A duration estimator for a continuous time war of attrition game

2020 ◽  
pp. 1-19
Author(s):  
Frederick J. Boehmke ◽  
Douglas Dion ◽  
Charles R. Shipan
Keyword(s):  
Economic Theory ◽  
Continuous Time ◽  
Hazard Rate ◽  
Time Horizon ◽  
Mixed Strategy ◽  
Fixed Time ◽  
Likelihood Estimator ◽  
International Crises ◽  
War Of Attrition ◽  
Weak Competitor

Abstract We developed a maximum likelihood estimator corresponding to the predicted hazard rate that emerges from a continuous time game of incomplete information with a fixed time horizon (i.e., Kreps and Wilson, 1982, Journal of Economic Theory27, 253–279). Such games have been widely applied in economics and political science and involve two players engaged in a war of attrition contest over some prize that they both value. Each player can be either a strong or weak competitor. In the equilibrium of interest, strong players do not quit whereas weak players play a mixed strategy characterized by a hazard rate that increases up to an endogenous point in time, after which only strong players remain. The observed length of the contest can therefore be modeled as a mixture between two unobserved underlying durations: one that increases until it abruptly ends at an endogenous point in time and a second involving two strong players that continues indefinitely. We illustrate this estimator by studying the durations of Senate filibusters and international crises.

scholarly journals A Numerical Approach for Evaluating the Time-Dependent Distribution of a Quasi Birth-Death Process

2021 ◽  
Author(s):  
Michel Mandjes ◽  
Birgit Sollie
Keyword(s):  
Continuous Time ◽  
Real Life ◽  
Numerical Approach ◽  
Time Dependent ◽  
Death Process ◽  
Continuous Time Markov Chain ◽  
Likelihood Estimator ◽  
Real Life Data ◽  
The Matrix ◽  
Birth Death

AbstractThis paper considers a continuous-time quasi birth-death (qbd) process, which informally can be seen as a birth-death process of which the parameters are modulated by an external continuous-time Markov chain. The aim is to numerically approximate the time-dependent distribution of the resulting bivariate Markov process in an accurate and efficient way. An approach based on the Erlangization principle is proposed and formally justified. Its performance is investigated and compared with two existing approaches: one based on numerical evaluation of the matrix exponential underlying the qbd process, and one based on the uniformization technique. It is shown that in many settings the approach based on Erlangization is faster than the other approaches, while still being highly accurate. In the last part of the paper, we demonstrate the use of the developed technique in the context of the evaluation of the likelihood pertaining to a time series, which can then be optimized over its parameters to obtain the maximum likelihood estimator. More specifically, through a series of examples with simulated and real-life data, we show how it can be deployed in model selection problems that involve the choice between a qbd and its non-modulated counterpart.

A Model for Farm Management with Continuous Time Horizon

2001 ◽  
Author(s):  
B. Recio ◽  
F. Rubio ◽  
M.Teresa Ortuño ◽  
Begoña Vitoriano
Keyword(s):  
Continuous Time ◽  
Time Horizon ◽  
Farm Management

scholarly journals Building Reputation in a War of Attrition Game: Hawkish or Dovish Stance?

2016 ◽  
Vol 16 (2) ◽  
Author(s):  
Selçuk Özyurt
Keyword(s):  
Continuous Time ◽  
Cost Ratio ◽  
War Of Attrition ◽  
Benefit Cost Ratio ◽  
Benefit Cost

AbstractThis paper examines a two-player war of attrition game in continuous-time, where (1) fighting (i. e., escalating the conflict) is costless for a player unless he quits, (2) at any point in time, each player can attack to his opponent and finalize the game with a costly war, (3) there is two-sided uncertainty regarding the players’ resolve, and (4) each player can choose his tone/stance (either hawkish or dovish) at the beginning of the game, which affects his quitting cost. The results imply that choosing hawkish (dovish) regime is optimal if and only if the benefit-cost ratio of the dispute is sufficiently high (low). If hawkish tone is going to give a player upper hand in a dispute, then choosing a more aggressive tone does not increase his payoff. However, choosing a more dovish tone increases a player’s payoff whenever dovish regime is optimal.

Hazard rate and reversed hazard rate monotonicities in continuous-time Markov chains

1998 ◽  
Vol 35 (3) ◽  
pp. 545-556 ◽  
Author(s):  
Masaaki Kijima
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Continuous Time ◽  
Hazard Rate ◽  
First Passage Time ◽  
Death Process ◽  
Continuous Time Markov Chain ◽  
Reversed Hazard Rate ◽  
The Right ◽  
Birth Death

A continuous-time Markov chain on the non-negative integers is called skip-free to the right (left) if only unit increments to the right (left) are permitted. If a Markov chain is skip-free both to the right and to the left, it is called a birth–death process. Karlin and McGregor (1959) showed that if a continuous-time Markov chain is monotone in the sense of likelihood ratio ordering then it must be an (extended) birth–death process. This paper proves that if an irreducible Markov chain in continuous time is monotone in the sense of hazard rate (reversed hazard rate) ordering then it must be skip-free to the right (left). A birth–death process is then characterized as a continuous-time Markov chain that is monotone in the sense of both hazard rate and reversed hazard rate orderings. As an application, the first-passage-time distributions of such Markov chains are also studied.

