Abstract: We experimentally test welfarism and scale invariance, two prominent simplifying assumptions that are often used to characterize bargaining solutions in theoretical models. Our study relies on a context-rich bargaining environment and varies the parameters of the bargaining problem along with the information that bargaining parties have about each other. Under the auxiliary assumption of selfishness, it aims at understanding whether bargaining is guided by abstract utilities as assumed by the classic version of cooperative bargaining theory or rather by comparisons in observables (e.g., money) as often assumed by behavioral models of decision-making. The experimental results show that welfarism and scale invariance are supported when the relevant information is only privately known. In general, bargaining outcomes are robust to rescaling that only affects the anchoring points of the utility scale (welfarism), but not to rescaling that affects the units on the utility scale (scale invariance). Overall, our experimental data deliver scarce empirical support to classic theoretical bargaining solutions based on abstract utility units. 

Abstract: This paper aims to characterize classes or types of values for transferable utility games in partition function form, accounting for externalities where the worth of a coalition depends on the cooperation structure outside it. We follow an axiomatic approach, focusing on values that represent two-stage anticipations. In the first stage, the worth of each coalition is computed as a weighted average of each of its possible worths (depending on the cooperation structure outside the coalition). In the second stage, these anticipated worths for all coalitions are used to derive the value for participating in the game, treating the game as if it were one without externalities. We extend previous work by Macho-Stadler et al. (Journal of Economic Theory, 135, 339–356, 2007; Games and Economic Behavior, 108, 49–64, 2018) beyond Efficiency and Symmetry, providing axiomatic characterizations for values based on both exogenous and endogenous weights. Additionally, we model first-step anticipations as operators from games with externalities to games without externalities, characterizing the family of weighted average operators. We also explore the relationship of the average approach with marginalism, highlighting that marginalist values constructed from the average approach require weights satisfying a consistency condition, termed recursivity, but not necessarily a symmetry condition. Finally, we contrast these results with Grabisch and Funaki’s (2012) coalition formation value, which involves averages over dynamic coalition formation processes but cannot be constructed from the average approach.

Abstract: We report experimental results and test axiomatic models of unstructured bargaining by checking the empirical relevance of the underlying axioms. Our data support strong efficiency, symmetry, independence of irrelevant alternatives and monotonicity, and reject scale invariance. Individual rationality and midpoint domination are violated by a significant fraction of agreements that implement equal division in highly unequal circumstances. Two well-known bargaining solutions that satisfy the confirmed properties explain the observed agreements reasonably well. The most frequent agreements in our sample are the ones suggested by the equal-division solution. In terms of the average Euclidean distance, the theoretical solution that best explains the data is the deal-me-out solution (Sutton, 1986; Binmore et al., 1989, 1991). Popular solutions that satisfy scale invariance, individual rationality, and midpoint domination, as the well-known Nash or Kalai-Smorodinsky bargaining solutions, perform poorly in the laboratory.

Abstract: We study the efficiency properties of the formation of an interbank network. Banks face a trade‐off by establishing connections in the interbank market. On the one hand, banks improve the diversification of their liquidity risk and therefore can obtain a higher expected payoff. On the other hand, banks not sufficiently capitalized have risk‐shifting incentives that expose them to the risk of bankruptcy. Connecting to such risky banks negatively affects expected payoff. We show that both the optimal and the decentralized networks are characterized by a core‐periphery structure. The core is made of the safe banks, whereas the periphery is populated by the risky banks. Nevertheless, the two network structures coincide only if counterparty risk is sufficiently low. Otherwise, the decentralized network is underconnected as compared to the optimal one. Finally, we analyze mechanisms that can avoid the formation of inefficient interbank networks.

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.

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.

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.

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. 

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.

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.

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).

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].