Speaker: Nina Anchugina & Arkadii Slinko
Affiliation: The University of Auckland
Title: Two talks see titles below
Date: Thursday, 7 May 2015
Time: 5:00 pm
Location: Room 260-325, Owen Glenn Building
1. Speaker: Nina Anchugina.
Title: A simple framework for the axiomatization of exponential and quasi-hyperbolic discounting
Time: 30 min.
Abstract: The main goal of this talk is to investigate which normative requirements, or axioms, lead to exponential and quasi-hyperbolic forms of discounting in inter-temporal decision-making. Exponential discounting has a well-established axiomatic foundation originally developed by Koopmans (1960) with subsequent contributions by several other authors. Hayashi (2003) and Olea and Strzalecki (2014) axiomatize quasi-hyperbolic discounting. In this talk we provide an alternative foundation for exponential and quasi-hyperbolic discounting, with simple, transparent axioms and relatively straightforward proofs. Using techniques by Fishburn (1982) and Harvey (1986), we show that Anscombe and Aumann’s (1963) version of Subjective Expected Utility (SEU) theory can be readily adapted to axiomatize the aforementioned types of discounting, in both finite and infinite horizon settings.
This is a joint work with Matthew Ryan.
2. Speaker: Arkadii Slinko
Title: Condorcet Domains and Median Graphs
Time 30 min
Abstract: A set of linear orders D is called a Condorcet domain if every profile composed from preferences from D has acyclic majority relation. Maximal Condorcet domains have been a subject of intense investigation, especially by Fishburn and Monjardet. Demange (2012) generalized the classical single-crossing property to the intermediate property on median graphs and proved that for every intermediate profile R with an odd number of voters on a median graph G there is a representative voter whose preference order coincides with the majority relation. We complement her result with proving that the linear orders of any profile which is intermediate on a median graph form a Condorcet domain. We prove that for any median graph there exists a profile that is intermediate with respect to that graph and that one may need at least as many alternatives as vertices to construct such a profile. We provide a polynomial-time algorithm to recognise whether or not a given profile is intermediate with respect to some median graph.
This is a joint work with Adam Clearwater (The University of Auckland) and Clemens Puppe (Karlsruhe Institute of Technology, Germany).
The video from the seminar “Non-transitive Games in Business” by Valery Pavlov is now available on the CMSS YouTube channel.
Speaker: Valery Pavlov
Affiliation: Information Systems and Operations Management
Title: Non-transitive games in business
Date: Tuesday, 24 Mar 2015
Time: 5:00 pm
Location: Owen Glen building, room 260-321
This paper studies a model of competition between two players who are concerned not only with their expected profits but also with their chance of earning more than the other player. As a result, the game has some similarities with the well-known Rock-Paper-Scissors game. We conduct an experiment that tests (i) the hypothesis that such competition may arise without monetary rewards, purely as a result of intrinsic competitiveness and (ii) whether such social preferences can be easily mitigated. The experimental data provide strong evidence of the intrinsic competitiveness hypothesis and indicate some possibilities for its mitigation.
We hope this study may be of interest for practicing managers. First, it broadly captures a number of common situations in which “popular” decisions clash with “good” ones. Popular decisions bring pleasing results more often than good decisions but the difference in such is not that big whereas when outcomes of good decisions result in much higher gains albeit less often. Second, the competition mechanism we analyzed may explain why employees may be reluctant to share their own decisions and when decisions of the best employees are shared with the rest the overall performance of the company may be driven away from the optimum.
The CMSS was fortunate to have visitors Nimrod Talmon & Piotr Faliszewski present seminars over the last few days. Recordings from both seminars are now available on the CMSS YouTube channel.
Speaker: Piotr Faliszewski
Affiliation: AGH Institute of Technology (Krakow)
Title: Finding a Collective Set of Items: From Proportional Multirepresentation to Group Recommendation
Date: Tuesday, 3 Mar 2015
Time: 5:00 pm
Location: Owen Glenn building, room 260-321
We consider the following problem: There is a set of items (e.g., movies) and a group of agents (e.g., passengers on a plane); each agent has some intrinsic utility for each of the items. Our goal is to pick a set of K items that maximize the total derived utility of all the agents (i.e., in our example we are to pick K movies that we put on the plane’s entertainment system). However, the actual utility that an agent derives from a given item is only a fraction of its intrinsic one, and this fraction depends on how the agent ranks the item among the chosen, available, ones. We provide a formal specification of the model and provide concrete examples and settings where it is applicable. We show that the problem is hard in general, but we show a number of tractability results for its natural special cases.
Speaker: Nimrod Talmon
Affiliation: Technical University of Berlin
Title: Multi-Player Diffusion Games on Graph Classes
Date: Tuesday, 24 Feb 2015
Time: 5:00 pm
Location: Owen G. Glenn building, room 260-321
We study competitive diffusion games on graphs introduced by Alon et al. (2010) to model the spread of influence in social networks. Extending results of Roshanbin (2014) for two players, we investigate the existence of pure strategy Nash-equilibria for at least three players on different classes of graphs including paths, cycles, and grid graphs. As a main result, we answer an open question proving that there is no Nash-equilibrium for three players on m × n grids for m and n not smaller than 5.
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.
Overview of the Centre for Mathematical Social Sciences
Mark Wilson, Computer Science and Centre for Mathematical Social Sciences (accompanied by Valery Pavlov)
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.