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The authors characterize the conditions under which a country may eventually split and when it splits within an infinite horizon multi-stage differential game.

In contrast to the existing literature, the authors do not assume that after splitting, players will adopt Markovian strategies. Instead, the authors assume that while the splitting country plays Markovian, the remaining coalition remains committed to the collective control of pollution and plays open-loop.

Within a full linear-quadratic model, the authors characterize the optimal strategies. The authors later compare with the outcomes of the case where the splitting country and the remaining coalition play both Markovian. The authors highlight several interesting results in terms of the implications for long-term pollution levels and the duration of coalitions under heterogenous strategies as compared to Markovian behavior.

In this paper, the authors have illustrated the richness of the simplications of enlarging the set of strategies in terms of the emergence of coalitions, their duration and the implied welfare levels per player. Varying only three parameters (the technological gap, pollution damage and coalition payoff share distribution across players), the authors have been able to generate, among other findings, quite different rankings of welfare per player depending on whether the remaining coalitions after split play Markovian or stay precommited to the pre-splitting period decisions.

This paper aims to extend the Shapley value (SV) into a discussion of Zakat, a Pillar of Islam. Lloyd Shapley was awarded the Nobel Prize in Economics in 2012. This study shows that their relationship is significant for all nations, that of levelling up. An important but neglected paper by Datta (1939) showed insights provided by the Power Law, or as it is sometimes called, the Pareto distribution, into the role of Zakat in raising the income of all above the subsistence level. The Pareto distribution describes the prevailing tendency. The SV illustrates the interdependence perspective of Zakat with the Pareto distribution, wealth, income and poverty. Payoffs apply equally to both givers and receivers. For this study’s purposes, payoffs are considered as transferable utilities. They are formed by individuals who willingly cooperate in society rather than atomistic individuals who act independently. Zakat represents the recognition that society needs to be cooperative rather than individualistic; people cooperate in groups or societies to create value. SV implications and axioms are evaluated with an illustration.

This study extends Datta’s approach by introducing distribution weights into the SV. The authors set out the concept of weighted Shapley values that retain the elements of randomness and marginal contribution to a coalition contained in pure/true SVs and weights that follow a ley-Pareto distribution. This paper is a viewpoint work that relies primarily on the author’s qualitative interpretation.

The findings indicate that individual members of a coalition make multiple contributions that are often unrewarded. The contribution of one member of a coalition is dependent upon the contribution of others. The measure of contributions is payoffs, which have both monetary and non-monetary aspects; transferable payoffs or utilities are usually assumed. Furthermore, the significant agents in society or an organisation are stakeholders rather than the usual categories: managers, staff, shareholders, etc.

Contextualising these concepts within the Islamic values and principles that guide Zakat administration is crucial to ensure that the distribution of Zakat funds is fair, equitable and meets the needs of all eligible recipients. By applying these concepts appropriately, Zakat administrators can ensure that the Zakat system functions effectively and fulfils its religious obligation.

The novelty of this paper is that it blends the SV and the idea behind Zakat by introducing the idea of alternatives of Shapley weights. The link between the institution of Zakat and SV in terms of equality, poverty elimination and wealth distribution should be at the top of the research agenda.

Social enterprises are embedded in ecosystems with multiple actors interested in the field’s growth. One way to enhance social enterprises is through public policies and developing countries like Brazil included this in the public agenda. After an important mobilization of private organizations and public managers, the Brazilian federal government implemented in 2017 the National Impact Investment and Business Strategy (ENIMPACTO) renamed in 2023 to National Impact Economy Strategy with the same abbreviation. Since its creation, ENIMPACTO saw significant modifications leading to a decree in 2023 extending its mandate, amplifying membership and changing its name to the National Impact Economy Strategy while maintaining the same acronym. This experience leads us to the following question: How was ENIMPACTO created and developed?

We used institutional arrangements and advocacy coalition theory to analyze the key elements that contributed to ENIMPACTO’s creation and its evolution through time. A qualitative, single-case study on the Brazilian experience implementing ENIMPACTO was conducted through semi-structured interviews with national strategy members, participant observation, document and data analysis.

