scholarly journals Cooperative Stochastic Games with Mean-Variance Preferences

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 230
Author(s):  
Elena Parilina ◽  
Stepan Akimochkin
Keyword(s):  
Standard Deviation ◽  
Stochastic Games ◽  
Stochastic Game ◽  
Stochastic Variable ◽  
Expected Payoff ◽  
The Core ◽  
Risk Sensitive ◽  
Payoff Functions ◽  
Cooperative Solutions ◽  
Mean Variance

In stochastic games, the player’s payoff is a stochastic variable. In most papers, expected payoff is considered as a payoff, which means the risk neutrality of the players. However, there may exist risk-sensitive players who would take into account “risk” measuring their stochastic payoffs. In the paper, we propose a model of stochastic games with mean-variance payoff functions, which is the sum of expectation and standard deviation multiplied by a coefficient characterizing a player’s attention to risk. We construct a cooperative version of a stochastic game with mean-variance preferences by defining characteristic function using a maxmin approach. The imputation in a cooperative stochastic game with mean-variance preferences is supposed to be a random vector. We construct the core of a cooperative stochastic game with mean-variance preferences. The paper extends existing models of discrete-time stochastic games and approaches to find cooperative solutions in these games.

scholarly journals On a Simplified Method of Defining Characteristic Function in Stochastic Games

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1135
Author(s):  
Elena Parilina ◽  
Leon Petrosyan
Keyword(s):  
Characteristic Function ◽  
Stochastic Games ◽  
Stochastic Game ◽  
New Method ◽  
Characteristic Functions ◽  
Zero Sum Games ◽  
Subgame Consistency ◽  
The Core ◽  
Simplified Method ◽  
Zero Sum

In the paper, we propose a new method of constructing cooperative stochastic game in the form of characteristic function when initially non-cooperative stochastic game is given. The set of states and the set of actions for any player is finite. The construction of the characteristic function is based on a calculation of the maximin values of zero-sum games between a coalition and its anti-coalition for each state of the game. The proposed characteristic function has some advantages in comparison with previously defined characteristic functions for stochastic games. In particular, the advantages include computation simplicity and strong subgame consistency of the core calculated with the values of the new characteristic function.

scholarly journals Risk and the Market’s Reaction to M&A Announcements

2021 ◽  
Vol 14 (7) ◽  
pp. 334
Author(s):  
Ye Cai ◽  
Hersh Shefrin
Keyword(s):  
Standard Deviation ◽  
Large Firms ◽  
Total Risk ◽  
Basis Point ◽  
Acquiring Firms ◽  
Risk Sensitive ◽  
Point Increase

We estimate how an acquiring firm’s risk changes depending on whether the market initially judges the acquisition to be neutral, strongly negative, or strongly positive for the shareholders of the acquiring firm. We found that for an average neutral acquisition, the annualized standard deviation of an acquiring firm’s total return declines by 5%. In contrast, acquisitions judged negatively by the market result in a 5% increase in total risk, while acquisitions judged positively by the market feature a 30-basis-point increase in total risk. We found the median acquisition to be value creating, not value destructive. Value destruction tends to be concentrated among large firms and to be associated with extreme negative outliers. Acquiring firms with longholder CEOs are more prone to undertake acquisitions and more prone to take on risk, but are less prone to engage in value-destructive acquisitions than acquiring firms with non-longholder CEOs. In this respect, acquiring firms with non-longholder CEOs are more apt to undertake risky bad acquisitions, especially when their prior returns lie above the industry average. In addition, acquiring firms with non-longholder CEOs are less prone to take on good acquisitions that are high in risk. As a general matter, firms with longholder CEOs are less risk sensitive to changes in prior returns than firms with non-longholder CEOs.

scholarly journals Zero-sum risk-sensitive stochastic games for continuous time Markov chains

2016 ◽  
Vol 34 (5) ◽  
pp. 835-851 ◽  
Author(s):  
Mrinal K. Ghosh ◽  
K. Suresh Kumar ◽  
Chandan Pal
Keyword(s):  
Markov Chains ◽  
Continuous Time ◽  
Stochastic Games ◽  
Continuous Time Markov Chains ◽  
Risk Sensitive ◽  
Zero Sum

