Abstracts

Sören Christensen  (Invited Speaker)

Title: Existence of Markovian randomized equilibria exemplified by war-of-attrition type stopping games 

Abstract: One of the fundamental results in optimal stopping theory states that for Markovian problems, optimal stopping times exist in the class of (Markovian) first-entry times. Yet, when we delve into the realm of stopping games, clarity diminishes.  There are relatively general existence results for equilibria in randomized stopping times. While broad existence theorems for equilibria in randomized stopping times are known, they fall short in Markovian contexts. The vastness of the class hinders the pinpointing of explicit equilibria, and the inherent path-dependency of general randomized stopping times compromises subgame perfection. Therefore, the consideration of Markovian stopping times seems much more natural.

In this talk, we consider general nonzero-sum Dynkin games of the war-of-attrition type for linear diffusions and develop the machinery to prove the existence of Markovian equilibria. We expect that the developed approach can be similarly applied to many other stopping games. We illustrate the general existence result with examples.

The talk is based on work in progress with Erik Ekström (Uppsala) and Boy Schultz (Kiel).

Kaustav Das (Invited Speaker) 

Title: Strategic Disclosure in Research Races

(with Kalyan Chatterjee (Penn State) and Miaomiao Dong (Penn State)) 

Abstract: We study a research race between two players. Each player works on an identical two-step project. To work on step 2, a player must complete step 1. Each step is completed with a discovery. Once a discovery is made, a player decides whether and when to disclose it. Disclosure of an intermediate discovery gives an immediate reward to the player, but it also allows the opponent to copy it and compete for a final reward from the final discovery. We show that a higher final reward has a U-shaped effect on when the intermediate finding is disclosed and when the final finding is discovered: A higher final reward speeds up both if and only if the final reward is low.

 Jean-Paul Décamps (Invited Speaker)

Title: The war of attrition under uncertainty: theory and robust testable implications

(with Fabien Gensbittel and Thomas Mariotti) 

Abstract: We study the war of attrition with symmetric information when players' payoffs depend on a homogeneous linear diffusion. We first show that a player's mixed Markov strategy can be represented by an intensity measure over the state space along with a subset of the state space over which the player concedes with probability 1. We then show that, if players are asymmetric, then, in all mixed-strategy Markov-perfect equilibria, these intensity measures must be discrete, and characterize any such equilibrium through a variational system for the players' value functions. We illustrate these findings by revisiting the standard model of exit in a duopoly under uncertainty and construct a mixed-strategy Markov-perfect equilibrium in which attrition takes place on path despite firms having different liquidation values. We show that firms' stock prices comove negatively over the attrition zone and exhibit patterns documented by technical analysis. 

Samuel Häfner (Invited Speaker)

Title: Shakeouts and Staggered Exits from an R&D Race with Moral Hazard 

Abstract: This article analyzes the interaction between competition and agency frictions in R&D, which is often experienced by young and externally funded firms. Symmetric cash-constrained firms compete to access a profitable market in a continuous-time R&D race with stochastic breakthroughs. Each firm is funded by a different investor. R&D efforts are subject to moral hazard, and the investors make mutually optimal incentive-compatible contract offers. The profitable market accommodates more than one firm. If entering first is very valuable (relative to entering second), investors set asymmetric funding deadlines, resulting in staggered exits from the race when no breakthrough occurs for a sufficiently long time. If entering first is not that valuable, some deadlines are symmetric, leading to shakeouts. The comparative statics follow from a contractual externality and the cost of moral hazard. The model speaks to asymmetries in VC contracts and the phenomenon of industry shakeouts.

