We consider a class of games played on networks in which the utility 4 functions consist of both deterministic and random terms. In order to find the Nash 5 equilibrium of the game we formulate the problem as a variational inequality in a 6 probabilisticLebesguespacewhichissolvednumericallytoprovideapproximations 7 for the mean value of the random equilibrium. We also numerically compare the 8 solution thus obtained, with the solution computed by solving the deterministic 9 variational inequality derived by taking the expectation of the pseudo-gradient of 10 the game with respect to the random parameters.

Passacantando, M., Raciti, F. (2022). A Variational Formulation of Network Games with Random Utility Functions. In N.J. Daras, T.M. Rassias (a cura di), Approximation and Computation in Science and Engineering (pp. 667-677). Springer [10.1007/978-3-030-84122-5_36].

### A Variational Formulation of Network Games with Random Utility Functions

#### Abstract

We consider a class of games played on networks in which the utility 4 functions consist of both deterministic and random terms. In order to find the Nash 5 equilibrium of the game we formulate the problem as a variational inequality in a 6 probabilisticLebesguespacewhichissolvednumericallytoprovideapproximations 7 for the mean value of the random equilibrium. We also numerically compare the 8 solution thus obtained, with the solution computed by solving the deterministic 9 variational inequality derived by taking the expectation of the pseudo-gradient of 10 the game with respect to the random parameters.
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Capitolo o saggio
Network game; Nash equilibrium; Random utility function; Variational inequality
English
Approximation and Computation in Science and Engineering
Daras, NJ; Rassias, TM
2022
978-3-030-84121-8
180
Springer
667
677
Passacantando, M., Raciti, F. (2022). A Variational Formulation of Network Games with Random Utility Functions. In N.J. Daras, T.M. Rassias (a cura di), Approximation and Computation in Science and Engineering (pp. 667-677). Springer [10.1007/978-3-030-84122-5_36].
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/10281/391578`