Speaker: Arkadii Slinko (University of Auckland)

Paper to be presented: “Secret Sharing and Prisonner’s Dilemma” joint with Yvo Desmedt (University of Texas at Dallas)

Date, Time and Venue: Wednesday, 21 August 2019, 15:00-16:00, 260-5115 [Business School Building, Level 5]

Abstract: The study of Rational Secret Sharing initiated by Halpern and Teague (2004) regards the reconstruction of the secret in secret sharing as a game. It was shown that participants (parties) may refuse to reveal their shares and so the reconstruction may fail. Moreover, a refusal to reveal the share may be a dominant strategy of a party. In this paper we consider secret sharing as a sub-action or subgame of a larger action/game where the secret opens a possibility of consumption of a certain common good. We claim that utilities of participants will be dependent on the nature of this common good. In particular, Halpern and Teague (2014)’s scenario corresponds to a rivalrous and excludable common good. We consider the case when this common good is non-rivalrous and non-excludable and many natural Nash equilibria. We list several applications of secret sharing to demonstrate our claim and give corresponding scenarios. In such circumstances the secret sharing scheme facilitates a power sharing agreement in the society. We also state that non-reconstruction may be beneficial for this society and give several examples.

Everyone Welcome!

Speaker: David Kelsey (University of Exeter)

Paper to be presented: “Tort Liability and Unawareness” joint with Surajeet Chakravarty (Exeter University, UK) and Joshua Teitelbaum (Georgetown University, USA)

Date, Time and Venue: Wednesday, 14 August 2019, 15:00-16:00, 260-5115 [Business School Building, Level 5]

Abstract: Unawareness is a form of bounded rationality where a person fails to conceive all feasible acts or consequences or to perceive as feasible all conceivable act-consequence links. We study the implications of unawareness for tort law, where relevant examples include the discovery of a new product or technology (new act), of a new disease or injury (new consequence), or that a product can cause an injury (new link). We argue that negligence has an important advantage over strict liability in a world with unawareness-negligence, through the stipulation of due care standards, spreads awareness about the updated probability of harm.

Everyone Welcome!

Speaker: Michael Gordon (PhD Candidate, Massey University)

Paper to be presented: “Can we predict outcomes of systematic replication studies? Decision Markets Part 2 – Real World Applications”

Date, Time and Venue: Monday, 27 May 2019, 14:00-15:00, 260-6115 [Business School Building, Level 6]

Abstract: The credibility of scientific findings is of fundamental importance to enhance future research. One potential approach of collecting information about this credibility is to elicit beliefs about the reproducibility of scientific claims among scientists. Four studies have recently used surveys and prediction markets to estimate beliefs about replication in systematic large scale replication projects, but the sample size in each study has been small. Here we pool data for the four studies (n = 104) to assess the performance of surveys and prediction markets. This dataset and subsequent analysis allow us to comment on the real world success of prediction markets in terms of eliciting and aggregating information.

Everyone Welcome!

Speaker: Thomas Pfeiffer (NZIAS, Massey University)

Paper to be presented: “Predict to decide: An Introduction to decision markets”

Date, Time and Venue: Monday, 20 May 2019, 14:00-15:00, 260-6115 [Business School Building, Level 6]

Abstract: Prediction markets are popular tools to “crowd-source” distributed information and aggregate it into forecasts. Such forecasts can be very valuable for decision makers. Commercial companies, for instance, can benefit from accurate forecasts regarding the future demand for their products. Many decision-making problems, however, require conditional forecasts. To decide, for instance, between alternative marketing campaigns, a company needs to understand how each of the alternatives will affect sales. Finding mechanisms that properly incentivise participants to provide their information for such conditional forecasts is non-trivial, but can be done through so-called decision markets. I will kick off a mini-series on decision markets by describing how they work and giving an overview of our research activities on this topic.

Everyone Welcome!

Speaker: Matthew Ryan (AUT)

Paper to be presented: “Rationalising Random Choice as Random Consideration”

Date, Time and Venue: Monday, 13 May 2019, 14:00-15:00, 260-6115 [Business School Building, Level 6]

Abstract: Attempts to rationalise experimental evidence of pervasive randomness in choice behaviour may be divided into four categories: (i) models of deliberate randomisation; (ii) models of noisy utility maximisation (bounded rationality); (iii) random preferences models; and (iv) random consideration models. Category (i) has largely been explored by economists; (ii) and (iii) are mainly associated with mathematical psychologists and (iv) with researchers in marketing science. Recently, economists have taken an increasing interest in (iv), following the pioneering work of Manzini and Mariotti (Econometrica, 2014). This talk will briefly introduce random consideration models and their relationships with random preference models. A new random consideration model will also be proposed and “axiomatised”. This new model allows preferences to be ill-behaved on subsets of alternatives that are never considered together. In other words, the model is predicated on the implicit (and hopefully plausible) assumption that consideration is necessary to discipline preference.

