Abstract
Coalition formation is often analysed in an almost non-cooperative way, as a two-stage game that consists of a first stage comprising membership actions and a second stage with physical actions, such as the provision of a public good. We formalised this widely used approach for the case where actions are simultaneous in each stage. Herein, we give special attention to the case of a symmetric physical game. Various theoretical results, in particular, for cartel games, are provided. As they are crucial, recent results on the uniqueness of coalitional equilibria of Cournot-like physical games are reconsidered. Various concrete examples are included. Finally, we discuss research strategies to obtain results about equilibrium coalition structures with abstract physical games in terms of qualitative properties of their primitives.
Highlights
Non-cooperative game theory plays an important role in the modern theory of coalition formation.1 Modelling coalition formation as a two-stage game under almost non-cooperative conditions is a very promising approach, albeit theoretically challenged
We provide a formalisation of a specific variant of the two-stage game approach in the case of complete information, transferable payoffs, and in each stage, independent simultaneous actions
There are various articles on two-stage coalition formation games, there is, to the best of our knowledge, no theoretical result about equilibrium coalition structures that holds for an abstract class of physical games in terms of qualitative properties of the primitives of the physical game; only results for concrete physical games are available
Summary
Non-cooperative game theory plays an important role in the modern theory of coalition formation. Modelling coalition formation as a two-stage game under almost non-cooperative conditions is a very promising approach, albeit theoretically challenged. The procedure to solve the game is as follows: the unique Nash equilibrium corresponds to a physical action for each individual player, which in turn corresponds to a payoff for each individual player In this way the two-stage game ( N; R; Γ) leads to a game in strategic form G, referred to as an “effective game.”. There are various articles on two-stage coalition formation games, there is, to the best of our knowledge, no theoretical result about equilibrium coalition structures that holds for an abstract class of physical games in terms of qualitative properties (such as convexity, monotonicity and symmetry) of the primitives of the physical game; only results for concrete (mostly symmetric) physical games (mostly with linear or quadratic conditional payoff functions) are available (see, for example, [4,16,17,18,19,20]).
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