---
_id: '1767'
abstract:
- lang: eng
text: 'Conditional Value-at-Risk, denoted as CVaRα, is becoming the prevailing measure
of risk over two paramount economic domains: the insurance domain and the financial
domain; α∈(0,1) is the confidence level. In this work, we study the strategic
equilibria for an economic system modeled as a game, where risk-averse players
seek to minimize the Conditional Value-at-Risk of their costs. Concretely, in
a CVaRα -equilibrium, the mixed strategy of each player is a best-response. We
establish two significant properties of CVaRα at equilibrium: (1) The Optimal-Value
property: For any best-response of a player, each mixed strategy in the support
gives the same cost to the player. This follows directly from the concavity of
CVaRα in the involved probabilities, which we establish. (2) The Crawford property:
For every α, there is a 2-player game with no CVaRα-equilibrium. The property
is established using the Optimal-Value property and a new functional property
of CVaRα, called Weak-Equilibrium-for- VaRα, we establish. On top of these properties,
we show, as one of our two main results, that deciding the existence of a CVaRα-equilibrium
is strongly NP-hard even for 2-player games. As our other main result, we show
the strong NP-hardness of deciding the existence of a V-equilibrium, over 2-player
games, for any valuation V with the Optimal-Value and the Crawford properties.
This result has a rich potential since we prove that the very significant and
broad class of strictly quasiconcave valuations has the Optimal-Value property.'
accept: '1'
author:
- first_name: Marios
full_name: Mavronicolas, Marios
last_name: Mavronicolas
- first_name: Burkhard
full_name: Monien, Burkhard
last_name: Monien
citation:
ama: 'Mavronicolas M, Monien B. Conditional Value-at-Risk: Structure and Complexity
of Equilibria. In: *Proceedings of the 10th International Symposium on Algorithmic
Game Theory (SAGT 2017)*. Vol 10504. LNCS. ; 2017:131--143. doi:10.1007/978-3-319-66700-3_11'
apa: 'Mavronicolas, M., & Monien, B. (2017). Conditional Value-at-Risk: Structure
and Complexity of Equilibria. In *Proceedings of the 10th International Symposium
on Algorithmic Game Theory (SAGT 2017)* (Vol. 10504, pp. 131--143). L’Aquila,
Italy. https://doi.org/10.1007/978-3-319-66700-3_11'
bibtex: '@inproceedings{Mavronicolas_Monien_2017, series={LNCS}, title={Conditional
Value-at-Risk: Structure and Complexity of Equilibria}, volume={10504}, DOI={10.1007/978-3-319-66700-3_11},
booktitle={Proceedings of the 10th International Symposium on Algorithmic Game
Theory (SAGT 2017)}, author={Mavronicolas, Marios and Monien, Burkhard}, year={2017},
pages={131--143}, collection={LNCS} }'
chicago: 'Mavronicolas, Marios, and Burkhard Monien. “Conditional Value-at-Risk:
Structure and Complexity of Equilibria.” In *Proceedings of the 10th International
Symposium on Algorithmic Game Theory (SAGT 2017)*, 10504:131--143. LNCS, 2017.
https://doi.org/10.1007/978-3-319-66700-3_11.'
ieee: 'M. Mavronicolas and B. Monien, “Conditional Value-at-Risk: Structure and
Complexity of Equilibria,” in *Proceedings of the 10th International Symposium
on Algorithmic Game Theory (SAGT 2017)*, L’Aquila, Italy, 2017, vol. 10504,
pp. 131--143.'
mla: 'Mavronicolas, Marios, and Burkhard Monien. “Conditional Value-at-Risk: Structure
and Complexity of Equilibria.” *Proceedings of the 10th International Symposium
on Algorithmic Game Theory (SAGT 2017)*, vol. 10504, 2017, pp. 131--143, doi:10.1007/978-3-319-66700-3_11.'
short: 'M. Mavronicolas, B. Monien, in: Proceedings of the 10th International Symposium
on Algorithmic Game Theory (SAGT 2017), 2017, pp. 131--143.'
conference:
end_date: 2017-09-14
location: L'Aquila, Italy
name: 10th International Symposium on Algorithmic Game Theory (SAGT 2017)
start_date: 2017-09-12
date_created: 2018-03-23T13:58:02Z
date_updated: 2019-01-03T13:12:13Z
ddc:
- '000'
department:
- _id: '7'
doi: 10.1007/978-3-319-66700-3_11
file:
- access_level: closed
content_type: application/pdf
creator: ups
date_created: 2018-11-02T14:53:56Z
date_updated: 2018-11-02T14:53:56Z
file_id: '5287'
file_name: ConditionalValue-at-RiskStruct.pdf
file_size: 352365
open_access: 1
relation: main_file
success: 1
file_date_updated: 2018-11-02T14:53:56Z
intvolume: ' 10504'
language:
- iso: eng
page: 131--143
project:
- _id: '1'
name: SFB 901
- _id: '2'
name: SFB 901 - Project Area A
- _id: '7'
name: SFB 901 - Subproject A3
publication: Proceedings of the 10th International Symposium on Algorithmic Game Theory
(SAGT 2017)
series_title: LNCS
status: public
title: 'Conditional Value-at-Risk: Structure and Complexity of Equilibria'
type: conference
user_id: '477'
volume: 10504
year: '2017'
...