Anonymity in nonatomic games

Anonymity in Nonatomic Games

Coalitions in Nonatomic Network Congestion Games

This work shows that the formation of a finite number of coalitions in a nonatomic network congestion game benefits everyone. At the equilibrium of the composite game played by coalitions and individuals, the average cost to each coalition and the individuals’ common cost are all lower than in the corresponding nonatomic game (without coalitions). The individuals’ cost is lower than the average...

Asymptotic interpretations for equilibria of nonatomic games

We show that a mixed equilibrium of a semi-anonymous nonatomic game can be used to generate pure-strategy profiles for finite games randomly generated from the type distribution of the nonatomic game. As the numbers of players involved in the finite games increase, the generated profiles will be asymptotically equilibrium. The converse of this result is also true, i.e., a mixed-strategy profile...

Potentials and Weighted Values of Nonatomic Games

The “potential approach” to value theory for finite games was introduced by Hart and Mas-Colell (1989). Here this approach is extended to non-atomic games. On appropriate spaces of differentiable games there is a unique potential operator, that generates the Aumann and Shapley (1974) value. As a corollary we obtain the uniqueness of the Aumann-Shapley value on certain subspaces of games. Next, ...

Monotone equilibria in nonatomic supermodular games. A comment

Recently Yang and Qi (2013) stated an interesting theorem on existence of complete lattice of equilibria in a particular class of large nonatomics supermodular games for general action and types spaces. Unfortunately, their result is incorrect. In this note, we detail the nature of the problem with the stated theorem, provide a counterexample, and then correct the result under additional assump...