On the exhaustiveness of truncation and dropping strategies in many-to-many matching markets

We consider two–sided many–to–many matching markets in which each worker may work for multiple firms and each firm may hire multiple workers. We study individual and group manipulations in centralized markets that employ (pairwise) stable mechanisms and that require participants to submit rank order lists of agents on the other side of the market. We are interested in simple preference manipulations that have been reported and studied in empirical and theoretical work: truncation strategies, which are the lists obtained by removing a tail of least preferred partners from a preference list, and the more general dropping strategies, which are the lists obtained by only removing partners from a preference list (i.e., no reshuffling). We study when truncation / dropping strategies are exhaustive for a group of agents on the same side of the market, i.e., when each match resulting from preference manipulations can be replicated or improved upon by some truncation / dropping strategies. We prove that for each stable mechanism, truncation strategies are exhaustive for each agent with quota 1 (Theorem 1). We show that this result cannot be extended neither to group manipulations (even when all quotas equal 1 – Example 1), nor to individual manipulations when the agent’s quota is larger than 1 (even when all other agents’ quotas equal 1 – Example 2). Finally, we prove that for each stable mechanism, dropping strategies are exhaustive for each group of agents on the same side of the market (Theorem 2), i.e., independently of the quotas.

Conflict and negotiation: a game theoretical approach

We study economic conflicts using a game theoretical approach. We model a conflict between two agents where each one has two possible strategies: cease-fire or neglect the truce. Under this setting, we use the concept of pre-donations, namely, a redefinition of the game where agents commit to transfer a share of their output to the other agent (Sertel, 1992), and explain under which conditions a system of pre-donations can facilitate a truce. We find that for conflicts involving high costs there is a distributive mechanism, acceptable for both parties, such that, the best strategy for both parties is Cease-Fire. However, in many cases there are no sufficient conditions for the scheme or pre-donations to be effective. We also analyze some limitations of this framework and extend the model in order to deal with some of these flaws. Finally, in order to illustrate the relevance of the theoretical results we briefly describe some of the circumstances that characterized the negotiation processes between the Colombian government and different illegal groups.