Identification of efficient equilibria in multiproduct trading with indivisibilities and non-monotonicity

This paper focuses on multiproduct trading with indivisibilities and where a representative agent may have non-monotonic preferences. In this framework, the set of firms' profits (which comes from efficient subgame perfect Nash equilibria) is the Pareto frontier of some projection of the core of the game. We show that under monotonicity efficient subgame perfect Nash equilibria are achieved by single offers and the equilibrium characterization is easy to obtain. When dealing with non-monotonic preferences the problem becomes more challenging. Then, we define a pair of primal-dual linear programming problems that fully identifies the core of the game. A set of modified versions of the dual programming problem characterizes the Pareto-optimal frontier of the core projection on firms' coordinates. Although this approach gives us the payoff-equivalence class (Strong Nash equilibria) of all the efficient subgame perfect Nash equilibria, the number of problems to be solved may be huge.