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Our main objective hear to say what we can regarding the emergence of stable club networks\u2014and therefore, stable coalition structures\u2014based on the stability properties of strategically determined equilibrium network formation dynamics. Because club networks are layered networks, our work here can be thought of as a first work on the strategic dynamics of layered networks. In addition to constructing a discounted stochastic game model (i.e., a <jats:italic>DSG<\/jats:italic> model) of club network formation, (1) we show that our <jats:italic>DSG<\/jats:italic> of network formation possesses a stationary Markov perfect equilibrium in players\u2019 membership-action strategies; (2) we identify the assumptions on primitives which ensure that the induced equilibrium Markov process of layered club network formation satisfies the Tweedie Stability Conditions (Tweedie in Stoch Process Appl 92:345\u2013354, 2001) and (3) we show that, as a consequence, the equilibrium Markov network formation process generates a unique decomposition of the set of state-network pairs into a transient set together with <jats:italic>finitely many<\/jats:italic> basins of attraction. Moreover, we show that if there is a basin containing a <jats:italic>vio set (a visited infinitely often set)<\/jats:italic> of club networks sufficiently close together, then the coalition structures across club networks in the vio set will be the same (i.e., closeness across networks in a vio set leads to invariance in coalition structure across networks in a vio set).<\/jats:p>","DOI":"10.1007\/s13235-022-00478-4","type":"journal-article","created":{"date-parts":[[2022,10,8]],"date-time":"2022-10-08T19:04:46Z","timestamp":1665255886000},"page":"636-668","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Layered Networks, Equilibrium Dynamics, and Stable Coalitions"],"prefix":"10.1007","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3560-8716","authenticated-orcid":false,"given":"Jing","family":"Fu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7485-9940","authenticated-orcid":false,"given":"Frank","family":"Page","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jean-Pierre","family":"Zigrand","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,10,8]]},"reference":[{"key":"478_CR1","volume-title":"Infinite dimensional analysis: a Hitchhiker\u2019s guide","author":"CD Aliprantis","year":"2006","unstructured":"Aliprantis CD, Border KC (2006) Infinite dimensional analysis: a Hitchhiker\u2019s guide, 3rd edn. 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