On the Online Coalition Structure Generation Problem

We consider the online version of the coalition structure generation problem, in which agents, corresponding to the vertices of a graph, appear in an online fashion and have to be partitioned into coalitions by an authority (i.e., an online algorithm). When an agent appears, the algorithm has to decide whether to put the agent into an existing coalition or to create a new one containing, at this moment, only her. The decision is irrevocable. The objective is partitioning agents into coalitions so as to maximize the resulting social welfare that is the sum of all coalition values. We consider two cases for the value of a coalition: (1) the sum of the weights of its edges, and (2) the sum of the weights of its edges divided by its size. Coalition structures appear in a variety of application in AI, multi-agent systems, networks, as well as in social networks, data analysis, computational biology, game theory, and scheduling. For each of the coalition value functions we consider the bounded and unbounded cases depending on whether or not the size of a coalition can exceed a given value α. Furthermore, we consider the case of a limited number of coalitions and various weight functions for the edges, i.e., unrestricted, positive and constant weights. We show tight or nearly tight bounds for the competitive ratio in each case.

Loyalty in Cardinal Hedonic Games

A common theme of decision making in multi-agent systems is to assign utilities to alternatives, which individuals seek to maximize. This rationale is questionable in coalition formation where agents are affected by other members of their coalition. Based on the assumption that agents are benevolent towards other agents they like to form coalitions with, we propose loyalty in hedonic games, a binary relation dependent on agents' utilities. Given a hedonic game, we define a loyal variant where agents' utilities are defined by taking the minimum of their utility and the utilities of agents towards which they are loyal. This process can be iterated to obtain various degrees of loyalty, terminating in a locally egalitarian variant of the original game. We investigate axioms of group stability and efficiency for different degrees of loyalty. Specifically, we consider the problem of finding coalition structures in the core and of computing best coalitions, obtaining both positive and intractability results. In particular, the limit game possesses Pareto optimal coalition structures in the core.

Tweeting #RamNavami: A Comparison of Approaches to Analyzing Bipartite Networks

Bipartite networks, also known as two-mode networks or affiliation networks, are a class of networks in which actors or objects are partitioned into two sets, with interactions taking place across but not within sets. These networks are omnipresent in society, encompassing phenomena such as student-teacher interactions, coalition structures and international treaty participation. With growing data availability and proliferation in statistical estimators and software, scholars have increasingly sought to understand the methods available to model the data-generating processes in these networks. This article compares three methods for doing so: (a) Logit (b) the bipartite Exponential Random Graph Model (ERGM) and (c) the Relational Event Model (REM). This comparison demonstrates the relevance of choices with respect to dependence structures, temporality, parameter specification and data structure. Considering the example of Ram Navami, a Hindu festival celebrating the birth of Lord Ram, the ego network of tweets using #RamNavami on 21April 2021 is examined. The results of the analysis illustrate that critical modelling choices make a difference in the estimated parameters and the conclusions to be drawn from them.

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.

Optimisation for Coalitions Formation Considering the Fairness in Flexibility Market Participation

This paper proposes a coalitional game-theoretical model for consumers’ flexibility coalition formation, supported by an optimization model based on differential evolution. Traditionally, the participation in conventional electricity markets used to be limited to large producers and consumers. The final end-users contract their energy supply with retailers, since due to the smaller quantity available for trading, they cannot participate in electricity market transactions. Nowadays, the growing concept of local electricity market brings many advantages to the end-users. The flexibility negotiation considering local areas is an important procedure for network operators and it is incorporating a local electricity market opportunity. A coalition formation model to facilitate small players participation in the flexibility market proposed by the network operator is addressed in this work. The inclusion of Shapley value in the proposed model enables finding the best coalition structures considering the fairness of the coalitions in addition to the potential income achieved by the consumers when selling their flexibility. An optimization model based on differential evolution is also proposed as the way to find the optimal coalition structures based on the multi-criteria specifications.

Comparing Discourse and Policy Network Approaches: Evidence from Water Policy on Micropollutants

To understand how actors make collective policy decisions, scholars use policy and discourse network approaches to analyze interdependencies among actors. While policy networks often build on survey data, discourse networks typically use media data to capture the beliefs or policy preferences shared by actors. One of the reasons for the variety of data sources is that discourse data can be more accessible to researchers than survey data (or vice versa). In order to make an informed decision on valid data sources, researchers need to understand how differences in data sources may affect results. As this remains largely unexplored, we analyze the differences and similarities between policy and discourse networks. We systematically compare policy networks with discourse networks in respect of the types of actors participating in them, the policy proposals actors advocate and their coalition structures. For the policy field of micropollutants in surface waters in Germany, we observe only small differences between the results obtained using the policy and discourse network approaches. We find that the discourse network approach particularly emphasizes certain actor types, i.e., expanders who seek to change the policy status quo. The policy network approach particularly reflects electoral interests, since preferences for policies targeting voters are less visible. Finally, different observation periods reveal some smaller differences in the coalition structures within the discourse network. Beyond these small differences, both approaches come to largely congruent results with regards to actor types, policy preferences and coalition structures. In our case, the use of discourse and policy network approaches lead to similar conclusions regarding the study of policy processes.