A Behavioral Model of Bargaining with Endogenous Types

We enrich a simple two-person bargaining model by introducing "behavioral types" who concede more slowly than does the average person in the economy. The presence of behavioral types profoundly influences the choices of optimizing types. In equilibrium, concessions are calculated to induce "reciprocity": a substantial concession by player i is followed by a period in which j is much more likely to make a concession than usual. This favors concessions by i that are neither very small nor large enough to end the bargaining immediately. A key difference from the traditional method of perturbing a game is that the actions of our behavioral types are not specified in absolute terms, but relative to the norm in the population. Thus their behavior is determined endogenously as part of a social equilibrium.Bargaining, Reputation, Endogenous type

Markov equilibria in a model of bargaining in networks

We study the Markov perfect equilibria (MPEs) of an infinite horizon game in which pairs of players connected in a network are randomly matched to bargain. Players who reach agreement are removed from the network without replacement. We establish the existence of MPEs and show that MPE payoffs are not necessarily unique. A method for constructing pure strategy MPEs for high discount factors is developed. For some networks, we find that all MPEs are asymptotically inefficient as players become patient

Bargaining and efficiency in networks

We study an infinite horizon game in which pairs of players connected in a network are randomly matched to bargain over a unit surplus. Players who reach agreement are removed from the network without replacement. The global logic of efficient matchings and the local nature of bargaining, in combination with the irreversible exit of player pairs following agreements, create severe hurdles to the attainment of efficiency in equilibrium. For many networks all Markov perfect equilibria of the bargaining game are inefficient, even as players become patient. We investigate how incentives need to be structured in order to achieve efficiency via subgame perfect, but non-Markovian, equilibria. The analysis extends to an alternative model in which individual players are selected according to some probability distribution, and a chosen player can select a neighbor with whom to bargain

Evolutionary Stability in a Reputational Model of Bargaining

A large and growing literature on reputation in games builds on the insight that the possibility of one or more players being other than fully rational can have significant effects on equilibrium behavior. This literature leaves unexplained the presence of behavioral players in the first place, and the particular forms of irrationality assumed. In this paper we endogenize departures from rationality on the basis of an evolutionary stability criterion, under the assumption that rational players incur a cost which reflects the greater sophistication of their behavior. This cost may be arbitrarily small. Within the context of a reputational model of bargaining, we show that evolutionary stability necessitates the presence of behavioral players, and places significant restrictions on the set of behavioral types that can coexist. It is consistent, however, with a broad variety of outcomes ranging from immediate agreement to complete surplus dissipation. The long run population share of behavioral types is greatest at states in which surplus dissipation is either negligible or almost complete.Reputation, Evolutionary Stability, Bargaining