the destination ontology
•Typically generates a fully connected
bi-partite graph
• Need to select edges that result in an
injective (one-to-one) graph, or matching
4
City
Contribution
Country
Event
Organization
Person
Administrator
Assistant
Author
Chair_PC
Member_PC
Participant
Scholar
Science_Worker
Volunteer
Topic
Bid
Conference
Decision
Document
Person
Chairman
ConferenceMember
ExternalReviewer
ProgramCommitteeMember
User
Administrator
Author
Reviewer
Preference
ProgramCommittee
SubjectArea

5. The 18th International Semantic Web Conference, Auckland 2019Truthful Mechanisms for Multi Agent Self-Interested Correspondence Selection
Finding the right correspondences
•Different approaches available for
generating a matching
• Find the optimal solution
• maximise the combination of edges, or Social Welfare
• Hungarian Algorithm etc
• can be computationally costly ( )
• Find a sub-optimal solution
• identify the best edges between nodes
• Greedy edge-weighted Algorithm, Stable Marriage etc
• faster ( or less), but are they as “good”?
•Not always clear which approach is best
O(n3
)
O(n2
)
5
City
Contribution
Country
Event
Organization
Person
Administrator
Assistant
Author
Chair_PC
Member_PC
Participant
Scholar
Science_Worker
Volunteer
Topic
Bid
Conference
Decision
Document
Person
Chairman
ConferenceMember
ExternalReviewer
ProgramCommitteeMember
User
Administrator
Author
Reviewer
Preference
ProgramCommittee
SubjectArea

6. The 18th International Semantic Web Conference, Auckland 2019Truthful Mechanisms for Multi Agent Self-Interested Correspondence Selection
Finding the right correspondences
•Optimal: considers every possible
combination of edges
• finds the highest combined weight, or maximises social
welfare - e.g.
• may not include the best correspondence
•Sub-optimal: a greedy solution
considers individual edges
• focus on selecting edges with the highest individual weight
in each round
• in only one correspondence is selected, but it has the
highest individual weight ( )
M1
M2
1 + ϵ
6
editor
author
writer
contributor
e1
e2
e3
v = 1
v = 1
v = 1 + ϵ
This bipartite graph has two possible
matchings:
where
where
M1 = {e1, e3}
∑
e∈M1
e = 2
M2 = {e2}
∑
e∈M2
e = 1 + ϵ

7. The 18th International Semantic Web Conference, Auckland 2019Truthful Mechanisms for Multi Agent Self-Interested Correspondence Selection
Taking a decentralised view
•Most knowledge integration tasks are centralised
• Alignment is an offline process
• Centralised oracle can be provided full details of ontologies
•A service oriented (decentralised) landscape involves
different stakeholders
• Autonomous (online) approach taken to aligning ontologies
• Can result in a strategic approach to alignment construction
• Stakeholders may not want to reveal their ontology to their collaborator
• They may prefer specific alignments that could maximise some utility emerging from the transaction
7

8. The 18th International Semantic Web Conference, Auckland 2019Truthful Mechanisms for Multi Agent Self-Interested Correspondence Selection
Taking a decentralised view
•Assume that service providers/consumers may:
• Possess some knowledge about different correspondences from different
sources, based on previous interactions
• This knowledge is incomplete, with more than one candidate correspondence for a given entity
• Associate some weight to each unique correspondence
• Based on similarity, efficacy, etc
• Declare these weights (as bids) when negotiating an alignment
• Risk that the declaration may be non-truthful
•This requires a mechanism for combining the stakeholders bids,
and generating an alignment
8

9. The 18th International Semantic Web Conference, Auckland 2019Truthful Mechanisms for Multi Agent Self-Interested Correspondence Selection
Decentralised Alignment Construction Problem
•Aim is to find an alignment (equivalent
to a matching ) that maximises:
• i.e. find the optimal solution for
•Assume that each agent:
• has a non-negative private valuation function for
each edge
• declares these values as a bid profile
M
M
bi(e)
9
∑e∈M
v(e)
Proofreader
Writer
Publisher
Editor
e1
e2
e3
Contributor Author
e5
e4
3
4
5
5
3
3
6
4
5
6
Mopt = {e1, e3, e5}, v(Mopt) = 23
Mstable = {e2, e4}, v(Mstable) = 21

10. The 18th International Semantic Web Conference, Auckland 2019Truthful Mechanisms for Multi Agent Self-Interested Correspondence Selection
Why would agents lie?
•One agent may have a preference for a specific alignment
• Prior transactions typically result in “better” outcomes
• There could be incentive to mis-represent weights of correspondences to
manipulate final alignment
• This could adversely affect the other agent’s outcome
•We want to avoid strategic manipulation of a game
• Agent may over-estimate weight of an edge to “encourage” its inclusion in
the alignment
• Want mechanism where agents always do worse if they bid strategically
10

11. The 18th International Semantic Web Conference, Auckland 2019Truthful Mechanisms for Multi Agent Self-Interested Correspondence Selection
Alignment construction with Payment
•We want to incentivise agents to tell the truth
• Agents can’t gain any advantage from lying!
• Optimal, complex mechanisms exist that are truth incentive (e.g. VCG)
•We want to know:
Is it possible to have a faster, non-optimal, approximate
and truthful mechanism for our problem?
11

12. The 18th International Semantic Web Conference, Auckland 2019Truthful Mechanisms for Multi Agent Self-Interested Correspondence Selection
Alignment construction with Payment
•Each agent submits a bid profile for a set of desired correspondences
• Only correspondences in the alignment would incur a cost based on the bid
•A mechanism then determines a matching
• Allocation rule determines the solution (matching) based on combined bid profile
• Payment scheme assigns a vector of payments to each agent based on the solution
• Utility for agent given the is determined by its “cost” for the solution and the
payment scheme:
•The aim is to maximise social welfare given both agents bids profiles
bi
𝒜(b)
b = (bL, br)
𝒫(b)
ui(b) i vi(𝒜(b))
ui(𝒜(b) = vi(𝒜(b)) − 𝒫i(b)
SW
12