Taking Sides in Wars of Attrition

2017 ◽  
Vol 111 (2) ◽  
pp. 219-236 ◽  
Author(s):  
ROBERT POWELL
Keyword(s):  
Asymmetric Information ◽  
Continuous Time ◽  
Formal Analysis ◽  
Third Parties ◽  
The Other ◽  
Third Party ◽  
War Of Attrition ◽  
The Third ◽  
Boomerang Effect ◽  
Formal Framework

Third parties often have a stake in the outcome of a conflict and can affect that outcome by taking sides. This article studies the factors that affect a third party's decision to take sides in a civil or interstate war by adding a third actor to a standard continuous-time war of attrition with two-sided asymmetric information. The third actor has preferences over which of the other two actors wins and for being on the winning side conditional on having taken sides. The third party also gets a flow payoff during the fighting which can be positive when fighting is profitable or negative when fighting is costly. The article makes four main contributions: First, it provides a formal framework for analyzing the effects of endogenous intervention on the duration and outcome of the conflict. Second, it identifies a “boomerang” effect that tends to make alignment decisions unpredictable and coalitions dynamically unstable. Third, it yields several clear comparative-static results. Finally, the formal analysis has implications for empirical efforts to estimate the effects of intervention, showing that there may be significant selection and identification issues.

SKOROKHOD EMBEDDINGS IN BOUNDED TIME

2011 ◽  
Vol 11 (02n03) ◽  
pp. 215-226 ◽  
Author(s):  
STEFAN ANKIRCHNER ◽  
PHILIPP STRACK
Keyword(s):  
Brownian Motion ◽  
Time Horizon ◽  
Sufficient Conditions ◽  
Stopping Time ◽  
Fixed Time ◽  
Stopping Times ◽  
Embedding Problem ◽  
Brownian Motion With Drift ◽  
Necessary And Sufficient ◽  
Skorokhod Embedding Problem

This article deals with the Skorokhod embedding problem in bounded time for the Brownian motion with drift Xt = κt + Wt: Given a probability measure μ we aim at finding a stopping time τ such that the law of Xτ is μ, and τ is almost surely smaller than some given fixed time horizon T > 0. We provide necessary and sufficient conditions on the distribution μ for the existence of such bounded stopping times.

scholarly journals IDENTIFYING THE BROWNIAN COVARIATION FROM THE CO-JUMPS GIVEN DISCRETE OBSERVATIONS

2012 ◽  
Vol 28 (2) ◽  
pp. 249-273 ◽  
Author(s):  
Cecilia Mancini ◽  
Fabio Gobbi
Keyword(s):  
Risk Factors ◽  
Monte Carlo ◽  
Time Horizon ◽  
Limit Theorems ◽  
Estimation Error ◽  
Asymptotic Variance ◽  
Fixed Time ◽  
Finite Sample ◽  
Discrete Observations ◽  
Measures Of Dependence

When the covariance between the risk factors of asset prices is due to both Brownian and jump components, the realized covariation (RC) approaches the sum of the integrated covariation (IC) with the sum of the co-jumps, as the observation frequency increases to infinity, in a finite and fixed time horizon. In this paper the two components are consistently separately estimated within a semimartingale framework with possibly infinite activity jumps. The threshold (or truncated) estimator $I\hat C_n $ is used, which substantially excludes from RC all terms containing jumps. Unlike in Jacod (2007, Universite de Paris-6) and Jacod (2008, Stochastic Processes and Their Applications 118, 517–559), no assumptions on the volatilities’ dynamics are required. In the presence of only finite activity jumps: 1) central limit theorems (CLTs) for $I\hat C_n $ and for further measures of dependence between the two Brownian parts are obtained; the estimation error asymptotic variance is shown to be smaller than for the alternative estimators of IC in the literature; 2) by also selecting the observations as in Hayashi and Yoshida (2005, Bernoulli 11, 359–379), robustness to nonsynchronous data is obtained. The proposed estimators are shown to have good finite sample performances in Monte Carlo simulations even with an observation frequency low enough to make microstructure noises’ impact on data negligible.

scholarly journals On a Model for the Storage of Files on a Hardware: Statistics at a Fixed Time and Asymptotic Regimes

2009 ◽  
Vol 2009 ◽  
pp. 1-24
Author(s):  
Vincent Bansaye
Keyword(s):  
Point Process ◽  
Real Line ◽  
Continuous Time ◽  
Poisson Point Process ◽  
Fixed Time ◽  
The Real ◽  
Parking Problem ◽  
The Right

We consider a version in continuous time of the parking problem of Knuth. Files arrive following a Poisson point process and are stored on a hardware identified with the real line, in the closest free portions at the right of the arrival location. We specify the distribution of the space of unoccupied locations at a fixed time and give asymptotic regimes when the hardware is becoming full.

The War of Attrition in Continuous Time with Complete Information

1988 ◽  
Vol 29 (4) ◽  
pp. 663 ◽  
Author(s):  
Ken Hendricks ◽  
Andrew Weiss ◽  
Charles Wilson
Keyword(s):  
Continuous Time ◽  
Complete Information ◽  
War Of Attrition
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