The 2010 summer workshop archive now contains almost all the slides for the talks.
The 2011 workshop is tentatively planned for December, and will have logic as a theme. More details will follow throughout the year.
Mark Wilson is now the Director of CMSS and the seminar organizer is Arkadii Slinko. Please contact us if you want to give a talk in the seminar, or otherwise visit us.
We expect some visitors in 2011, including Nadja Betzler from Germany.
We are planning a workshop in December. The first announcement from Arkadii Slinko:
The Centre for Mathematical Social Science at The University of Auckland (New Zealand) is planning a series of lectures and seminars given by visitors
and members of the Centre in the period of 13–22 of December 2010. At the moment the following visitors have expressed their intention to participate and give lectures:
– Clemens Puppe (KIT, Karlsruhe)
– Bill Zwicker (Union College, New York)
– Toby Walsh (University of NSW and NICTA)
– Igor Shparlinski (Macquarie University, Sydney)
This will be accompanied by discussions of future research directions and research collaborations in small groups with participation of visitors and local researchers including PhD and graduate students. The talks will take place in mornings and in the afternoon we will have sessions for discussions on topics relevant to the lectures.
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TOPICS AND DATES:
13 Dec (Monday) – Registration. Welcoming drink at Old Government House.
14 Dec (Tuesday) – Simple games and Secret Sharing.
15 Dec (Wednesday) – Cryptography.
17 Dec (Friday) – Comparative probabilities and simple games.
20 Dec (Monday) – Voting theory.
21 Dec (Tuesday) – Uncertainty, Ambiguity and Choice.
The exact schedule for each day will be announced later. During the weekend 18-19 of December we are planning an excursion.
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APPROXIMATE SCHEDULE:
Simple Games and Secret Sharing (organiser Arkadii Slinko)
1. Arkadii Slinko – Complete simple games and hierarchical secret sharing schemes.
2. Bill Zwicker – Hereditary rough weigtedness in simple games.
3. Ali Hameed – Weighted and roughly weighted ideal secret sharing schemes.
Topics for discussions in the afternoon session: simple games and secret sharing schemes, hereditary rough weightedness and its
characterisations, hierarchical simple games (access structures) and their properties.
Cryptography (organiser Steven Galbraith)
1. Igor Shparlinski – Group structures of elliptic curves over finite fields
2. Steven Galbraith – Introduction to “Learning With Errors” and lattice-based cryptography
3. Edoardo Persichetti – Compact McEliece keys using quasi-dyadic Srivastava codes
Topics for discussions in the afternoon session: Cryptography from codes, Homomorphic encryption, Lattices in cryptography.
Comparative probabilities and simple games (organiser Arkadii Slinko)
1. Arkadii Slinko – Abstract simplicial complexes which are initial segments of comparative probability orders
2. Tatyana Gvozdeva – On Edelman’s conjecture about simple games obtained from comparative probability orders
3. Ilya Chevyrev – On the number of facets of the convex polytope of a comparative probability order.
Topics for discussions in the afternoon session: Edelman’s conjecture, characterisations of weighted simple
games by polytopes
Uncertainty, Ambiguity and Choice (Organiser Matthew Ryan)
1. Clemens Puppe – “Majoritarian Indeterminacy and Path-Dependence: The Condorcet Efficient Set”
(based on joint work with Klaus Nehring and Markus Pivato)
2. Matthew Ryan – Abstract Convex Geometries and Decision Theory
3. Patrick Girard, Jeremy Seligman – Logic of Social Choice
Topics for discussions in the afternoon session: Abstract convexity in decision theory; abstract convexity in social choice; modal logic for ambiguous semantics.
Voting Theory (organiser Mark Wilson)
1. 1. Bill Zwicker – “The Geometry of Influence: Weighted Voting and Hyper-ellipsoids,” joint work with Nicolas Houy.
