Cooperation through social influence

Molinero, Xavier; Riquelme, Fabián; Serna, María

doi:10.1016/j.ejor.2014.11.006

Cited by 41 publications

(58 citation statements)

References 39 publications

(54 reference statements)

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“…Here we have a tuple (G, w, f , q, N), where (G, w, f ) is a both vertex and edge-labeled directed graph, N ⊆ V (G) and for any X ⊆ N, X represents a winning coalition if and only if it can spread its influence to at least q vertices in the graph (Molinero et al, 2015b) (see also Riquelme, 2014). It is also known that influence games capture the complete class of simple games and that some simple games require a representation as unweighted influence games with exponential number of vertices.…”

Section: Discussionmentioning

confidence: 99%

Forms of representation for simple games: Sizes, conversions and equivalences

Molinero

Riquelme

Serna

2015

Mathematical Social Sciences

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h i g h l i g h t s• We survey the main forms of representation for simple games, regular games and weighted games in literature.• We study the complexity of the conversion problem, i.e., the problem of computing a representation of a simple game given another representation.• We prove that several changes of representation that require exponential time can be solved with polynomial-delay. a b s t r a c tSimple games are cooperative games in which the benefit that a coalition may have is always binary, i.e., a coalition may either win or loose. This paper surveys different forms of representation of simple games, and those for some of their subfamilies like regular games and weighted games. We analyze the forms of representations that have been proposed in the literature based on different data structures for sets of sets. We provide bounds on the computational resources needed to transform a game from one form of representation to another one. This includes the study of the problem of enumerating the fundamental families of coalitions of a simple game. In particular we prove that several changes of representation that require exponential time can be solved with polynomial-delay and highlight some open problems.

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Section: Discussionmentioning

confidence: 99%

Forms of representation for simple games: Sizes, conversions and equivalences

Molinero

Riquelme

Serna

2015

Mathematical Social Sciences

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“…They solve such intervention problems by exploiting the singular value decomposition of strategic interaction matrices. [54] apply another approach, based on cooperative games, to influence. More precisely, they model an influence game as a cooperative simple game in which a team of agents succeeds if it is able to convince enough agents to participate in the task, e.g., to vote in favor of a decision.…”

Section: Related Literaturementioning

confidence: 99%

Opinion formation and targeting when persuaders have extreme and centrist opinions

Rusinowska

Taalaibekova

2019

Journal of Mathematical Economics

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We consider a model of competitive opinion formation in which three persuaders characterized by (possibly unequal) persuasion impacts try to influence opinions in a society of individuals embedded in a social network. Two of the persuaders have the extreme and opposite opinions, and the third one has the centrist opinion. Each persuader chooses one individual to target, i.e., he forms a link with the chosen individual in order to spread his own "point of view" in the society and to get the average long run opinion as close as possible to his own opinion. We examine the opinion convergence and consensus reaching in the society. We study the existence and characterization of pure strategy Nash equilibria in the game played by the persuaders with equal impacts. This characterization depends on influenceability and centrality (intermediacy) of the targets. We discuss the effect of the centrist persuader on the consensus and symmetric equilibria, compared to the framework with only two persuaders having the extreme opinions. When the persuasion impacts are unequal with one persuader having a sufficiently large impact, the game has only equilibria in mixed strategies.

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“…See the details how to construct an influence game from a simple game, and how to construct a simple game from an influence game, in [18]. Note that there exists a construction such that the influence game which define a simple game just use unweighted influence graphs.…”

Section: Theorem 2 ([18])mentioning

confidence: 99%

“…Each step can be computed in polynomial time whether the simple game Γ is given by either (N, W) or (W m ) (see Theorem 1 in [18]). …”

Section: Theorem 2 ([18])mentioning

confidence: 99%

Combinatorial structures to modeling simple games and applications

Molinero

2017

AIP Conference Proceedings

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Abstract. We connect three different topics: combinatorial structures, game theory and chemistry. In particular, we establish the bases to represent some simple games, defined as influence games, and molecules, defined from atoms, by using combinatorial structures. First, we characterize simple games as influence games using influence graphs. It let us to modeling simple games as combinatorial structures (from the viewpoint of structures or graphs). Second, we formally define molecules as combinations of atoms. It let us to modeling molecules as combinatorial structures (from the viewpoint of combinations). It is open to generate such combinatorial structures using some specific techniques as genetic algorithms, (meta-)heuristics algorithms and parallel programming, among others.

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Cooperation through social influence

Cited by 41 publications

References 39 publications

Forms of representation for simple games: Sizes, conversions and equivalences

Forms of representation for simple games: Sizes, conversions and equivalences

Opinion formation and targeting when persuaders have extreme and centrist opinions

Combinatorial structures to modeling simple games and applications

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