Partial cooperation in strategic multi-sided decision situations

We consider a normal-form game in which there is a single exogenously given coalition of cooperating players that can write a binding agreement on pre-selected actions. The actions representing other dimensions of the strategy space remain under the sovereign, individual control of the players. We consider a standard extension of the Nash equilibrium concept denoted as a partial cooperative equilibrium as well as an equilibrium concept in which the coalition of cooperators has a leadership position. Existence results are stated and we identify conditions under which the various equilibrium concepts are equivalent. We apply this framework to existing models of multi-market oligopolies and international pollution abatement. In a multi-market oligopoly, typically, a merger paradox emerges in the partial cooperative equilibrium. The paradox vanishes if the cartel attains a leadership position. For international pollution abatement treaties, cooperation by a sufficiently large group of countries results in a Pareto improvement over the standard tragedy of the commons outcome described by the Nash equilibrium.     

Status-seeking in hedonic games with heterogeneous players

We study group formation by heterogeneous players when players’ preferences are dictated by status-seeking. Status can be intrinsic or associative. Considering these two types of status as either complements or substitutes results in non-emptiness of the core of the corresponding games and allows for a full characterization of the core stable outcomes.     

Strategic behavior under partial cooperation

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.