Speaker:     Egor Ianovski
Affiliation: The University of Auckland
Title:       Logics of belief change
Date:        Thursday, 9 Jun 2011
Time:        4:00 pm
Location:    Room 6115, Owen Glenn Building

We are at war with Eurasia. We have always been at war with Eurasia. Eastasia is our ally. How then, should we respond to an announcement of war with Eastasia? Is it enough to drop the belief that Eastasia is our ally, or do we need to revise our entire belief set?

What if the next day we are led to believe that we are at war with Eurasia again? Can we revert to our prior belief set, or has the first announcement changed our beliefs forever? If I have a friend that heard the same announcements, what can I conclude about their beliefs? Did they change the same way as mine or if not, for what reasons? In this talk we examine two main trends in the logical treatment of belief change, with focus on problems that arise with iteration and a multi-agent setting.

Note an unusual day of the week! Everyone welcome!

Speaker:     Simona Fabrizi
Affiliation: Massey University (Albany)
Title:       Suggested retail prices with downstream competition
Date:        Tuesday, 24 May 2011
Time:        4:00 pm
Location:    Room 6115, Owen Glenn Building

We analyze a manufacturer’s choice whether to recommend retail prices (RRP) to horizontally differentiated downstream competing retailers or to use more traditional vertical price restraints, such as resale price maintenance (RPM), when consumers have reference-dependent preferences. If recommended prices are taken as a reference point, consumers can suffer from loss aversion when facing retail prices above this reference point, but also benefit from gain proneness when prices are set below this level. In equilibrium, retailers do not set prices above their recommended levels; manufacturers prefer RPM over RRP when retailers follow the recommendation strictly; but manufacturers prefer RRP over RPM when the recommendation is undercut by retailers (discounting occurs). Two types of conflicts with respect to consumers’ surplus potentially arise when manufacturers can choose between RRP and RPM. There are combinations of gain proneness and degrees of competition for which either (i) manufacturers choose traditional resale price maintenance (RPM) even though recommending prices would have been consumers’ surplus enhancing; or, vice versa (ii) manufacturers choose to recommend retail prices (RRP) despite it would have been consumers’ surplus enhancing not to do so.

This paper is written Jointly with Steffen Lippert (Massey University), Clemens Puppe (Karlsruhe University of Technology) and Stephanie Rosenkranz (Utrecht University)

Speaker:    Mark C. Wilson
Affiliation: The University of Auckland
Title:       Decisiveness, power, and value
Date:        Tuesday, 10 May, 2011
Time:        4:00 pm
Location:    Room 6115, Owen G. Glenn Building

The connection between individual contribution and collective value  has been studied in the framework of cooperative (coalitional) games with transferable utility, most famously in terms of the Shapley value which has led to a general theory of “values”. In the special case of simple games, the concept of (voting) power has been studied, most famously by Banzhaf, again leading to a substantial literature, with more controversy than in the TU game case. In each case, there is a collective notion which yields the individual one in a straightforward way, and which is less understood than the individual one. I will attempt to give a unified presentation of  all these ideas and their relationships, with the aim of shedding some light on some arguments over definitions of power and pointing the way to further research. This is a preliminary discussion of several possible papers in progress with Geoff Pritchard and Reyhaneh Reyhani. Audience contributions are encouraged.

Speaker: Matthew Ryan
Affiliation: The University of Auckland
Title: Path Independent Choice and the Ranking of Opportunity Sets
Date: Tuesday, 29 Mar 2011
Time: 4:00 pm
Location: Room 6115, Owen Glenn Building

An opportunity set is a non-empty subset of a given set X. A decision-maker, when confronted with an opportunity set, is allowed to choose one element from it.
We assume that the decision-maker has some reflexive and transitive ordering over opportunity sets. Such an ordering is called an “indirect utility ordering” if there
exists a weak order (preference relation) on X such that opportunity set A is weakly preferred to opportunity set B iff the most preferred element(s) from A∪B includes
at least one element of A. Necessary and sufficient conditions for an opportunity set ranking to be an indirect utility ordering are well-known (Kreps, 1979). We give
necessary and sufficient conditions for an ordering of opportunity sets to be consistent with a path independent choice function, or “Plott consistent”. That is, opportunity set A is weakly
preferred to opportunity set B iff the acceptable choice(s) from A∪B include at least one element of A. The proof employs results from the theory of abstract convex geometries.

Speaker: Arkadii Slinko
Affiliation: The University of Auckland
Title: Hierarchical games
Date: Tuesday, 15 Mar 2011
Time: 4:00 pm
Location: Room 6115, Owen Glenn Building

In many situations, both in human and artificial societies, cooperating agents have different status with respect to the activity and it is not uncommon that certain actions are only allowed to coalitions that satisfy certain criteria, e.g., to sufficiently large coalitions or coalitions which involve players of sufficient seniority. Simmons (1988) formalised this idea in the context of secret sharing schemes by defining the concept of a (disjunctive) hierarchical access structure.

The mathematical concept which describe access structures of secret sharing schemes is that of a simple game. In this paper we aim to start a systematic study of hierarchical games, both disjunctive and conjunctive, and our results show that they deserve such a treatment. We prove the duality between disjunctive and conjunctive hierarchical games. We introduce a canonical representation theorem for both and characterise disjunctive hierarchical games as complete games with a unique shift-maximal losing coalition. We give a short combinatorial proof of the Beimel-Tassa-Weinreb characterisation theorem of weighted disjunctive hierarchical games. By duality we get similar theorems for conjunctive hierarchical games.

This is a joint work with Tatiana Gvozdeva and Ali Hameed.

Speaker: Nadja Betzler
Affiliation: Technical University of Berlin
Title: Parameterized algorithmics for Kemeny’s voting system
Date: Tuesday, 1 Mar 2011
Time: 4:00 pm
Location: Room 6115, Owen Glenn Building

Kemeny’s voting system is concerned with optimally aggregating a multiset of preference lists into a consensus list. We study the parameterized complexity of the underlying decision problem, called Kemeny Score, with respect to several different parameterizations.This includes a discussion about the relevance and motivation of the parameterizations illustrating the usefulness of a multivariate complexity analysis for voting problems.
We further extend this study by introducing the concept of “partial kernelization”. Based on this, we devise an additional result for the parameter measuring the average distance between pairs of input votes. Moreover, the partial kernelization concept naturally leads to additional parameterizations. Finally, we provide experimental results for computing optimal Kemeny rankings based on some of the previously introduced methods.

Speaker: John McCabe Dansted
Affiliation: University of Western Australia
Title: Axioms for obligation and robustness with temporal logic
Date: Tuesday, 15 Feb 2011
Time: 4:00 pm
Location: Room 6115, Owen Glenn Building

Deontic logics are used to reason about norms. These norms may include
policies, relating to operation of an automated system, that are
subject to violation. We present a Temporal Logic of Robustness
(RoCTL*) that is intended to verify that a system is Robust to
some number of norm violations. We present sound and complete
axiomatisations of fragments of this logic and briefly discuss the
philosophical background to these axioms, including which axioms may
be relevant in fields other than robust systems. Although every
property that can be expressed in RoCTL* can be expressed in an
existing logic (CTL*), RoCTL* can express some properties much more
succinctly than CTL*.

Everyone welcome!