Christian Kellner  (Invited Speaker)

Title:  Timing decisions under model uncertainty

(with Sarah Auster, University of Bonn) 

Abstract:  We study the effect of ambiguity on timing decisions. An agent faces a stopping problem with an uncertain stopping payoff and a stochastic time limit. The agent is unsure about the correct model quantifying the uncertainty and seeks to maximize her payoff guarantee over a set of plausible models. As time passes and the agent updates, the worst-case model used to evaluate a given strategy can change, creating a problem of dynamic inconsistency. We characterize the stopping behavior in this environment, describing the conditions under which

the agent stops prematurely or waits excessively with respect to the initially optimal plan. We further show that, while the agent’s myopic incentives are fragile to small changes in the set of considered models, the best consistent plan from which no future self has incentives to deviate is robust. 

Nicolas Klein (Invited Speaker)

Title:  Racing with a Rearview Mirror: Innovation Lag and Investment Dynamics

(with Chantal Marlats and Lucie Ménager) 

Abstract:  We analyze a dynamic investment model in which short-lived agents sequentially decide how much to invest in a project of uncertain feasibility. The outcome of the project (success/failure) is observed after a fixed lag. We characterize the unique equilibrium and show that, in contrast with the case without lag, the unique equilibrium dynamics is not in thresholds. If the initial belief is relatively high, investment decreases monotonically as agents become more pessimistic about the feasibility of the innovation. Otherwise, investment is not monotone in the public belief: players alternate periods of no investment and periods of positive, decreasing investment. The reason is that the outcome lag creates competition between a player and her immediate predecessors. A player whose predecessors did not invest may find investment attractive even if she is more pessimistic about the technology than her predecessors. We compare the total investment obtained in this equilibrium with that obtained with an alternative reward scheme where a mediator collects all the information about the players' experiences until some deadline, and splits the payoff between all the players who obtained a success before the deadline. 

Kristofer Lindensjö (Invited Speaker)

Title:  Markovian randomized equilibria for stopping games 

Abstract:  One of the most well-known results in classical game theory is that randomized strategies facilitate Nash equilibrium existence. This talk is about recent research regarding the role of randomized strategies for stopping games based on Markov processes. In particular, we are interested in defining Markovian randomized stopping strategies that allow for equilibrium existence as well as characterization similar to how non-randomized solutions to Markovian stopping problems can be characterized using e.g., variational inequalities (continuous time) and Wald-Bellman equations (discrete time).

Based on joint works with Andi Bodnariu (Stockholm), Berenice Neumann (Trier), and Sören Christensen (Kiel). 

Pavel Kocourek (Invited Speaker)

Title:  Secrecy vs. Patenting in Innovation Races

Abstract:  This study examines the tradeoff between patenting and secrecy in innovation races, considering a model where two firms simultaneously compete in developing two products that can be substitutes or complements. Patenting ensures a claim on the product but discloses information to rivals, while secrecy may delay immediate profits for future technology leadership. We find that firms have more incentives to patent if they are impatient and if there are no significant technological spillovers. In a scenario where firms are patient and moderate technological spillovers exist, they exhibit a greater tendency to patent products acting as perfect complements rather than perfect substitutes. These findings are in line with the empirical evidence by Cohen, Nelson, and Walsh (2000), who argue that firms are more likely to keep the innovation secret in "simple" industries, where goods have many potential substitutes, as opposed to "complex" industries, where a new product involves many complementary components. (Joint work with Eugen Kovac)

Jan Palczewski (Invited Speaker)

Title: Stochastic game of exit from a duopoly with private information 

Abstract:  We examine a game of exit from a market with stochastic profits in which players do not know their competitor's exit payoffs (private information). The market uncertainty, observed by both players, is represented by a general one-dimensional diffusion. Each player faces a double decision: when to leave the duopoly market and, should they become a single player, when to abandon the monopoly market. This results in a non-zero sum stopping game with asymmetric information and the payoff involving the value function of an optimal stopping problem of monopoly exit. Under the condition that certain optimal stopping problems have solutions of a threshold type, we construct a symmetric equilibrium in pure strategies. Due to the generality of the setup, our arguments are probabilistic in nature.