Speaker: Bettina Klaus

Affiliation: University of Lausanne

Title: Non-Revelation Mechanisms for Many-to-Many Matching: Equilibria versus Stability

Date: Monday, 31 October 2016

Time: 4:00-5:00 pm

Location: 260-307

We study many-to-many matching markets in which agents from a set A are matched to agents from a disjoint set B through a two-stage non-revelation mechanism. In the first stage, A-agents, who are endowed with a quota that describes the maximal number of agents they can be matched to, simultaneously make proposals to the B-agents. In the second stage, B-agents sequentially, and respecting the quota, choose and match to available A-proposers. We study the subgame perfect Nash equilibria of the induced game. We prove that stable matchings are equilibrium outcomes if all A-agents’ preferences are substitutable. We also show that the implementation of the set of stable matchings is closely related to the quotas of the A-agents. In particular, implementation holds when A-agents’ preferences are substitutable and their quotas are non-binding.

A copy of the paper to be presented is available for downloads here

Everyone welcome!

Speaker:     Konstantin Sorokin
Affiliation: Higher School of Economics (Moscow)
Title:       Candidate utility invariance under stochastic voting
Date:        Friday, 16 Jan 2015
Time:        3:00 pm
Location:    Room 412, Science Centre (303)

Previous work by the authors (Zakharov, 2012, Sorokin and Zakharov, 2014) demonstrated
that the shape of the functions that translate vote shares into payoffs does have an effect on
the equilibrium actions of candidates in two-candidate voting games with a finite number of
stochastic voters. In particular, we have shown that the „mean voter theorem‰ that predicts
candidates choosing identical policy positions in fact holds only for a small set of candidate
utility functions (a set that includes both winner-take-all and proportional utility).

In this work, we take our research one step further. First, we show that, as the number of
voters becomes large, the outcome of an electoral competition game is invariant with respect
to the candidate utility functions. Second, we show that this invariance holds only if the votes
are cast independently. If there is, say, a common shock to the utilities that all voters receive, then candidate payoffs will affect the equilibrium even in the limiting games when the number of voters is infinite.

Everyone welcome!

Title:
Overview of the Centre for Mathematical Social Sciences

Speaker:
Mark Wilson, Computer Science and Centre for Mathematical Social Sciences (accompanied by Valery Pavlov)

Abstract:
The Centre for Mathematical Social Sciences at the University of Auckland is sometimes confused with COMPASS by outsiders. Although our structure, research methods and levels of funding have been quite different, it does seem that more collaboration could be explored.
I will give a quick overview of CMSS and discuss a few current research projects.

Date, Time, Venue: Friday September 12, 1-2, COMPASS meeting room (second floor, Fale Pacifika building)

Speaker: Nina Anchugina
Affiliation: PhD student, Department of Mathematics
Title: Evaluating Long-Term Investment Projects: What Should The Discounting Method Be?
Date: Wednesday, 27 Aug 2014
Time: 4:00 pm
Location: CAG17/114-G17 (Commerce A)

Increasingly today there is a necessity to evaluate projects, policies and activities, whose consequences will be spread over a long period of time.

Projects are usually analysed by converting the future values into present values by attaching some weight to each period; this procedure is known as discounting. Several methods of discounting have been developed but a universal one does not exist. The choice of discounting method, however, may be vital for deciding whether a certain project should be implemented or not. The question is: Which method of discounting should be used when evaluating long-term public projects?

In this talk we will firstly consider two main types of discounting, namely exponential and hyperbolic discounting, their functional forms, properties and implications. I will provide an example which illustrates how the choice of discounting method appears to be crucial for making a decision. Secondly, we will analyse an appropriate social discount function for a public project implied by an aggregation of the individual discount functions. Finally, we will investigate the situation when there is an uncertainty about discount rates for exponential discounting, which is a common case for long-term projects. I will also present some new results on the choice of a discount rate of the hyperbolic discounting when there is uncertainty about future rates .

Speaker: Golbon Zakeri
Affiliation: UoA Engineering Science
Title: Electricity market modelling, economics and analytics
Date: Wednesday, 20 Aug 2014
Time: 4:00 pm
Location: CAG17/114-G17 (Commerce A)

Over the past 2 decades there has been a major shift to meet the electricity needs of various countries and jurisdictions through markets. We will start by describing issues common to the vast majority of electricity systems and reasons that rationalised the move to electricity markets in developed countries. We will then discuss issues that arise from a transition to an electricity market with a particular focus on the NZ electricity market. This is a rich source of mathematical modelling, economics and analytics problems. We will lay out some of the more interesting problems that we have tackled and go in more depth to explore consequences of the introduction of renewables and our proposed solutions.

This talk is targeted towards members with varied backgrounds.

Everyone welcome!

Speaker: Jeremy Seligman
Affiliation: The University of Auckland (Philosophy)
Title: Secret tweets and network discovery
Date: Wednesday, 6 Aug 2014
Time: 5:00 pm
Location: Room 405, Engineering (403)

You are a secret agent with a secret S that you would like to transmit to a fellow agent a unobtrusively using a very public network like Twitter. Any information you tweet will be received by your followers on the network. You correctly assume that they will send the message on to their followers (retweet it) if and only if it does not conflict with any information they already possess. With luck, your message will be tweeted through the network until it eventually reaches a. Under what conditions is it possible for you to convey S to a in this way, without other agents in the network learning this information? Clearly,you cannot tweet S itself, but if, for example, a is the only agent to know that K then the message `if K then S’ may work, if there is a suitable path from you to a. To know whether you can succeed or not and what to tweet, you need to know something about the network and the information already possessed by the other agents. But you can learn something about this with a test tweet. If, for example, you know that you have two followers b and c and only b believes P and then you tweet the message `not P’ then if, after a certain length of time, someone tweets P to you, you know that there is a loop back to you via c. This talk will report on recent joint work on these and similar questions with Mostafa Raziebrahimsaraei.

Speaker: Matthew Ryan
Affiliation: Department of Economics, UoA
Title: Binary Stochastic Choice under Risk or Uncertainty
Date: Tuesday, 3 Jun 2014
Time: 5:00 pm
Location: Room 412, Science Centre (303)

Economists usually model choice as deterministic, via preference relations, though occasionally — and usually for econometric convenience — choice is allowed to be stochastic. Psychologists, on the other hand, typically model choice behaviour as intrinsically stochastic. In psychophysics, for example, it is common to model the probability of choosing one option over another (in a binary choice problem) as an increasing function of the difference in “utility” stimuli associated with the options. This is called a “strong utility representation” (SUP) for the binary choice probabilities.

These models of binary stochastic choice generate numerous interesting mathematical problems. This talk will introduce a small sample. The main focus will be on binary choice problems in which each option is a “lottery”, with risky or uncertain value. Given a specification of choice probabilities for all possible pairs of lotteries, under what conditions (on these probabilities) does there exist a SUP? What if we additionally require that the utility scale exhibit particular properties, such as linearity?