Speaker: Motty Perry
Affiliation: Hebrew University of Jerusalem and University of Warwick
Title: Dynamic Optimal Contracts with Adverse Selection and Moral Hazard
Date: Wednesday, 15 September 2010
Time: 4pm
Location:    301-242 [Science Centre, Symonds Street]
Abstract:  This paper studies a novel dynamic principle – agent setting with moral hazard and adverse selection (persistent as well as repeated). In the model an expert whose skills is his private information, faces a finite sequence of tasks, one after the other. Each task’s level of difficulty is an independent random variable revealed, upon arrival, to the expert only. On each task in turn the expert choose whether to pass or to work, and how much effort to exert. While the choice of work/pass is public, his effort is his private information.

The optimal contract-pair which takes advantage of the dynamic nature of the interaction is characterized. It is shown that as the length of the contract increases, the expected transfer per-period goes down and in the limit approaches the optimal payment when agent’s skills are publicly known.

One example of such a dynamic interaction is the one occurs between a money manager who receives funds from investors, and then observes a sequence of investment opportunities. Another example that nicely fits this model is the design of optimal contracts to surgeons of different quality, to treat a flow of patients whose problems are the surgeon’s private information.

Joint work with A. Gershkov.

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.

This talk is at COMPASS seminar (reciprocal visit after P. Davis talk last year in our seminar)

Speaker: Arkadii Slinko
Title: Proportional Representation and Strategic Voters
Date: Friday 21 May 2010
Time: 12pm
Location: Fale Pacifika Building 273 Rm 104
Abstract: This paper was initially motivated by a desire to explain the behaviour of voters at the New Zealand general election held September 17th, 2005. The New Zealand electoral system is mixed member proportional (MMP). Anecdotal evidence has suggested that some voters voted insincerely even though their doing so could have cost their most preferred party seats. We analyse the election and present two models that account for the behaviour observed in the election. We rigorously investigate opportunities for strategic voting under proportional representation (PR), other than those that emerge due to rounding. This talk is based on the paper “Proportional Representation and Strategic Voters” written jointly with Shaun White which is to appear in Journal of Theoretical Politics.

Slides are available.

Speaker: Tatiana Gvozdeva
Affiliation: The University of Auckland
Title: Roughly weighted games with interval thresholds
Date: Friday, 30 Apr 2010
Time: 3:00 pm
Location: Room 401 (small math seminar room)

It is very well-known that not every simple game has a representation as weighted majority game. The first step in attempt to characterise non-weighted games was the introduction of the class of roughly weighted games. This concept proved to be useful. It realises a very common idea in Social Choice that sometimes the rule needs an additional tie-breaking rule that helps to decide who is the winner if the results of all candidates are on a certain ‘threshold’. We gave a criterion of rough weightedness in the previous talk at this seminar. However not all games are even roughly weighted. Hence we need a more general construction to represent all games.

In this paper we introduce and explore several concepts that generalise roughly weighted games in several directions. One idea is to make the threshold thicker, i.e. use not a number but an interval for it. A good example of this situation would be a faculty vote. If neither side controls a 2/3 majority (calculated in faculty members or their grant dollars), then the Dean would decide the outcome. We can keep weights normalised so that the lower end of the interval is fixed at 1, then the right end of the interval becomes a “resource” parameter. We show that all class of games split into the hierarchy of classes of games define by this parameter. We show that as it increases we get strictly greater descriptive power, i.e., if the resource parameter gets larger, strictly more games can be described.

A situation when the number of players n is fixed also of interest. Then there is an interval [1,s(n)], numbers from which provide us with a resource parameter for every game. There will be finitely many numbers q in this interval such that the interval [1,q] represents more n-player games that any interval [1,q’] with q'<q. We call the set of such numbers the nth spectrum. We calculate the spectrum for n<7. Also we present an upper bound for s(n).

Another hierarchy of games emerges when we restrict the number of possible values that the weight of a coalition might be when this weight is in the threshold interval.