13. The 18th International Semantic Web Conference, Auckland 2019Truthful Mechanisms for Multi Agent Self-Interested Correspondence Selection
Alignment construction with Payment
•Each agent submits a bid profile for a set of desired correspondences
• Only correspondences in the alignment would incur a cost based on the bid
•A mechanism then determines a matching
• Allocation rule determines the solution (matching) based on combined bid profile
• Payment scheme assigns a vector of payments to each agent based on the solution
• Utility for agent given the is determined by its “cost” for the solution and the
payment scheme:
•The aim is to maximise social welfare given both agents bids profiles
bi
𝒜(b)
b = (bL, br)
𝒫(b)
ui(b) i vi(𝒜(b))
ui(𝒜(b) = vi(𝒜(b)) − 𝒫i(b)
SW
13

14. The 18th International Semantic Web Conference, Auckland 2019Truthful Mechanisms for Multi Agent Self-Interested Correspondence Selection
Alignment construction with Payment
•Each agent submits a bid profile for a set of desired correspondences
• Only correspondences in the alignment would incur a cost based on the bid
•A mechanism then determines a matching
• Allocation rule determines the solution (matching) based on combined bid profile
• Payment scheme assigns a vector of payments to each agent based on the solution
• Utility for agent given the is determined by its “cost” for the solution and the
payment scheme:
•The aim is to maximise social welfare given both agents bids profiles
bi
𝒜(b)
b = (bL, br)
𝒫(b)
ui(b) i vi(𝒜(b))
ui(𝒜(b) = vi(𝒜(b)) − 𝒫i(b)
SW
14

15. The 18th International Semantic Web Conference, Auckland 2019Truthful Mechanisms for Multi Agent Self-Interested Correspondence Selection
Alignment construction with Payment
•Theorem 1:
• For the alignment problem with payment, any mechanism which does not
adopt an optimal solution when agents declare their true valuations is
either non-truthful, or if truthful, the non-optimal solution has an
approximation ratio of at least 2
•i.e. if we have a non-optimal mechanism, then either:
• It is not truthful, or
• It is truthful, but the solution has an approximation factor smaller than 2
• i.e solution is within 50% of the optional solution
15

16. The 18th International Semantic Web Conference, Auckland 2019Truthful Mechanisms for Multi Agent Self-Interested Correspondence Selection
Alignment construction with Payment
•Theorem 2:
• For the alignment problem with payment, any deterministic mechanism which
does not adopt an optimal solution when agents declare their true valuation
is either non-truthful, or is a maximal-in-range mechanism
•If a mechanism is truthful, but not optimal, it must be
maximal-in-range
• if there is a fixed subset of solutions and a bid vector
• then the mechanism will generate one of these solutions in that maximises
social welfare with respect to
R v
R
v
16

17. The 18th International Semantic Web Conference, Auckland 2019Truthful Mechanisms for Multi Agent Self-Interested Correspondence Selection
Alignment construction with Payment
•Theorem 3:
• For the alignment problem with payment, the only truthful mechanisms are
those that are maximal-in-range with an approximation ratio of at least 2
•This provides the constraints for our truthful mechanisms
1. optimal solutions exist (e.g. VCG) that are truth incentive, but are
computationally expensive
2. non-optimal solutions exist that are faster, where agents can do no better
than be truthful if the solution is maximal in range
3. the non-optimal solution is at least 50% of optimal
17

18. The 18th International Semantic Web Conference, Auckland 2019Truthful Mechanisms for Multi Agent Self-Interested Correspondence Selection
Adopting a Greedy Algorithm
•First Price Greedy Matching
Algorithm
• Extended version of the
NaiveDescending algorithm by
Meilicke & Stuckenschmidt (2007)
• Maximal-in-range
• Sub-optimal (2-approximate)
• Computationally efficient
18
Algorithm 1: Greedy Algorithm
Require:
, where are
candidate correspondences
are the bids of the left/right agent
Return:
A matching (alignment)
1. Let
2. if then
3. Find the edge that maximises
4. Let
5. Remove from the edge
6. Remove from the edges incident to
7. end if
G = (𝒪L ∪ 𝒪L, E) E
bL, bR
M
M = ∅
E ≠ ∅
e ∈ E be
L + be
R
M := M ∪ {e}
E e
E e

19. The 18th International Semantic Web Conference, Auckland 2019Truthful Mechanisms for Multi Agent Self-Interested Correspondence Selection
Analysis of the Greedy Algorithm
•What are the formal properties of this algorithm:
• Price of Anarchy
• i.e. the trade-off of obtaining an approximate solution wrt to optimal one
•Theorem 6:
• The price of anarchy (PoA) of the first price greedy matching game is
precisely 4
• This follows from two other theorems:
• Theorem 4: The price of anarchy (PoA) of the first price greedy matching game is at least 4
• Theorem 5: The price of anarchy (PoA) of a first price greedy matching game is at most 4
19

20. The 18th International Semantic Web Conference, Auckland 2019Truthful Mechanisms for Multi Agent Self-Interested Correspondence Selection
Conclusions
•Finding matchings has been central to much of the work on
Ontology Alignment systems
• In service-oriented or distributed domains, there is a need to decentralise this
approach
• Agents may be strategic when declaring their known correspondences
•We’ve analysed this from a Game Theoretic perspective
• We show the properties of sub-optimal agents when being truthful
• We show that agents do no better than to be honest with a simple additive greedy
algorithm
• We analyse its properties when finding equilibria
20