PcP from the nuclear explosion BILBY September 13, 1963

1965 ◽  
Vol 55 (2) ◽  
pp. 441-461
Author(s):  
Goetz G. R. Buchbinder
Keyword(s):  
Standard Deviation ◽  
Seismic Velocity ◽  
Nuclear Explosion ◽  
Amplitude Ratios ◽  
The Core ◽  
Core Boundary

Abstract The core-reflected phase, PcP, from the BILBY event, received at stations between 19° and 88°, arrived early by an average of 1.80 seconds with respect to the Jeffries-Bullen tables. The standard deviation of these data was 0.77 seconds. The corresponding P phases were early by 1.34 seconds. The tables therefore need adjustments. If the core boundary is to be moved by more than 10 km from the value of 2898 km then the mantle seismic velocity immediately above the core must be changed also. The PcP/P amplitude ratios are nearly always much larger than those predicted theoretically.

scholarly journals Existence of Nash equilibria in stochastic games of resource extraction with risk-sensitive players

Top ◽  
2019 ◽  
Vol 27 (3) ◽  
pp. 502-518
Author(s):  
Hubert Asienkiewicz ◽  
Łukasz Balbus
Keyword(s):  
Nash Equilibria ◽  
Stochastic Games ◽  
Resource Extraction ◽  
Risk Sensitive

scholarly journals Sample size for estimating average trunk diameter and plant height in eucalyptus hybrids

2016 ◽  
Vol 46 (7) ◽  
pp. 1192-1199 ◽  
Author(s):  
Alberto Cargnelutti Filho ◽  
Rafael Beltrame ◽  
Dilson Antônio Bisognin ◽  
Marília Lazarotto ◽  
Clovis Roberto Haselein ◽  
...  
Keyword(s):  
Standard Deviation ◽  
Confidence Interval ◽  
Sample Size ◽  
Plant Height ◽  
Tree Height ◽  
Trunk Diameter ◽  
Diameter At Breast Height ◽  
Breast Height ◽  
Variance Homogeneity ◽  
Mean Variance

ABSTRACT: In eucalyptus crops, it is important to determine the number of plants that need to be evaluated for a reliable inference of growth. The aim of this study was to determine the sample size needed to estimate average trunk diameter at breast height and plant height of inter-specific eucalyptus hybrids. In 6,694 plants of twelve inter-specific hybrids it was evaluated trunk diameter at breast height at three (DBH3) and seven years (DBH7) and tree height at seven years (H7) of age. The statistics: minimum, maximum, mean, variance, standard deviation, standard error, and coefficient of variation were calculated. The hypothesis of variance homogeneity was tested. The sample size was determined by re sampling with replacement of 10,000 re samples. There was an increase in the sample size from DBH3 to H7 and DBH7. A sample size of 16, 59 and 31 plants is adequate to estimate DBH3, DBH7 and H7 means, respectively, of inter-specific hybrids of eucalyptus, with amplitude of confidence interval of 95% equal to 20% of the estimated mean.

scholarly journals A formula for the value of a stochastic game

2019 ◽  
Vol 116 (52) ◽  
pp. 26435-26443 ◽  
Author(s):  
Luc Attia ◽  
Miquel Oliu-Barton
Keyword(s):  
Dynamic Model ◽  
Discount Rate ◽  
Stochastic Games ◽  
Stochastic Game ◽  
Solution Concept ◽  
Robust Solution ◽  
General Dynamic

In 1953, Lloyd Shapley defined the model of stochastic games, which were the first general dynamic model of a game to be defined, and proved that competitive stochastic games have a discounted value. In 1982, Jean-François Mertens and Abraham Neyman proved that competitive stochastic games admit a robust solution concept, the value, which is equal to the limit of the discounted values as the discount rate goes to 0. Both contributions were published in PNAS. In the present paper, we provide a tractable formula for the value of competitive stochastic games.

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