2. Toby Walsh – Manipulation of Borda and related voting rules
3. Reyhaneh Reyhani – Dynamics in voting games
4. Egor Ianovski – Safe manipulation of Borda
Topics for discussions in the afternoon session: Manipulation of Borda and related voting rules,
Manipulation with partial information, Lotteries and voting rules. Interplay between manipulability and decisiveness
Speaker: John Hillas
Affiliation: Department of Economics, UoA
Title: Backward Induction in Games with Imperfect Recall (with D. Kvasov)
Date: Wednesday, 13 October 2010
Time: 4:00 pm
Location: 301-242 [Science Centre, Symonds Street]
ABSTRACT
The standard solution concepts motivated by the idea of backward induction, subgame perfect equilibrium, extensive form perfect equilibrium, sequential equilibrium, and quasi-perfect equilibrium were explicitly defined only for games with perfect recall. In games with imperfect recall a literal application of the same definitions is clearly inappropriate. We give definitions that coincide with the standard definitions in games with perfect recall and define sensible solutions in games without perfect recall.
The basic idea is to look, at subsets of each player’s information sets, at the pure strategies that make that those subsets reachable and to define a system of beliefs as associating to that strategy and that subset a distribution over the other players’ strategies. We define the relevant solution concepts and show (conjecture) that the inclusions and the relation to proper equilibrium of the associated normal that were true for games with perfect recall remain true.
Very much work in progress.
Speaker: Mark C. Wilson
Affiliation: University of Auckland, Computer Science
Title: The probability of safe manipulation
Date: Wednesday, 25 August 2010
Time: 4:00 pm
Location: 301.242
Manipulation by a coalition in voting games is a well-studied occurrence, yet the underlying model is rather unconvincing. Slinko and White recently introduced the more restricted concept of safe manipulation and studied some basic properties. They posed the question of the probability that safe manipulation can occur. We present some results for positional scoring rules. The numerical results for 3 candidates show that the susceptibility of such rules to safe manipulation differs substantially from that for coalitional manipulation.
Joint work with Reyhaneh Reyhani, to be presented at COMSOC 2010 in Dusseldorf.
Speaker: Suren Basov
Affiliation: La Trobe University
Title: The Inclusiveness of Exclusion
Date: Tuesday, 22 Jun 2010
Time: 3:00 pm
Location: Room 401
Consider a monopolist who produces a good of quality x to sell to consumers.
A consumer’s utility from consuming the good is given by u(a, x) – t, where a is
a parameter, which is privately known to the consumer, x is the quality of the
good purchased, and t is the price paid. The monopolist does not observe a,
but knows the distribution of a in the population of the consumers and chooses
tariff t(x) to maximize her profits. Early models assumed that a belongs either
to a finite set or a one-dimensional continuum. Under these assumptions it was
shown that the monopolist may sometimes choose not to serve some fraction of
consumers in equilibrium, even when there is positive surplus associated with
those consumers. This phenomenon is known as exclusion. However, whether the
exclusion occurs in early models depended on the distribution of types and both
cases exclusion and full coverage were robust with respect to small perturbations of
the model. In a multidimensional screening models a is assumed to be distributed
over a set of dimension greater than one. One of the most celebrated results in the
theory of multidimensional screening comes from Armstrong (1996) where he shows
that under some technical assumptions exclusion always occur in such models.
Though important, Armstrong’s result relies on strong technical assumptions on
both preferences and market structure, which made it hard to apply to many
interesting practical questions. We extend Armstrong’s result on exclusion
in multi-dimensional screening models in two key ways, providing support for the
view that this result is quite generic and applicable to many different markets.
First, we relax the strong technical assumptions he imposed on preferences and
consumer types. Second, we extend the result beyond the monopolistic market
structure to generalized oligopoly settings with entry. We also analyze applications
to several quite different settings: credit markets, automobile industry, research
grants, the regulation of a monopolist with unknown demand and cost functions,
and involuntary unemployment in the labor market.
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