Speaker: Gerardo Berbeglia
Affiliation: Melbourne Business School
Title: The Effect of a Finite Time Horizon in the Durable Good Monopoly Problem with Atomic Consumers
Date: Monday, 27 June 2016
Location: OGGB, Room 6115
A durable good is a long-lasting good that can be consumed repeatedly over time, and a duropolist is a monopolist in the market of a durable good. In 1972, Ronald Coase conjectured that a duropolist who lacks commitment power cannot sell the good above the competitive price if the time between periods approaches zero. Coase’s counterintuitive conjecture was later proven by Gul et al. (1986) under an infinite time horizon model with non-atomic consumers. Remarkably, the situation changes dramatically for atomic consumers and an infinite time horizon. Bagnoli et al. (1989) showed the existence of a subgame-perfect Nash equilibrium where the duropolist extracts all the consumer surplus. Observe that, in these cases, duropoly profits are either arbitrarily smaller or arbitrarily larger than the corresponding static monopoly profits — the profit a monopolist for an equivalent consumable good could generate. In this paper we show that the result of Bagnoli et al. (1989) is in fact driven by the infinite time horizon. Indeed, we prove that for finite time horizons and atomic agents, in any equilibrium satisfying the standard skimming property, duropoly profits are at most an additive factor more than static monopoly profits. In particular, duropoly profits are always at least static monopoly profits but never exceed twice the static monopoly profits. Finally we show that, for atomic consumers, equilibria may exist that do not satisfy the skimming property. For two time periods, we prove that amongst all equilibria that maximise duropoly profits, at least one of them satisfies the skimming property. We conjecture that this is true for any number of time periods.
The website for the CMSS summer workshop has been updated with the programme and information about the workshop location, including maps.
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.