In this lecture, we review the classic "Prisoner's Dilemma" game-theoretic model of the challenges of cooperation in a world of strong temptation to defect, and then we contrast it with two other models that are possibly more realistic (but similarly simple) models of cooperation and competition in the real world -- the stag hunt model and the Hawk–Dove model. The stag hunt is a model of positive externalities, like those that characterize public goods games. We discuss how the stag hunt is like a Prisoner's Dilemma with a stronger reward for cooperation (stronger positive externalities) than a temptation to defect. This lets us introduce coordination games, assurance games, and correlated equilibria. In general, the stag hunt shows us that there are more fundamental issues to cooperation beyond incentives -- there are barriers to the coordination of actions and information limitations that prevent cooperation even when it is favored. We extend the stag hunt to the N-player stag hunt, which is a better model of public goods problems, in order to introduce the idea of a mixed (Nash) equilibrium. We then close with an introduction of the Hawk–Dove game, which is a model of competition and negative externalities that often characterize common-pool resources problems ("tragedies of the commons"). We will continue discussion of the Hawk–Dove next time and explore why it is a better match to tragedy of the commons problems than the Prisoner's Dilemma.
Whiteboard notes for this lecture can be found at: https://www.dropbox.com/s/qajxqqx5a3z1jn8/SOS220-LectureH3-2023-04-13-Game_Theoretic_Models_of_Social_Interactions-Part_2.pdf?dl=0
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