Stable sets for exchange economies with interdependent preferences

Abstract

We introduce the notion of stable sets with externalities and prove its existence. Stable sets provide a successful alternative to core notions of externalities (i.e., α-core, β-core and strong Nash equilibrium), which are typically empty. However, the stable sets do exist in situations where the above core notions are empty

Stable cores in information graph games

“…Characterization of those coalitional games with a stable core is still an open question although a stronger notion of the stable core is characterized in Jain and Vohra (2010). Stable sets have been found on several classes of games, such as assignment games (Núñez and Rafels, 2013), linear production games Shitovitz, 2000, 2010), pillage games (MacKenzie et al, 2015), patent licensing games (Hirai and Watanabe, 2018), matching problems (Herings et al, 2017), tournaments (Brandt, 2011), voting games (Talamàs, 2018), and exchange economies (Graziano et al, 2015(Graziano et al, , 2017. Non-cooperative foundations of stable sets can be found in Anesi (2010); Diermeier and Fong (2012).…”

Core and stable sets of exchange economies with externalities

“…When there is an externality in consumption, the utility function of each trader depends not only on his own consumption bundle but also on the consumption profile of some or all of the remaining consumers in the economy. As a consequence, several dominance relations can be considered according to how the countercoalition N \ S reacts to a deviation by S. In Graziano et al (2017), we introduce the notion of stable sets with externalities for economies with a finite number of commodities and a finite set of agents and prove their existence and uniqueness for different classes of dominance relations. Precisely, we adopt a taxonomy based on the viewpoint of the blocking coalition S towards the reaction of the counter-coalition N \ S 1 .…”

Social loss with respect to the core of an economy with externalities

“…3 See e.g. the results for cooperative solutions in Dufwenberg et al (2011), Velez (2016, Graziano et al (2017).…”

“…A related approach is employed in delMercato (2006a) to study the non emptiness of the core for a pure exchange economy without externalities, and inGraziano et al (2017) to study the existence and the uniqueness of stable sets for exchange economies with interdependent preferences.…”