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Speaker: Mariya Teteryatnikova (Department of Economics at the National Research University Higher School of Economics, Moscow)

Paper to be presented: “On the Existence of Perfect Pairwise Stable Weighted Networks” joint with Philippe Bich (Paris School of Economics and University of Paris 1 Pantheon-Sorbonne)

Date, Time and Venue: Monday, 6 May 2019, 14:00-15:00, 260-6115 [Business School Building, Level 6]

Abstract: We introduce a new concept of stability in network formation, perfect pairwise stability, and prove that a perfect pairwise stable network exists under very general assumptions. Perfect pairwise stability strictly refines the pairwise stability concept of Jackson and Wolinsky (1996), by transposing the idea of “trembling hand” perfection from non-cooperative games to the framework of cooperative pairwise network formation. The existence result extends that of Bich and Morhaim (2017). We prove that our concept is distinct from strong pairwise stability, a refinement concept introduced by Jackson and Van den Nouweland (2005). We also introduce a sequential framework for network formation and define a natural concept of sequential pairwise stability. By analogy with non-cooperative games, we prove that the sequential framework can be associated with a static one, and that the sequential pairwise stable networks correspond exactly to perfect pairwise stable networks in the static framework.

Short Bio: Mariya Teteryatnikova received her PhD in 2010 from the European University Institute in Florence, Italy. After that, she worked for six years as an Assistant professor at the University of Vienna and for another year at WU- Vienna University of Economics and Business. Since September 2017 she holds a position of an Assistant professor at Higher School of Economics in Moscow and since July 2018 – also a position of a Research associate at WU in Vienna. Her main research fields are (mostly applied) game and network theory and industrial organization.

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Speaker: Zach Weber (University of Otago)

Title: “Non-classical logic and inconsistent mathematics”

Date, Time and Venue: Monday, 1 April 2019, 14:00-15:00, 260-6115 [Business School Building, Level 6]

Abstract: Faced with logical paradoxes like the liar and the sorites, there are several options, including classical and non-classical (paracomplete and paraconsistent) approaches. I will briefly review some costs and benefits of each. Then I will mainly focus on the paraconsistent approach, using logics that allow for some contradictions. I will outline how paraconsistent logic may be applied in the foundations of mathematics, especially in naive set theory. I’ll conclude with a brief discussion of the wider inconsistent mathematics program as it stands today.

Everyone welcome!

Speaker: Patrick Girard (University of Auckland)

Title: “Mini-Series on Paradoxes”

Date, Time and Venue: Monday, [to start with] 11 and 25 March 2019, 14:00-15:00, 260-6115 [Business School Building, Level 6]

Abstract: Patrick will offer 2-3 seminars on paradoxes. He will start with historical/conceptual paradoxes (about God, being bald, and there being no change). He will then talk about modern logical paradoxes that involve truth, set membership and conditionals. He will end with paradoxes involving probability. The journey will take you from a conceptual/historical understanding of paradoxes in philosophy, go via problems in mathematics and logic, and end with more specific paradoxes behind the kind of mathematics that CMSS members are using in social choice theory and the like.

Everyone welcome!

Speaker: Addison Pan (University of Auckland)

Title: “A Note on The Pivotality Condition”

Date, Time and Venue: Wednesday, 23 May 2018, 14:00-15:00, 260-319 [Business School Building, Level 3]

Abstract: This note provides simple derivations of the equilibrium conditions for different voting games with incomplete information. In the standard voting game à la Austen-Smith and Banks (1996), voters update their beliefs only based on the probability that they are pivotal. However, in voting games such as those in Ellis (2016) and Fabrizi and Pan (2017), given a closed and convex set of priors, the ambiguous averse voters select the prior from this set in a strategy-contingent manner. Therefore, it is shown in this paper that in ambiguous voting games the conditional probability of being pivotal alone is not sufficient to determine each voter’s best response.

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Speaker: Arkadii Slinko (University of Auckland)

Title: “What Do Multiwinner Voting Rules Do? Some Simulations Over the Two-Dimensional Euclidean Domain”, joint work with Edith Elkind, Piotr Faliszewski, Jean-Francois Laslier, Piotr Skowron and Nimrod Talmon

Date, Time and Venue: Wednesday, 9 May 2018, 14:00-15:00, 260-319 [Business School Building, Level 3]

Abstract: We visualize aggregate outputs of several multiwinner voting rules—SNTV, STV, Bloc, k-Borda, Monroe, Chamberlin–Courant, and PAV—for elections generated according to the two-dimensional Euclidean model. We consider three applications of multiwinner voting, namely, parliamentary elections, portfolio/movie selection, and shortlisting, and we use our results to understand which of these rules seem to be best suited for each application. In particular, we show that STV (one of the few nontrivial rules used in real high-stake elections) exhibits excellent performance, whereas the Bloc rule (also often used in practice) performs poorly. We also visualise three approximation algorithms for the computationally hard Chamberlin–Courant and Monroe rules. Our results show that the best approximation algorithms on offer (one of which is introduced in this paper) can be safely used instead of the original rules themselves.

Everyone welcome!