MLSE Seminar

Authors: Galit Ashkenazi-Golan, János Flesch (UM, KE), Eilon Solan

Date and time: September 9th, 12:00-13:00 

Title: Games with an infinite past

Abstract: We study multi-player games with perfect information and general payoff functions, where the set of stages is the set of non-positive integers {...,−2,−1,0}. We define two related equilibrium notions: one only considering deviations at finitely many stages and another considering all deviations. We show that (i) The sets of equilibrium plays coincide for the two equilibrium notions, provided that at least two players are active along each infinite play. (ii) For win-lose games, the game has an equilibrium if the winning sets have Borel rank at most 2, and we provide a counter-example showing that this is no longer true for Borel rank 3. (iii) In general non-zerosum games, the game has an equilibrium if either (i) the payoff functions have finite range and Borel rank at most 2, or (ii) the payoff functions are continuous, for example, with reversed-time discounted payoffs. The challenge for all these results is that not all strategy profiles admit a consistent infinite play, hampering the use of backward induction arguments.

Authors: J. Bizzotto, J. Rüdiger, Stefan Terstiege (UM, MPE)

Date and time: September 23rd, 13:00-14:00

Title: Design and sale of market segments

Abstract: A platform segments a market and runs auctions in which firms bid for the access to market segments. Segmenting the market more finely allows firms to extract more profits from consumers but can decrease competition in the auctions. We first characterize extremal markets: markets that cannot be segmented further without reducing auction revenue. Second, we employ this result to characterize
optimal segmentations in a Hotelling environment. Our results give an insight into the welfare losses and consumer surpluses resulting from for-profit market segmentation.

Author: Andrés Perea (UM, KE)

Date and time: November 4th, 13:15-14:15

Title: Pure backward induction reasoning in dynamic games

Abstract: Pure backward induction reasoning means that the solution of a game, when applied to a subgame, should yield the same as applying the solution to the subgame in isolation. Remarkably, none of the existing backward induction concepts in the literature satisfies this criterion. The purpose of this paper is to present, and analyze, a reasoning concept that does meet the pure backward induction principle. In the concept, a player can only commit to his current action, not to his future actions. At every history, the player holds a probabilistic belief about the opponents' current and future actions, and his own future actions, and chooses his current action based on that belief. The key conditions are that a player believes that he, and his opponents, will choose rationally in the future, that he believes that every opponent believes that he, and the other players, will choose rationally in the future and so on. We show that the resulting actions can be obtained by an easy-to-use iterated elimination procedure, which may be viewed as a natural generalization of the backward induction procedure. In finitely repeated games, the procedure reduces to an even easier algorithm that can be used to compute the possible actions at every period.

Authors: Jean-Jacques Herings, Christian Seel (UM, MPE), Arkadi Predtetchinski (UM, MPE)

Date and time: November 18th, 13:15-14:15

Title: Random networks

Abstract: Akin to the literature on random games, we analyze pairwise stability (Jackson and Wolinsky, 1996) for two models of socioeconomic networks in which the utilities of each individual are drawn at random. In the case of network-dependent utilities, the utility is drawn at random for each possible network, whereas in the case of neighbor-dependent utilities, the utility is required to be the same whenever the individual has the same set of links.

For each model, as the network gets large, the probability that at least one pairwise stable network exists approaches one, but the expected fraction of pairwise stable networks approaches zero. We also obtain lower and upper bounds on the expected number of pairwise stable networks as the network gets large. For the case of network-dependent utilities, we provide additional results on the distribution of pairwise stable networks.

Authors: Jaap Bos, Robin Cowan, and Stefan Weiland (UM, FINANCE)

Date and time: November 25th, 13:15-14:15

Title: Spatial Competition Under Production Uncertainty: Evolutionary Dynamics of Strategic Search

Abstract: In real-world contexts, firms may face high levels of uncertainty about (1) their production functions including how to produce distinct product variants and/or how to produce most productively, (2) the strategic behavior of their competitors, and/or (3) consumers' preferences. In this paper, we study how firms in an oligopolistic setting (should) act in the face of production uncertainty to maximize profits. In particular, we ask: when there is substantial uncertainty about the production function, is it more profitable to prioritize searching over production processes that drive product variants, or over those that drive productivity and cost levels? As a motivating application, we combine an NK rugged landscape model (Kauffman 1993) with a spatial competition model á la Mussa and Rosen (1978) in a dynamic setting, and we use the model to compare the performance outcome of various evolutionary strategies of search. As it turns out, the optimal strategy depends on the characteristics of the production environment. When switching between product variants is cheap and productive processes are easy to find, it is better to first search along the productivity dimension - an advantage that grows further when productive processes are harder to discover. Conversely, when switching variants is costly but productive processes are easy to identify, prioritizing the quality dimension is more profitable. Perhaps most interestingly, when both switching and discovery are difficult, the superior strategy depends on the time horizon: focusing on productivity dominates in the short run, while quality-first search prevails in the long run. Our findings can be used for predictive purposes in matters concerning industry evolution, and they can inform strategic decision making in settings where the standard assumptions of spatial competition models do not hold. Further, our model can help to explain when and why empirical tests of competition yield inconclusive or counterintuitive results.