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

The relative efficiency of direct and maximum likelihood estimates of mean waiting time in the simple queue, M/M/1

1972 ◽  
Vol 9 (2) ◽  
pp. 396-403 ◽  
Author(s):  
John H. Jenkins
Keyword(s):  
Maximum Likelihood ◽  
Waiting Time ◽  
Continuous Time ◽  
Relative Efficiency ◽  
Asymptotic Variance ◽  
Complete Information ◽  
Maximum Likelihood Estimates ◽  
Time Study ◽  
Direct Estimate ◽  
Mean Waiting Time

A problem of estimating waiting time in the statistical analysis of queues is investigated. The continuous time study of the M/M/1 queue made by Bailey is adapted to obtain the asymptotic variance of a direct estimate of waiting time as obtained under conditions of incomplete information. This is then compared with the asymptotic variance of the maximum likelihood estimate as obtained under conditions of complete information and based on the results of Clarke.

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.

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.

The spectral gap and perturbation bounds for reversible continuous-time Markov chains

2004 ◽  
Vol 41 (4) ◽  
pp. 1219-1222 ◽  
Author(s):  
A. Yu. Mitrophanov
Keyword(s):  
Markov Chains ◽  
Continuous Time ◽  
Spectral Gap ◽  
Complete Information ◽  
Stationary States ◽  
Perturbation Bounds ◽  
Continuous Time Markov Chains ◽  
Distribution Vector

We show that, for reversible continuous-time Markov chains, the closeness of the nonzero eigenvalues of the generator to zero provides complete information about the sensitivity of the distribution vector to perturbations of the generator. Our results hold for both the transient and the stationary states.

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.

The relative efficiency of direct and maximum likelihood estimates of mean waiting time in the simple queue, M/M/1

1972 ◽  
Vol 9 (02) ◽  
pp. 396-403 ◽  
Author(s):  
John H. Jenkins
Keyword(s):  
Maximum Likelihood ◽  
Waiting Time ◽  
Continuous Time ◽  
Relative Efficiency ◽  
Asymptotic Variance ◽  
Complete Information ◽  
Maximum Likelihood Estimates ◽  
Time Study ◽  
Direct Estimate ◽  
Mean Waiting Time

A problem of estimating waiting time in the statistical analysis of queues is investigated. The continuous time study of the M/M/1 queue made by Bailey is adapted to obtain the asymptotic variance of a direct estimate of waiting time as obtained under conditions of incomplete information. This is then compared with the asymptotic variance of the maximum likelihood estimate as obtained under conditions of complete information and based on the results of Clarke.

scholarly journals The absence of attrition in a war of attrition under complete information

2022 ◽  
Vol 131 ◽  
pp. 171-185
Author(s):  
George Georgiadis ◽  
Youngsoo Kim ◽  
H. Dharma Kwon
Keyword(s):  
Complete Information ◽  
War Of Attrition

scholarly journals Private Monitoring and Communication in the Repeated Prisoner’s Dilemma

Games ◽  
2021 ◽  
Vol 12 (4) ◽  
pp. 80
Author(s):  
Yu Awaya
Keyword(s):  
Poisson Process ◽  
Continuous Time ◽  
Prisoner's Dilemma ◽  
Prisoner’S Dilemma ◽  
Complete Information ◽  
Private Monitoring ◽  
Repeated Prisoner’S Dilemma ◽  
Informative Signals ◽  
Repeated Prisoner's Dilemma

This paper provides a model of the repeated prisoner’s dilemma in which cheap-talk communication is necessary in order to achieve cooperative outcomes in a long-term relationship. The model is one of complete information. I consider a continuous time repeated prisoner’s dilemma game where informative signals about another player’s past actions arrive following a Poisson process; actions have to be held fixed for a certain time. I assume that signals are privately observed by players. I consider an environment where signals are noisy, and the correlation of signals is higher if both players cooperate. We show that, provided that players can change their actions arbitrary frequently, there exists an equilibrium with communication that strictly Pareto-dominates all equilibria without communication.

scholarly journals Continuous-Time Insider Trading with Risk-Neutral Insider under Imperfect Observation

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Yonghui Zhou ◽  
Guanglong Zhuang ◽  
Kai Xiao
Keyword(s):  
Insider Trading ◽  
Continuous Time ◽  
Imperfect Information ◽  
Complete Information ◽  
Market Depth ◽  
Asset Value ◽  
Risk Neutral ◽  
Maximal Profit ◽  
Expectation Theory ◽  
Open Question

A model of insider trading in continuous time in which a risk-neutral insider possesses long-lived imperfect information on a risk asset is studied. By conditional expectation theory and filtering theory, we turn it into a model with insider knowing complete information about the asset with a revised risky value and deduce its linear Bayesian equilibrium consisting of optimal insider trading strategy and semistrong pricing rule. It shows that, in the equilibrium, as the degree of insider observing the signal of the risky asset value is more and more accurate, market depth, trading intensity, and residual information are all decreasing and the total expectation profit of the insider is increasing and that the information about the asset value incorporated into the equilibrium price, which has nothing to do with the volatility of noise trades, is increasing as time goes by, but not all information of asset value is incorporated into the price in the final disclosed time due to the incompleteness of insider’s observation, though the market depth is still a time-independent constant. Some simulations are illustrated to show these features. However, it is an open question of how to make maximal profit if the insider is risk-averse.

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