Abstract
We investigate how a group of players might cooperate with each other within the setting of a non-cooperative game. We pursue two notions of partial cooperative equilibria that follow a modification of Nash’s best response rationality rather than a core-like approach. Partial cooperative Nash equilibrium treats non-cooperative players and the coalition of cooperators symmetrically, while the notion of partial cooperative leadership equilibrium assumes that the group of cooperators has a first-mover advantage. We prove existence theorems for both types of equilibria. We look at three well-known applications under partial cooperation. In a game of voluntary provision of a public good we show that our two new equilibrium notions of partial cooperation coincide. In a modified Cournot oligopoly, we identify multiple equilibria of each type and show that a non-cooperator may have a higher payoff than a cooperator. In contrast, under partial cooperation in a symmetric Salop City game, a cooperator enjoys a higher return.
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Previous drafts were circulated under the title “Conflict and Cooperation in Symmetric Games Revisited” and “Partial Cooperation in Symmetric Games”.
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Chakrabarti, S., Gilles, R.P. & Lazarova, E.A. Strategic behavior under partial cooperation. Theory Decis 71, 175–193 (2011). https://doi.org/10.1007/s11238-011-9246-7
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DOI: https://doi.org/10.1007/s11238-011-9246-7