Coordinating choice in partial cooperative equilibrium

In this paper we consider symmetric aggregative games and investigate partial cooperation between a portion of the players that sign a cooperative agreement and the rest of the players. Existence results of partial cooperative equilibria are obtained when the players who do not sign the agreement play a Nash equilibrium game having multiple solutions. Some applications in the supermodular case are discussed.Noncooperative games, cooperation, aggregative games, supermodular games.

Partial Cooperation and Non-Signatories Multiple Decision

In this paper we investigate partial cooperation between a portion of the players and the rest of the players who do not cooperate and play a Nash game having multiple equilibria. Some properties of the partial cooperative equilibrium are studied and applied to a public goods situation.noncooperative games, cooperation, public goods games

Multi-Leader Multi-Follower Model with Aggregative Uncertainty

We study a non-cooperative game with aggregative structure, namely when the payoffs depend on the strategies of the opponent players through an aggregator function. We assume that a subset of players behave as leaders in a Stackelberg model. The leaders, as well the followers, act non-cooperatively between themselves and solve a Nash equilibrium problem. We assume an exogenous uncertainty affecting the aggregator and we obtain existence results for the stochastic resulting game. Some examples are illustrated

Conflict & Cooperation under Stackelberg Assumption

EnIn a Game Theory context, we consider partial cooperation between a portion of the players and the rest of the players who do not cooperate and play a Nash game. The players may decide their strategy simultaneously or in a two-stage model. In both cases, some properties of the partial cooperative equilibrium are studied and applied to a different practical situations

Softening bilevel problems via two-scale Gibbs measures

We introduce a new, and elementary, approximation method for bilevel optimization problems motivated by Stackelberg leader-follower games. Our technique is based on the notion of two-scale Gibbs measures. The first scale corresponds to the cost function of the follower and the second scale to that of the leader. We explain how to choose the weights corresponding to these two scales under very general assumptions and establish rigorous Γ-convergence results. An advantage of our method is that it is applicable both to optimistic and to pessimistic bilevel problems

Game theoretic foundations of the Gately power measure for directed networks

We introduce a new network centrality measure founded on the Gately value for cooperative games with transferable utilities. A directed network is interpreted as representing control or authority relations between players--constituting a hierarchical network. The power distribution of a hierarchical network can be represented through a TU-game. We investigate the properties of this TU-representation and investigate the Gately value of the TU-representation resulting in the Gately power measure. We establish when the Gately measure is a Core power gauge, investigate the relationship of the Gately with the $\beta$-measure, and construct an axiomatisation of the Gately measure

Gately Values of Cooperative Games

We investigate Gately's solution concept for cooperative games with transferable utilities. Gately's conception introduced a bargaining solution that minimises the maximal quantified ``propensity to disrupt'' the negotiation process of the players over the allocation of the generated collective payoffs. Gately's solution concept is well-defined for a broad class of games. We also consider a generalisation based on a parameter-based quantification of the propensity to disrupt. Furthermore, we investigate the relationship of these generalised Gately values with the Core and the Nucleolus and show that Gately's solution is in the Core for all regular 3-player games. We identify exact conditions under which generally these Gately values are Core imputations for arbitrary regular cooperative games. Finally, we investigate the relationship of the Gately value with the Shapley value

On location-allocation problems for dimensional facilities

This paper deals with a bilevel approach of the location-allocation problem with dimensional facilities. We present a general model that allows us to consider very general shapes of domains for the dimensional facilities and we prove the existence of optimal solutions under mild, natural assumptions. To achieve these results we borrow tools from optimal transport mass theory that allow us to give explicit solution structure of the considered lower level problem. We also provide a discretization approach that can approximate, up to any degree of accuracy, the optimal solution of the original problem. This discrete approximation can be optimally solved via a mixedinteger linear program. To address very large instance sizes we also provide a GRASP heuristic that performs rather well according to our experimental results. The paper also reports some experiments run on test data.Ministerio de Economía y Competitividad (MINECO). Españ

Uncertainty in cooperative interval games: How Hurwicz criterion compatibility leads to egalitarianism

We study cooperative interval games. These are cooperative games where the value of a coalition is given by a closed real interval specifying a lower bound and an upper bound of the possible outcome. For interval cooperative games, several (interval) solution concepts have been introduced in the literature. We assume that each player has a different attitude towards uncertainty by means of the so-called Hurwicz coefficients. These coefficients specify the degree of optimism that each player has, so that an interval becomes a specific payoff. We show that a classical cooperative game arises when applying the Hurwicz criterion to each interval game. On the other hand, the same Hurwicz criterion can be also applied to any interval solution of the interval cooperative game. Given this, we say that a solution concept is Hurwicz compatible if the two procedures provide the same final payoff allocation. When such compatibility is possible, we characterize the class of compatible solutions, which reduces to the egalitarian solution when symmetry is required. The Shapley value and the core solution cases are also discussed