Abstract
The aim of this contribution is an overview on Potential Games. This class of games is special, in fact we can investigate their properties by a unique function: the potential function. We consider several types of potential games: exact, ordinal, bayesian and hierarchical. Some results are generalized to multicriteria decisions.
Similar content being viewed by others
References
Basar T. and Olsder G.J. (1982). Dynamic Noncooperative Games. Academic Press, New York
Branzei R., Mallozzi L. and Tijs S. (2003). Supermodular games and potential games. J. math. Econ. 39: 39–49
Briata, F., Moretti, S., Patrone, F., Tijs, S.: Printers: Non cooperative games from Tuic games, preprint (2006)
Daniele, P., Maugeri, A.: Vector variational inequalities and a continuum modelling of traffic equilibrium problem. In: Giannessi, F. (ed.) Vector Variational Inequalities and Vector Equilibria, pp. 97–112. Kluwer Academic Publishers (2000)
Daniele, P., Maugeri, A., Oettli, W.: Variational Inequalities and time dependent Traffic Equilibria C.R. Acad. Sci. Paris, 326, serie I (1998)
Daniele P., Maugeri A. and Oettli W. (1999). Time dependent traffic equilibria. J. Optim. Th. Appl. 103(3): 543–555
Facchini G., Van Megen F., Borm P. and Tijs S. (1997). Congestion models and weighted bayesian potential games. Theory and Decision 42: 193–206
Peleg B., Tijs S., Borm P. and van Heumann R. (1996). Characterization of solutions for Bayesian games. Theory and Decision 40: 103–129
Harsanyi, J.: Games with incomplete information played by bayesian players. Manage. Sci. 14, 159–182, 320–334, 486–502 (1967–1968)
Maugeri A. (1985). New classes of variational inequalities and applications to equilibrium problems. Methods Oper. Res. 53: 129–131
Margiocco M., Patrone F. and Pusillo L. (2002). On Tihkonov well-posedness of concave games and Cournot oligopoly. J. Optim. Theory Appl. 112: 361–369
Margiocco M. and Pusillo L. (2006). (ϵ, k) Equilibria and Well Posedness. Int. Game Theory Rev. 8(1): 33–44
Margiocco, M., Pusillo, L.: Potential Games and Well-posedness properties. Optimization (to appear)
Margiocco, M., Pusillo, L.: Stackelberg Well-Posedness and Hierarchical Potential Games. Anna. Dyna. Games (to appear)
Mallozzi L., Tijs S. and Voorneveld M. (2000). Infinite Hierarchical potential games. USSR J. Comp. Math. Math. Phys. J. Optimi. Theory Appl. 107: 287–296
Morgan J. (1989). Constrained well-posed two-level optimization problems. In: Clarke, F.H., Dem’yanov, V.F. and Giannessi, F. (eds) Nonsmooth Optimization and Related Topics, pp 307–325. Plenum Press, New York
Monderer P. and Shapley L. (1996). Potential games. Games Econ. Behav. 14: 124–143
Nash J.F. Jr (1950). Equilibrium points in n-person games. Proc. Nat. Acad. Sci. USA 36: 48–49
Patrone F. (2006). Decisori (razionali) interagenti.Una introduzione alla Teoria dei Giochi, ed. University Press, Pisa
Pusillo L. (2001). Approximate Solutions and Tikhonov Well-posedness for Nash Equilibria. In: Giannessi F., Maugeri A., Pardalos P. (eds). Equilibrium Problems:Non smooth Optimization and Variational Inequality Models. Kluwer Academic Publishers, pp. 231–244
Pusillo L.: Well posedness and optimization problems. In: Giannessi, F., Maugeri, A. (eds.) Variational Analysis and Applications. Springer (2005)
Pusillo, L., Tijs, S.: Multicriteria Games and Potentials, preprint D.I.M.A. n.524 (2005)
Rosenthal R.W. (1973). A class of games possessing pure strategy Nash equilibria. Int. J. Game Theory 2: 65–67
Tijs S.: Introduction to Game Theory. Hindustan Book Agency (2003)
von Stackelberg H. (1934). Marktform und Gleichgewitch. Springer, Vienna
Voorneveld, M.: Potential games and interactive decisions with multiple criteria. Ph.D. thesis CentER, Tilburg University (1999)
Voorneveld M., Tijs S., Mallozzi L. (1999) Sequential production situations and potentials. In: Patrone, F., Garcia Jurado, I., Tijs, S. (eds.) Game Practice Book. Kluwer Academic Publishers, Boston (1997)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Pusillo, L. Interactive decisions and potential games. J Glob Optim 40, 339–352 (2008). https://doi.org/10.1007/s10898-007-9209-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10898-007-9209-2