Tobias Harks We consider combinatorial multi-item markets and propose the notion of a ∆-regret Walras equilibrium, which is an allocation of items to players and a set of item prices that achieve the following goals: prices clear the market, the allocation is capacity-feasible, and the players’ strategies lead to a total regret of ∆. The regret is … Read more
Generalized Nash equilibrium problems with mixed-integer variables constitute an important class of games in which each player solves a mixed-integer optimization problem, where both the objective and the feasible set is parameterized by the rivals’ strategies. However, such games are known for failing to admit exact equilibria and also the assumption of all players being … Read more
We consider Nash equilibrium problems with mixed-integer variables in which each player solves a mixed-integer optimization problem parameterized in the rivals’ strategies. We distinguish between standard Nash equilibrium problems (NEP), where the parameterization acts only on the players’ cost functions and generalized Nash equilibrium problems (GNEPs), where, additionally, the strategy spaces of the players may … Read more
Hayrapetyan, Tardos and Wexler recently introduced a framework to study the impact of collusion in congestion games on the quality of Nash equilibria. We adopt their framework to network games and focus on the well established price of anarchy as a measure of this impact. We first investigate nonatomic network games with coalitions. For this … Read more