Resource selection games with unknown number of players

In the context of pre-Bayesian games we analyze resource selection games with unknown number of players. We prove the existence and uniqueness of a symmetric safety-level equilibrium in such games and show that in a game with strictly increasing linear cost functions every player benefits from the common ignorance about the number of players. In order to perform the analysis we define safety-level equilibrium for pre-Bayesian games, and prove that it exists in a compact-continuous-concave setup; in particular it exists in a finite setup.

[1]  R. Holzman,et al.  Strong Equilibrium in Congestion Games , 1997 .

[2]  Roger B. Myerson,et al.  Population uncertainty and Poisson games , 1998, Int. J. Game Theory.

[3]  Craig Boutilier,et al.  Regret Minimizing Equilibria and Mechanisms for Games with Strict Type Uncertainty , 2004, UAI.

[4]  Dimitris Bertsimas,et al.  Robust game theory , 2006, Math. Program..

[5]  Ronald M. Harstad,et al.  Equilibrium bid functions for auctions with an uncertain number of bidders , 1990 .

[6]  M. Shubik,et al.  A Model of Migration , 1994 .

[7]  Moshe Tennenholtz,et al.  Bundling equilibrium in combinatorial auctions , 2002, Games Econ. Behav..

[8]  Ron Holzman,et al.  Characterization of ex post equilibrium in the VCG combinatorial auctions , 2004, Games Econ. Behav..

[9]  Joseph Naor,et al.  Equilibria in online games , 2007, SODA '07.

[10]  Roger B. Myerson,et al.  Large Poisson Games , 2000, J. Econ. Theory.

[11]  M. Breton,et al.  Equilibria in a Model with Partial Rivalry , 1997 .

[12]  R. Rosenthal.  A class of games possessing pure-strategy Nash equilibria , 1973 .

[13]  Daniel M. Reeves,et al.  Notes on Equilibria in Symmetric Games , 2004 .

[14]  Christos H. Papadimitriou,et al.  Worst-case equilibria , 1999 .

[15]  R. McAfee,et al.  Auctions with a stochastic number of bidders , 1987 .

[16]  Mark Voorneveld,et al.  Congestion Games and Potentials Reconsidered , 1999, IGTR.

[17]  Itai Ashlagi,et al.  On the Value of Correlation , 2005, UAI.

[18]  Paul R. Milgrom,et al.  A theory of auctions and competitive bidding , 1982 .

[19]  Dan Levin,et al.  Auctions with uncertain numbers of bidders , 2004, J. Econ. Theory.

[20]  S. Rosenschein,et al.  On social laws for artificial agent societies: off-line design , 1996 .

[21]  L. Shapley,et al.  Potential Games , 1994 .

[22]  Moshe Tennenholtz,et al.  Artificial Social Systems , 1992, Lecture Notes in Computer Science.

[23]  Steven A. Matthews.  Comparing Auctions for Risk Averse Buyers: A Buyer's Point of View , 1987 .

[24]  Allan Borodin,et al.  Online computation and competitive analysis , 1998 .

[25]  R. Myerson.  Extended Poisson Games and the Condorcet Jury Theorem , 1998 .

[26]  I. Milchtaich,et al.  Congestion Games with Player-Specific Payoff Functions , 1996 .