**Research**

**PUBLICATIONS (My Citations at google scholar here, Ideas/Repec profile here, RG profile here) **

**Laruelle, A., N. Navarro, and R. Escobedo (2016) "Proficiency, Attitude and Conventions in MinorityLanguages"**

*. Sociological Methods and Research.*Forthcoming. Older version: Ikerlanak Working Paper IL 92/15. Dept. FAE I, EHU/UPV.

**Abstract: **In this paper we study a simple mathematical model of a bilingual community in which all agents are fluent in the majority language but only a fraction of the population has some degree of proficiency in the minority language. We investigate how different distributions of proficiency, combined with the speakers' attitudes towards or against the minority language, may influence its use in pair conversations.

**Navarro, N. (2014) "Expected Fair Allocation in Farsighted Network Formation",**

*Social Choice and Welfare*43 (2): 287-308. Older version: Ikerlanak Working Paper IL 70/13. Dept. FAE I, EHU/UPV.

**Abstract:**I consider situations in which a group of players extracts a value if they organise themselves in different network structures, and I define a solution concept to describe the decentralised decision that determines the network formation process and the allocation of the value. I demonstrate that there is a solution concept satisfying discounted expected versions of pairwise stability (Jackson and Wolinsky, 1996) and fairness (Myerson, 1977a) jointly with the requirement that the allocation rule be component efficient if the players' discount factor is sufficiently low.

**Danthine, S. and N. Navarro, (2013)**

**"How to Add Apples and Pears: Non-Symmetric Nash Bargaining and the Generalized Joint Surplus",**

*Economics Bulletin*Vol. 33 No. 4 pp. 2840-2850. Online appendix available here. Older version: Malaga Economic Theory Research Center Working Papers WP 2010-4.

**Abstract:**We find how to compute the non-symmetric Nash bargaining solution by means of a generalized property of linear division of the joint surplus, as an alternative of solving the maximization of the generalized Nash product. This generalized property of linear division in the non-symmetric Nash bargaining solution can be applied to the case when bargainers use different utility scales, in particular when they have different attitudes toward risk, as is the case of a risk neutral firm and a risk averse individual. The surplus each agent receives has to be expressed in compatible, or comparable, units across agents. This is contrary to what has been believed in the labor literature, where many authors have partially expressed surpluses in comparable units. We finally illustrate the conditions of applicability of our result by means of a well-known example.

**Navarro, N. and A. Perea, (2013) "A Simple Bargaining Procedure for the Myerson
Value", ***The BE Journal of Theoretical Economics (Advances) *13 (1): 1-20. Web Appendix here. Older version: Carlos III working paper 2001-21.

**Abstract**: We consider situations where the cooperation and negotiation
possibilities between pairs of agents are given by an undirected graph.
Every connected component of agents has a value, which is the total
surplus the agents can generate by working together. We present a
simple, sequential, bilateral bargaining procedure, in which at every
stage the two agents in a link, (i,j) bargain about their share from
cooperation in the connected component they are part of. We show that
this procedure yields the Myerson value (Myerson, 1977) if the marginal
value of any link in a connected component is increasing *in the number of links* in that connected component.

**Navarro, N. (2012) "Price
and Quality Decisions under Network Effects"**, *Journal of Mathematical Economics*. 48 (5): 263-270. Web appendix here. Older versions: "Quality Provision under
Referral Consumption," October 2008**. **Malaga Economic Theory
Research Center Working Papers WP 2008-12 and "Asymmetric Information, Word-of-mouth and
Social Networks: from the market for lemons to efficiency," January
2006. CORE Discussion Paper Series 2006/02. Université Catholique de
Louvain.

**Abstract**: I analyse monopoly pricing and quality decisions under network effects.
High quality premium and low quality punishment are found to depend on
how the impact of marginal costs on quality relates to the intensity of
the network effect and the optimism of the producer about final demand.
More precisely, marginal costs have to be low enough (but not too low)
with respect to the intensity of the network effects and/or the optimism
about final demand so that higher prices reflect higher quality. A
similar conclusion can be drawn about incentives for quality provision,
whenever quality is considered endogenous together with price.

**Navarro, N. and R. Veszteg (2011) ****"Demonstration of Power: Experimental Results on Bilateral Bargaining",** *Journal of Economic Psychology* 32 (5): 762-772.

**Abstract**: We test the empirical effectiveness of two theoretical proposals to
equilibrate bargaining power in bilateral bargaining. Our experimental
design is based on the two-player versions of the multibidding game (Pérez-Castrillo & Wettstein, 2001) and the bid-and-propose game (Navarro & Perea, 2005).
Both models build on the ultimatum game and balance parties’ bargaining
power by auctioning the role of the proposer in the first stage. We
find that proposers learn how to send an acceptable proposal by trial
and error, guided by responders’ rejections. The observed behavior
stabilizes for the final experimental rounds and the payoff gap between
the proposer and the responder seems to close down. However, the
strategies chosen by subjects are remarkably different from the
theoretical ones.

**Navarro, N., (2010) "Flexible Network Rules for Identified Externalities", ***Games and Economic Behavior* 69 (2): 401-410. A previous version was circulating under the title "A Sensitive Flexible-network Approach", Malaga Economic Theory Research Center Working Papers WP 2008-2.

**Abstract**: I propose three modifications of Jackson's flexible network axiom (Jackson, 2005)
when the structure of externalities across components have been
identified. The first one takes into account the information about the
externalities across components. The second one allows for coalitional
deviations once the network has been formed. Finally, the third one
tries to find a compromise with component efficiency (Myerson, 1977a).

**Navarro, N., (2007) ****"Fair Allocation in Networks with Externalities", ***Games and Economic Behavior* 58 (2): 354 -364. The omitted proof at the end of this paper is available here.

**Abstract**:* *I prove existence and uniqueness of a component efficient and fair
allocation rule when the value of the network is allowed to exhibit any
type of externalities across its components. This is done by means of a
new specification of the value function, generalizing partial results
appearing in Myerson [Myerson, R.B., 1977a. Graphs and cooperation in
games. Math. Operations Res. 2, 225–229], Feldman [Feldman, B.E., 1996.
Bargaining, coalition formation and value. PhD dissertation. State
University of New York at Stony Brook] and Jackson and Wolinsky
[Jackson, M.O., Wolinsky, A., 1996. A strategic model of social and
economic networks. J. Econ. Theory 71, 44–74]. This component efficient
and fair allocation rule is found closely related to an extension of the
Shapley value to TU-games in partition function form proposed by
Myerson [Myerson, R.B., 1977b. Values of games in partition function
form. Int. J. Game Theory 6 (1), 23–31].

*Unpublished work and work-in-progress*:

**"**

**Infant Food Rejection Risk: Another Poverty Trap"**

**(joint with Samuel Danthine)**, November 2016.

**"**

**Experiments on unstructured bargaining**

**"**

**(joint with Róbert Veszteg)**, November 2016.

**"**

**Forward-Looking Pairwise Stability in Networks with Externalities across Components",**May 2013. Ikerlanak Working Paper IL 71/13. Dept. FAE I, EHU/UPV.

**"(In)Efficient Interbank Networks" (joint with F. Castiglionesi)**Cahier du GREThA 2016-13

*GREThA*(Groupe de Recherche en Économie Théorique et Appliquée), CNRS, UMR 5113, Université de Bordeaux