---
_id: '597'
abstract:
- lang: eng
text: 'We consider strategic games in which each player seeks a mixed strategy to
minimize her cost evaluated by a concave valuation V (mapping probability distributions
to reals); such valuations are used to model risk. In contrast to games with expectation-optimizer
players where mixed equilibria always exist [15, 16], a mixed equilibrium for
such games, called a V -equilibrium, may fail to exist, even though pure equilibria
(if any) transfer over. What is the impact of such valuations on the existence,
structure and complexity of mixed equilibria? We address this fundamental question
for a particular concave valuation: expectation plus variance, denoted as RA,
which stands for risk-averse; so, variance enters as a measure of risk and it
is used as an additive adjustment to expectation. We obtain the following results
about RA-equilibria:- A collection of general structural properties of RA-equilibria
connecting to (i) E-equilibria and Var-equilibria, which correspond to the expectation
and variance valuations E and Var, respectively, and to (ii) other weaker or incomparable
equilibrium properties.- A second collection of (i) existence, (ii) equivalence
and separation (with respect to E-equilibria), and (iii) characterization results
for RA-equilibria in the new class of player-specific scheduling games. Using
examples, we provide the first demonstration that going from E to RA may as well
create new mixed (RA-)equilibria.- A purification technique to transform a player-specific
scheduling game on identical links into a player-specific scheduling game so that
all non-pure RA-equilibria are eliminated while new pure equilibria cannot be
created; so, a particular game on two identical links yields one with no RA-equilibrium.
As a by-product, the first-completeness result for the computation of RA-equilibria
follows.'
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. Minimizing Expectation Plus Variance. In: *Proceedings
of the 5th International Symposium on Algorithmic Game Theory (SAGT)*. LNCS.
; 2012:239-250. doi:10.1007/978-3-642-33996-7_21'
apa: Mavronicolas, M., & Monien, B. (2012). Minimizing Expectation Plus Variance.
In *Proceedings of the 5th International Symposium on Algorithmic Game Theory
(SAGT)* (pp. 239–250). https://doi.org/10.1007/978-3-642-33996-7_21
bibtex: '@inproceedings{Mavronicolas_Monien_2012, series={LNCS}, title={Minimizing
Expectation Plus Variance}, DOI={10.1007/978-3-642-33996-7_21},
booktitle={Proceedings of the 5th International Symposium on Algorithmic Game
Theory (SAGT)}, author={Mavronicolas, Marios and Monien, Burkhard}, year={2012},
pages={239–250}, collection={LNCS} }'
chicago: Mavronicolas, Marios, and Burkhard Monien. “Minimizing Expectation Plus
Variance.” In *Proceedings of the 5th International Symposium on Algorithmic
Game Theory (SAGT)*, 239–50. LNCS, 2012. https://doi.org/10.1007/978-3-642-33996-7_21.
ieee: M. Mavronicolas and B. Monien, “Minimizing Expectation Plus Variance,” in
*Proceedings of the 5th International Symposium on Algorithmic Game Theory (SAGT)*,
2012, pp. 239–250.
mla: Mavronicolas, Marios, and Burkhard Monien. “Minimizing Expectation Plus Variance.”
*Proceedings of the 5th International Symposium on Algorithmic Game Theory (SAGT)*,
2012, pp. 239–50, doi:10.1007/978-3-642-33996-7_21.
short: 'M. Mavronicolas, B. Monien, in: Proceedings of the 5th International Symposium
on Algorithmic Game Theory (SAGT), 2012, pp. 239–250.'
date_created: 2017-10-17T12:42:48Z
date_updated: 2020-05-07T05:27:47Z
ddc:
- '040'
doi: 10.1007/978-3-642-33996-7_21
file:
- access_level: closed
content_type: application/pdf
creator: florida
date_created: 2018-03-15T08:20:53Z
date_updated: 2018-03-15T08:20:53Z
file_id: '1254'
file_name: 597-newtocs_01.pdf
file_size: 345826
open_access: 1
relation: main_file
success: 1
file_date_updated: 2018-03-15T08:20:53Z
page: 239-250
project:
- _id: '1'
name: SFB 901
- _id: '7'
name: SFB 901 - Subprojekt A3
- _id: '2'
name: SFB 901 - Project Area A
publication: Proceedings of the 5th International Symposium on Algorithmic Game Theory
(SAGT)
series_title: LNCS
status: public
title: Minimizing Expectation Plus Variance
type: conference
user_id: '15504'
year: '2012'
...