Equilibrium existence and uniqueness in network games with additive preferences

Rébillé, Yann; Richefort, Lionel

doi:10.1016/j.ejor.2013.07.014

Cited by 7 publications

(7 citation statements)

References 24 publications

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“…This condition is known to guarantee the uniqueness of PSNE in network games of strategic complements or strategic substitutes (Ballester et al, 2006;Corbo et al, 2007;Ballester and Calvó-Armengol, 2010). Recent research on the uniqueness of PSNE in network games of strategic substitutes has moved beyond this spectral condition, showing that the lowest eigenvalue is key to PSNE outcomes when the network is undirected (Bramoullé et al, 2013;Rébillé and Richefort, 2013). In network games of strategic complements, there is no equilibrium whenever A0 is not met (Ballester et al, 2006;Corbo et al, 2007;Ballester and Calvó-Armengol, 2010).…”

Section: Discussionmentioning

confidence: 99%

Influence and Social Tragedy in Networks

Rébillé¹,

Richefort²

2015

Revue d'Économie Politique

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We model agents in a network game of strategic complements and negative externalities. Sufficient conditions for the existence of a unique Nash equilibrium and of a unique social optimum are established. Under these conditions, we find that players with more vulnerable locations in the network exert more effort at equilibrium, and that the most influential players should exert less effort at efficiency. We then find structural conditions under which each player exerts strictly more effort than her efficient level, whether the social optimum be interior or not.

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Section: Discussionmentioning

confidence: 99%

Influence and Social Tragedy in Networks

Rébillé¹,

Richefort²

2015

Revue d'Économie Politique

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“…See Bramoullé and Kranton (2007), Bloch and Zenginobuz (2007) and Bramoullé et al (2014) for the case of linear best responses. For the non-linear case, see Bramoullé et al (2014), Rébillé and Richefort (2014) and Allouch (2015).…”

Section: A Model Of Impure Altruism With Multiple Public Goodsmentioning

confidence: 99%

“…where b ij : R + → R + is a i 's benefit from p j 's total supply. Following the same lines as in the proofs of Lemma 1 and Theorem 2 in Rébillé and Richefort (2015), a sufficient condition for the uniqueness of a Nash equilibrium is that the Jacobian matrix of marginal utilities be a strictly row diagonally dominant matrix 13 , which here is equivalent to…”

Section: Existence Uniqueness and Local Stability Of The Nash Equilimentioning

confidence: 99%

Warm-glow giving in networks with multiple public goods

Richefort

2018

Int J Game Theory

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This paper explores a voluntary contribution game in the presence of warm-glow effects. There are many public goods and each public good benefits a different group of players. The structure of the game induces a bipartite network structure, where players are listed on one side and the public good groups they form are listed on the other side. The main result of the paper shows the existence and uniqueness of a Nash equilibrium. The unique Nash equilibrium is also shown to be locally asymptotically stable. Then the paper provides some comparative statics analysis regarding pure redistribution, taxation and subsidies. It appears that small redistributions of wealth may sometimes be neutral, but generally, the effects of redistributive policies depend on how public good groups are related in the contribution network structure.

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“…This question has been studied in detail for the case of a single public good. Several conditions have been established, whether the best replies are linear (see, e.g., Bloch and Zenginobuz, 2007;Ballester and Calvó-Armengol, 2010;Bramoullé et al, 2014) or non-linear (see, e.g., Rébillé and Richefort, 2014;Allouch, 2015). However, the more realistic case of several public goods has received much less attention.…”

Section: Equilibrium Uniquenessmentioning

confidence: 99%

“…5 Under complete information 6 , a uniqueness condition that depends on network structure only is established for three cases: linear best responses and unipartite network (Corbo et al, 2007;Ballester and Calvó-Armengol, 2010;Bramoullé et al, 2014), linear best responses and bipartite network (Ilkiliç, 2011), and non-linear best responses and unipartite network (Rébillé and Richefort, 2014;Allouch, 2015). Here we also study a fourth case, of non-linear best responses and bipartite network, which generalizes the three other cases.…”

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confidence: 99%

Networks of Many Public Goods with Non-Linear Best Replies

Rébillé

Richefort

2015

SSRN Journal

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We model a bipartite network in which links connect agents with public goods. Agents play a voluntary contribution game in which they decide how much to contribute to each public good they are connected to. We show that the problem of finding a Nash equilibrium can be posed as a non-linear complementarity one. The existence of an equilibrium point is established for a wide class of individual preferences. We then find a simple sufficient condition, on network structure only, that guarantees the uniqueness of the equilibria, and provide an easy procedure for building networks that respects this condition.

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Equilibrium existence and uniqueness in network games with additive preferences

Cited by 7 publications

References 24 publications

Influence and Social Tragedy in Networks

Influence and Social Tragedy in Networks

Warm-glow giving in networks with multiple public goods

Networks of Many Public Goods with Non-Linear Best Replies

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