Testing stability properties in graphical hedonic games

In hedonic games, players form coalitions based on individual preferences over the group of players they could belong to. Several concepts to describe the stability of coalition structures in a game have been proposed and analysed in the literature. However, prior research focuses on algorithms with time complexity that is at least linear in the input size. In the light of very large games that arise from, e.g., social networks and advertising, we initiate the study of sublinear time property testing algorithms for existence and verification problems under several notions of coalition stability in a model of hedonic games represented by graphs with bounded degree. In graph property testing, one shall decide whether a given input has a property (e.g., a game admits a stable coalition structure) or is far from it, i.e., one has to modify at least an $$\epsilon$$ ϵ -fraction of the input (e.g., the game’s preferences) to make it have the property. In particular, we consider verification of perfection, individual rationality, Nash stability, (contractual) individual stability, and core stability. While there is always a Nash-stable coalition structure (which also implies individually stable coalitions), we show that the existence of a perfect coalition structure is not tautological but can be tested. All our testers have one-sided error and time complexity that is independent of the input size.

Anchored Team Formation Games

We propose Anchored Team Formation Games (ATFGs), a new class of hedonic game inspired by tabletop role playing games.We establish the NP-hardness of determining whether Nash stable coalition structures exist, and provide results for three heuristics for this problem. We highlight costs and benefits of each heuristic and provide evidence that all three are capable of finding Nash stable coalition structures, when they exist, much more quickly than a deterministic algorithm.

The Presidential System with a Multiparty System is Based on the 1945 Constitution of the Republic of Indonesia

Coalitions of political parties built within the presidential system, especially in Indonesia, are non-binding and permanent. If government policies or programs are not famous or inline, political parties tend to engage in opposition. This study aims to determine the implementation of the presidential system with a multiparty system and efforts to realize a stable and dynamic government based on the Indonesian constitutional system. This research uses a normative approach. Types and sources of legal materials consist of primary legal materials, secondary legal materials, and tertiary legal materials. The analysis technique used in this research is the hermeneutic analysis method. The study results concluded that with the implementation of the presidential system with a multiparty system, it is rare for a President to be elected and from the majority party. Furthermore, with the election of a minority President and a majority in Parliament, the President will strengthen his position by forming a coalition. However, building a stable coalition is difficult in a multiparty presidential democracy. In this regard, the institutional engineering agenda that needs to be designed includes simplifying the number of factions in Parliament by tightening the threshold requirements for fraction formation; parliamentary coalition regulations aimed at both political blocs (coalition and opposition); strengthening the institution and authority of the Regional Representative Council to balance the House of Representatives so that checks and balances not only occur between the President and the House of Representatives but also between the House of Representatives and the Regional Representative Council.

Stable International Environmental Agreements: Large Coalitions that Achieve Little

A standard result of coalition formation games is that stable coalitions are very small if the coalition plays Nash vis-à-vis the rest of the world and if abatement costs are quadratic. It has been shown that larger coalitions and even the grand coalition are possible if the marginal abatement cost is concave. The paper confirms this result, but shows that abatement activities by large coalitions smaller than the grand coalition can be very small. This can be ‘repaired’ only by assuming that the marginal abatement cost curve changes its curvature extremely once the stable coalition has been reached.