On benefits of cooperation under strategic power
M. Gloria Fiestras-Janeiro, Ignacio García-Jurado, Ana Meca, Manuel A. Mosquera
TL;DR
This work defines TU-games with strategies, where each player selects a strategy that determines a corresponding TU-game, and then aggregates these into a single TU-game that captures bargaining power. It introduces the maxmin procedure $\psi$ with $\psi(X,V)(S)=\max_{x_S}\min_{x_{N\setminus S}}V(x_S,x_{N\setminus S})(S)$ and proves its uniqueness under five axioms: $\,$individual objectivity, $\,$monotonicity, $\,$irrelevance of weakly dominated strategies, $\,$irrelevance of weakly dominated threats, and $\,$merge invariance. The paper shows partial transmission of properties (e.g., superadditivity and monotonicity) through $\psi$, while balancedness may fail, and develops results for airport-games and simple-games with strategies. Through concrete examples (inheritance division, subsidy-driven cost allocation, Parliament power), it demonstrates how strategic action choices reshape cooperative outcomes and how the maxmin-transformed TU-game can yield more robust allocations. Overall, the approach offers a principled way to incorporate strategic pre-cooperation power into cooperative analysis and distinguishes itself from reductions to strategic games.
Abstract
We introduce a new model involving TU-games and exogenous structures. Specifically, we consider that each player in a population can choose an element in a strategy set and that, for every possible strategy profile, a TU-game is associated with the population. This is what we call a TU-game with strategies. We propose and characterize the maxmin procedure to map every game with strategies to a TU-game. We also study whether or not the relevant properties of TU-games are transmitted by applying the maxmin procedure. Finally, we examine two relevant classes of TU-games with strategies: airport and simple games with strategies.