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DTSTART:20221030T030000
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UID:calendar.129122.field_date.0@www.tse-fr.eu
DTSTAMP:20231202T024338Z
CREATED:20220720T081001Z
DESCRIPTION:Fabien Gensbittel ( Toulouse School of Economics)\, “Mixed Stra
tegy Equilibria in the War of Attrition under Uncertainty”\, MAD-Stat. Sem
inar\, Toulouse: TSE\, September 15\, 2022\, 11:00–12:15\, room Auditorium
3.\n\nWe study a generic family of two-player continuous-time nonzero-sum
stopping games modeling a war of attrition under complete information and
stochastic payoffs depending on a homogeneous linear diffusion. We first
show that any Markovian mixed strategy can be represented by a pair $(\mu\
,S)$ where $\mu$ is a measure on the state space representing the stopping
intensity and $S$ is a subset of the state space in which the player stop
s with probability 1. We prove that if the players are asymmetric\, then i
n all the Markov Perfect equilibria in mixed strategies\, the measures $\m
u$ have to be essentially discrete\, and we characterize any such equilibr
ium through a variational system satisfied by the equilibrium payoffs of t
he players. This contrasts with the existing literature in which only pure
equilibria or mixed equilibria using absolutely continuous stopping inten
sities in symmetric models were studied. We illustrate this result by revi
siting the model of exit in a duopoly under uncertainty\, and exhibit an e
quilibrium in mixed strategies with asymmetric players in which the player
s enter a war of attrition and delay their exit decision compare to the pu
re equilibria\, as it happens in the mixed equilibria in classical models
with deterministic payoffs. \n(Work with Jean-Paul Décamps and Thomas Mari
otti)
DTSTART;TZID=Europe/Paris:20220915T120000
DTEND;TZID=Europe/Paris:20220915T131500
LAST-MODIFIED:20220907T001001Z
LOCATION:Toulouse: TSE\, September 15\, 2022\, 11:00–12:15\, room Auditoriu
m 3
SUMMARY:MAD-Stat. Seminar
URL;TYPE=URI:https://www.tse-fr.eu/seminars/2022-mixed-strategy-equilibria-
war-attrition-under-uncertainty
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