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Alexander S. Belenky.
Zlotnik A. A., Chetverushkin B. N.
Doklady Mathematics. 2020. Vol. 101. No. 1. P. 35-41.
In bk.: Network Algorithms, Data Mining, and Applications. NET, Moscow, Russia, May 2018. Springer, 2020. P. 49-70.
Piontkovski D., La Scala R., Tiwari S.
arxiv.org. math. Cornell University, 2019
Topic: Preemptive versus Counter Offers
We consider an ultimatum-game setup, which has two key non-standard features: (1) The responder has an initial fallback position, which is her private information (except for the complete-information case), and (2) she can improve her initial fallback position further by means of a costly investment, which does not improve the joint surplus and thus is a deadweight loss. There are two sources of inefficiency: disagreement possibility and the deadweight-loss investment. The proposer ends up either making a counter offer to the responder after finding out the responder's type as well as her best outside offer or makes a particular preemptive offer before her investment and thus before the uncertainty about her type is not resolved (except for the incomplete-information case). Thus, any preemptive offer aims for agreement before investment, which, if accepted, avoids the deadweight-loss investment, and thus inefficiency; if rejected, it always leads to inefficiency as players receive their fallback payoffs. A counter offer, on the other hand, always guarantees agreement, but only after investment cost is incurred, and thus it is inefficient. We consider the complete-information as well as the no- and noisy-information cases. We find that in the complete-information case the unique equilibrium offer is a preemptive offer which always achieves efficiency and leads to agreement. In the other cases, if the proposer's (prior or posterior) belief about the responder's type is not precise enough, he might prefer to wait to make a counter offer until after the responder makes her investment and receives outside offers. It turns out that more precise information reduces both types of inefficiency by leading to preemptive offers which are accepted with higher probability. We also show that our results are robust to various extensions such as risk aversion by players, multiple offers by the proposer, continuum of responder types and type-dependent investment costs.
the joint seminar of Higher School of Economics on political economy, International Center for the Study of Institutions and Development (ICSID) and NES Center for the Study of Diversity and Social Interaction (NES CSDSI) was held on April 23.
Moderators: Alexei Zakharov (HSE), Konstantin Sonin (HSE, The University of Chicago Harris School of Public Policy)