MLSE Seminar

Author: Michal Bodicky joint with Ferdinand Pieroth (Yale Uni), Christian Seel (UM)
Date and time: January 30th, 2024 (13:00-14:00), TS53 A0.23
Title: Elimination Contests with Fatigue
Abstract: We study the effect of fatigue on elimination contests in a model with two competing semi-finalists and one directly qualified finalist. Fatigue enters the model as the promoted semi-finalist’s valuation for winning the final, decreasing her effort in the semi-final. Under the total effort maximizing seeding, the fatigue introduction might increase total effort and effort in each round. This result relies on the exclusion principle and a novel increased incentive for weak competitors in the semi-final. We discuss design implications for the timing of sports tournaments and promotion contests.

Author: Kaiqi Liu (UM, MPE) joint with Christian Seel (UM, MPE), Stefan Terstiege (UM, MPE) and Hannes Rusch (UM, MPE)
Date and time: February 6th, 2024 (14:00-15:00), TS53 C-1.05
Title: Equilibrium in Higher Education: Analysing Student Choices and Market Responses in the Presence of For-Profit Universities
Abstract: Our paper investigates the impact of the private for-profit universities on the global higher education market, including their interaction with existing institutions. We introduce a theoretical model that encompasses students, public universities, and both private non-profit and for-profit universities. This model is adaptable to different national contexts and allows for scenarios with either two or three types of universities. Our analysis focuses on students' application decisions, the resulting university rankings in the equilibria, and the optimal tuition fee-setting strategies at for-profit universities. We discover that, irrespective of the market composition, for-profit universities consistently attract lower-tier students in all equilibria. Conversely, the ranking of private non-profit and public universities varies across different equilibria. Under one plausible assumption, only the equilibria with the private non-profit university at the top are group strategy proof. Additionally, we analyse the optimal tuition fee structures for private for-profit universities in two specific equilibria. Given the various possible equilibria, it is ultimately the responsibility of policymakers to determine desired outcomes and set appropriate conditions. Our findings provide insights into policy formulation and facilitate cross-country comparisons in the higher education sector.

Author: Andrés Perea (UM, KE)
Date and time: March 19th, 2024 (13:00-14:00), TS53 H0.06
Title: Consequentialism in Decision Problems and Games.
Abstract: In many control problems there is only limited information about the actions that will be available at future stages. We introduce a framework where the Controller chooses actions sequentially, one at a time. Her goal is to maximize the probability that the infinite sequence of actions is an element of a given subset G. The set G, called the goal, is assumed to be a tail set. The Controller's choices are restricted: specifically, at any particular stage, she must choose an action from a given action set (these are the available actions); the action set may depend on the Controller’s previous choices. Action sets are chosen randomly by nature from a given distribution. We consider several information structures defined by how far ahead into the future the Controller knows what actions will be available.
In the special case where all action sets are singletons (and thus the Controller is a dummy), Kolmogorov’s 0-1 law says that the probability for the goal to be reached is 0 or 1. We construct a number of counterexamples to show that in general the value of the control problem can be strictly between 0 and 1, and derive several sufficient conditions for the 0-1 ``law" to hold.

Author: Markus Möller (joint with Aram Grigoryan (UC San Diego))
Date and time: April 9th, 2024 (13:00-14:00), TS53 A0.24
Title: A Theory of Auditability for Allocation Mechanisms 
Abstract: In centralized mechanisms and platforms, participants do not fully observe each others' type reports. Hence, if there is a deviation from the promised mechanism, participants may not be able to detect it. We formalize a notion of auditabilty that captures how easy or hard it is for participants to detect deviations from a mechanism. We find a stark contrast between the auditabilities of prominent mechanisms, such as the Deferred Acceptance, the Immediate Acceptance, and the Serial Dictatorship. We also provide tight characterizations of maximally auditable subclasses of allocation mechanisms.

Author: Andries Vermeulen (UM, KE) (joint with János Flesch, Chris Kops, and Anna Zseleva)
Date and time: April 23rd, 2024 (12:30-13:30), TS53 A1.23
Title: A general definition of perfect equilibrium 
Abstract: We propose a definition of perfect equilibrium that can be applied to a wide class of games in strategic form. The two key features in the definition are a) using nets instead of sequences, b) using a new concept of completely mixed nets of strategies, based on a more detailed interpretation of the notion of a carrier of a strategy. In the case of finite action sets our definition coincides with the original definition of Selten (1975), and in the compact-continuous case our definition yields a nonempty and compact set of perfect equilibria, which are all weak perfect equilibria according to the definition of Simon and Stinchcombe (1995).

We present several examples which both motivate and illustrate our definition, including games with discontinuous payoffs as well as games played with finitely additive strategies where our definition has a bite.

Author: Bas Dietzenbacher (UM, KE) (joint work with Emre Dogan)
Date and time: May 28th, 2024 (13:00-14:00), TS53 A0.23
Title: Population monotonicity and egalitarianism
Abstract: This paper identifies the maximal domain of transferable utility games on which population monotonicity (no player is worse off when additional players enter the game) and egalitarian core selection (no other core allocation can be obtained by a transfer from a richer to a poorer player) are compatible, which is the class of games with an egalitarian population monotonic allocation scheme. On this domain, which strictly includes the class of convex games, population monotonicity and egalitarian core selection together characterize the Dutta-Ray solution. We relate the class of games with an egalitarian population monotonic allocation scheme to several other classes of games.

Author: Andrew Mackenzie (joint work with Christian Trudeau)
Date and time: June 6th, 2024 (15:00-16:00), TS53 A0.24
Title: Auctions for a regulated monopolist
Abstract: A monopolist with a convex production technology must elicit consumer demand in order to determine price and quantity, and a regulator requires that efficient and fair allocations be implemented in dominant strategies. We characterize the class of mechanisms available to the regulated monopolist. Among those that moreover guarantee ex-post voluntary participation across both sides of the market, we find that (i) in line with previous results from the literature, the VCG mechanisms are optimal for the producer, and (ii) a novel class of mechanisms are optimal for consumers. This latter class involves sometimes distributing part of the production profit to consumers regardless of whether they purchase anything.

Author: Anh Trieu (UM, KE) (joint work with Iwan Bos, Marc Schroder, Dries Vermeulen)
Date and time: Jun 11th, 2024 (13:00-14:00), TS53 A0.24
Title: Matching Maximization Mechanism with Multiple Items
Abstract: There are many situations in which policymakers are primarily concerned with the availability and accessibility of goods or services. Examples include electricity, food, housing, medical supplies, et cetera. In such cases, the social goal may be to maximize the number of transactions, which we refer to as a maximal matching, instead of maximizing total utility. This paper attempts to answer the question whether such maximal matching outcome can be obtained in a multi-demand and multi-supply setting.