We argue that advocacy coalition and institutional arrangements frameworks combined are needed to understand Enimpacto’s complexity. The strategy presented an extensive multiple-actor articulation involving shared beliefs that were also important to gather support on recreating and expanding Enimpacto when external events threatened its continuity. Yet, it presented important challenges on how to achieve consensus and alignment regarding important concepts and regulation strategy among the actors and manage the public policy governance and activities implementation.

We combine institutional arrangements and advocacy coalition frameworks and apply them to analyze a public policy composed of actors of multiple sectors that play an active advocacy coalition role. We also present empirical evidence that elements of the advocacy coalition framework add analytical elements to institutional arrangements literature and how they affect each other. We point to two important elements of the institutional arrangements framework (territoriality and subsidiarity) that were not initially considered by ENIMPACTO and were later incorporated because of tensions in the field. We provide empirical evidence of the incipient role that public administration can play in promoting social enterprises' agenda that might base similar strategies to boost social enterprises in other locations.

This paper aims to determine the conditions for the core of the Triple Helix game to exist. The Triple Helix of university-industry-government relationships is a three-person cooperative game with transferable utility. Then, the core, the Shapley value and the nucleolus were used as indicators of the synergy within an innovation system. Whereas the Shapley value and the nucleolus always exist, the core may not.

The core of a three-person cooperative game with transferable utility exists only if and only if the game is convex. The paper applies the convexity condition to the Triple Helix game.

The Triple Helix game is convex if and only if there is output within the system; it is strictly convex if and only if all the three bilateral and the trilateral relationships have an output.

Convex games are competitive situations in which there are strong incentives towards the formation of large coalitions; therefore, innovation actors must cooperate to maximise their interests. Furthermore, a Triple Helix game may be split into subgames for comprehensive analyses and several Triple Helix games may be combined for a global study.

This paper extends the meaning of the Shapley value and the nucleolus for Triple Helix innovation actors: the Shapley value indicates the quantity a player wins because of the coalitions he involves in and the nucleolus the return for solidarity of an innovation actor.

Social media have become the main channel of direct communication between members of parliament and constituents. The study analyzes the content in all Israeli MPs' Facebook channels throughout an entire term of parliament and asks if the results are consistent with the equalization or the normalization hypotheses.

The study uses automatic analysis to produce a birds-eye-view of the content uploaded to the Facebook pages of all Israeli MPs during a full term of parliament. All 106 MP pages were automatically scraped. Some complementary information was added to each post in the dataset, such as post length (number of words) and whether the page belongs to a member of the opposition or coalition. The total of 441,974 posts was analyzed to compare engagement and publication rates between pages, coalition vs opposition MPs, MPs vs users etc.

The findings demonstrate that the MP-Facebook sphere is non-egalitarian, in that it follows skewed distributions by MPs in terms of post publication and engagement rates; non-inclusive, in that pages of coalition members receive significantly much more engagement vis-a-vis pages of members of the oppositions; and “top-down”, in that MP-authored posts receive dramatically more engagement then user-authored posts, suggesting MPs have a near-monopoly on setting the agendas manifest in their pages, while users have extremely limited agenda-setting capabilities in these pages.

Previous studies have looked at the character of the interactions between MPs and constituents on the Internet and particularly on online social media. Yet, to the best of the authors’ knowledge, no study provides a birds-eye-view of the content in all MPs' Facebook channels throughout a full term of parliament. Such an analysis provides a more comprehensive understanding of the character and dynamics of conversations that take place in such arenas.

This paper aims to propose an integrated use of balanced scorecard (BSC), data envelopment analysis (DEA) and game theory approach as an enhanced performance measurement technique to determine and rank the importance of manufacturing indicators of a steel company as a real case study.

An efficiency change ratio is defined to examine the characteristic function of each coalition which is super-additive. Then, the Shapley value index is used as the solution of the cooperative game to determine the importance of the BSC indicators of the company and rank order them.

The results reveal that “profitability rate” is the most important BSC indicator, whereas “customer satisfaction” is the least significant one. The ranking order of the importance of all BSC indicators makes it possible for the senior managers of the organization to realize the importance of each index separately and to improve the profitability and the number of customers by presenting programs according to the budget and time constraints.

The main contribution of this paper lies in the adoption of a game theory approach to performance measurement in the industrial sector that determines and ranks the importance of manufacturing indicators.