Speaker: Piotr Faliszewski
Affiliation: AGH University of Science and Technology, Krakow
Title: The Complexity of Campaign Management: Swap Bribery
Date: 6 May 2010
Time: 3:00pm
Location: MLT3 (Building 303)

Abstract: In voting theory, bribery is a form of manipulative behavior in which an external actor (the briber) offers to pay the voters to change their votes in order to get her preferred candidate elected. While bribery is typically associated with cheating in elections, its mathematical model can also be interpreted in terms of campaign management. In this work we study a model of bribery which is particularly well-suited for this campaign-management interpretation. Namely, we consider a model where the price of each vote depends on the amount of change that the voter is asked to implement and we focus on situations where the only allowed action is to shift the briber’s (campaign manager’s) preferred candidate forward on voters’ preference lists. We provide hardness results and polynomial time (approximate) algorithms for this type of bribery in many prominent voting rules.

Speaker: Patrick Girard
Affiliation: Department of Philosophy, University of Auckland
Title: Reasoning about social preferences
Date: Thursday, 1 Apr 2010
Time: 3:00 pm
Location: Room 401

A systematic way of aggregating individual preferences is to impose a hierarchy over groups of agents. I proceed in two steps, first by aggregating individual desires constrained by given hierarchies and second by defining preferences based on group desires. All this can be performed precisely in a hybrid modal logic (a basic modal logic augmented with names for states). This procedure avoids (some of) the consequences of Arrow’s impossibility theorem in social choice theory while retaining desirable aggregation properties, but the price to pay is the prioritization of agents. In this talk, I present the basic logic of preference aggregation and discuss the logical approach to the problem of preference aggregation.

Speaker: Arkadii Slinko
Affiliation: The University of Auckland, Mathematics
Title: Dagstuhl and manipulation by cloning candidates
Date: Thursday, 18 Mar 2010
Time: 3:00 pm
Location: Room 401

Firstly I will give my brief impressions of Dagstuhl meeting on Foundations of Computational Social Choice which took place last week. Then I will talk about an article written jointly with Piotr Faliszewski and Edith Elkind which I presented it at the workshop. Here I will give more details.

Abstract of the article

We consider the problem of manipulating elections via cloning candidates. In our model, a manipulator can replicate each candidate c by adding its several clones, i.e., new candidates that are so similar
to c that each voter simply replaces c in his vote with the block consisting of c and its clones. The outcome of the resulting election may then depend on how each voter orders the clones within the block. We formalize what it means for a cloning manipulation to be successful (which turns out to be a surprisingly delicate issue), and, for a number of prominent voting rules, characterise the preference profiles for which a successful cloning manipulation exists. We also consider the model where there is a cost associated with producing each new clone, and study the complexity of finding a minimum-cost cloning manipulation.

Speaker:     Tatyana Gvozdeva
Affiliation: The University of Auckland
Title:       A new bound for simple games
Date:        Monday, 13 Jul 2009
Time:        3:00 pm
Location:    Room 401

Comparative probability orders are closely related to simple games and cancellation conditions for these orders are very similar to trading transforms for games. In this talk we exploit this similarity to obtain new examples of simple games using Fishburn’s examples of comparative probability orders. These examples give us a new lower bound on the lengths of certificate of non-weightedness for simple games, which is better than the best known one given by Taylor and Zwicker (1992). Our lower bound is linear in the number of players while the one by Taylor and Zwicker is equal to the square root of n.

Speaker:     Matthew Ryan
Affiliation: Economics Department, The University of Auckland
Title:       Mixture Sets – An Introduction
Date:        Monday, 22 Jun 2009
Time:        3:00 pm
Location:    Room 401, Science Centre

A mixture set is an abstract convex structure introduced by Herstein and Milnor (Econometrica, 1953) as a foundation for the expected utility representation theorem (representation of preferernces by a linear utility function).  Mixture sets combine a set X with a ternary relation T that maps (x,y,t) to an element of X for each x,y in X and each t in [0,1] — the t-mixture of x and y.  Herstein and Milnor consider infinite mixture sets, but the notion is well-defined even for finite X.  This raises the question of the relationship between mixture sets and abstract convex geometries (discussed by Arkadii in previous Workshops).  It appears that neither is a special case of the other. This talk will introduce mixture sets, and what is — and isn’t — known about them.