We consider noncooperative games where each player minimizes the sum of a smooth function, which depends on the player, and of a possibly nonsmooth function that is the same for all players. For this class of games we consider two approaches: one based on an augmented game that is applicable only to a minmax game and another one derived by a smoothing procedure that is applicable more broadly. In both cases, centralized and, most importantly, distributed algorithms for the computation of Nash equilibria can be derived.

We consider noncooperative games where each player minimizes the sum of a smooth function, which depends on the player, and of a possibly nonsmooth function that is the same for all players. For this class of games we consider two approaches: one based on an augmented game that is applicable only to a minmax game and another one derived by a smoothing procedure that is applicable more broadly. In both cases, centralized and, most importantly, distributed algorithms for the computation of Nash equilibria can be derived. © 2014 Springer Science+Business Media New York.

Non-cooperative games with minmax objectives / Facchinei, Francisco; Jong Shi, Pang; Scutari, Gesualdo. - In: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS. - ISSN 0926-6003. - STAMPA. - 59:1-2(2014), pp. 85-112. [10.1007/s10589-014-9642-3]

Non-cooperative games with minmax objectives

FACCHINEI, Francisco;SCUTARI, GESUALDO
2014

Abstract

We consider noncooperative games where each player minimizes the sum of a smooth function, which depends on the player, and of a possibly nonsmooth function that is the same for all players. For this class of games we consider two approaches: one based on an augmented game that is applicable only to a minmax game and another one derived by a smoothing procedure that is applicable more broadly. In both cases, centralized and, most importantly, distributed algorithms for the computation of Nash equilibria can be derived. © 2014 Springer Science+Business Media New York.
We consider noncooperative games where each player minimizes the sum of a smooth function, which depends on the player, and of a possibly nonsmooth function that is the same for all players. For this class of games we consider two approaches: one based on an augmented game that is applicable only to a minmax game and another one derived by a smoothing procedure that is applicable more broadly. In both cases, centralized and, most importantly, distributed algorithms for the computation of Nash equilibria can be derived.
nash equilibrium problem; nondifferentiable objective function; smoothing; distributed algorithm
01 Pubblicazione su rivista::01a Articolo in rivista
Non-cooperative games with minmax objectives / Facchinei, Francisco; Jong Shi, Pang; Scutari, Gesualdo. - In: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS. - ISSN 0926-6003. - STAMPA. - 59:1-2(2014), pp. 85-112. [10.1007/s10589-014-9642-3]
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