On the convergence to the Nash bargaining solution for action-dependent bargaining protocols

We consider a non-cooperative multilateral bargaining game and study an action-dependent bargaining protocol, that is, the probability with which a player becomes the proposer in a round of bargaining depends on the identity of the player who previously rejected. An important example is the frequently studied rejector-becomes-proposer protocol. We focus on subgame perfect equilibria in stationary strategies which are shown to exist and to be efficient. Equilibrium proposals do not depend on the probability to propose conditional on the rejection by another player. We consider the limit, as the bargaining friction vanishes. In case no player has a positive probability to propose conditional on his rejection, each player receives his utopia payoff conditional on being recognized. Otherwise, equilibrium proposals of all players converge to a weighted Nash bargaining solution, where the weights are determined by the probability to propose conditional on one's own rejection.     

The Hot Versus Cold Effect in a Simple Bargaining Experiment

In this paper, the strategy method's impact on behavior in sequential bargaining games is investigated. Besides the decision procedure (hot versus cold), we varied the second mover punishment costs (high versus low). Significant impacts of both treatment variables were observed. For example, second movers punished significantly more often in the hot version of the low cost game. Furthermore, first mover behavior was significantly different in the hot and cold versions of both games. In the hot games, first mover behavior suggests an expectation of decreased rewards and/or punishments from second movers. We observed, however, no decrease in reward and an increase in punishment. The hot cold variable only informs first movers that the decision procedure used by second movers has changed. Therefore, first mover behavior must be shaped by their perceived assessment concerning how second movers make decisions. We argue that first mover behavior can be explained by the interaction of two well-known psychological effects: the consensus and positive self-image effects.     

FEE VERSUS ROYALTY POLICY IN LICENSING THROUGH BARGAINING: AN APPLICATION OF THE NASH BARGAINING SOLUTION

In this paper, we consider a Cournot duopoly market in which the patent‐holding firm negotiates with its rival firm about payments for licensing a cost‐reducing innovation. Applying the Nash bargaining solution, we compare two licensing policies, a fixed fee and a royalty. Our results are as follows. Royalty licensing is better than fixed fee licensing for both firms if the innovation is not drastic. So, royalty licensing is always carried out. Moreover, though there exists a case in which consumers prefer fixed fee licensing, royalty licensing is always superior to fixed fee licensing from the social point of view.     

谈判能力与标价策略

厂商能够通过策略性地选择不标价销售,利用其较强的谈判能力获取更多的利益。当厂商谈判能力较弱时,厂商将选择标价以最大化其利润。考虑消费者的谈判成本,厂商选择不标价时,其利润和谈判能力呈倒U型关系。当厂商谈判能力过高时,由于消费者将无利可图而放弃购买,因而厂商将选择标价的策略。在一定条件下,厂商实施策略性不标价不是市场有效的,可以通过强制标价实现市场的有效性。     

Strategic step-by-step negotiation

We analyze a specific type of negotiation process where parties proceed in stages taking into consideration that negotiation may end prematurely with an inefficient agreement. Parties negotiate only one increasing pie, thereby avoiding inefficiencies which are typical for issue-by-issue negotiations. For ann-stage game, we prove the existence of a unique subgame-perfect equilibrium. We then show that step-by-step negotiation can only improve players' expected payoffs if negotiation in stages reduces the difference between their equilibrium offers. For this to occur, however, the risk of negotiation must be affected by the agenda of the bargaining problem.     

Nonconvex n-person bargaining: efficient maxmin solutions

Summary. This paper provides an axiomatic characterization of a family of so-called efficient maxmin solutions which can be seen as generalizations of the Kalai-Smorodinsky solution to nonconvex n-person bargaining problems. Moreover, it is shown that even though there are several efficient maxmin solutions for some bargaining problems, there is typically a unique efficient maxmin solution. Received: February 15, 2001; revised version: November 14, 2001     

A cake for Cournot

A cake division mechanism is presented that is equivalent in terms of the size of the pieces of the cake n players’ receive in equilibrium to the quantities that n firms in a Cournot oligopoly supply in equilibrium. This mechanism extends to equivalence between cake division and Nash’s ‘divide the dollar’ game.     

The structure of information networks

We develop a strategic model of information acquisition in networks where agents pay for all the pieces of information they acquire, including those through indirect links. The cost of information depends on the distance it traverses in the network. We consider two possibilities in this context: (1) costs increasing with distance, and (2) costs decreasing with distance. The paper also examines situations where it is more expensive to acquire information of higher value. We show that there is almost no divergence between the efficient and Nash equilibrium information architectures. We then study the effect of decay in networks where information through longer paths is cheaper. Finally, we also examine a model with costly link formation that combines both types of cost related assumptionsWe are grateful to Hans Haller, Rob Gilles, Susanne Maria Schmidt, Sumit Joshi, Georg Erber, Beth Allen, Mark Machina, Bob Martin, Johanna Francis, Cheryl Long, Raja Kali, Kaz Miyagiwa, Micheal Kosfeld, Bibhudutta Panda and two anonymous referees for helpful suggestions. The paper has further benefited from the comments of participants at Game Theory and Applications Mumbai 2003, Royal Economic Society Meetings 2003, SED 2004 and GAMES 2004. Sudipta Sarangi acknowledges the hospitality of DIW Berlin where a part of this research was carried out. Rajgopal Kannan acknowledges the support of NSF grants IIS-0329738 and IIS-0312632     

Learning to Accept in Ultimatum Games: Evidence from an Experimental Design that Generates Low Offers

Focusing on responder behavior, we report panel data findings from both low and high stakes ultimatum bargaining games. Whereas Slonim and Roth (1998) find that offers are rejected fairly equally across rounds in both low and high stakes games, we find that learning does take place, but only when there is sufficient money on the table. The disparate results can be reconciled when one considers the added power that our experimental design provides-detecting subtle temporal differences in responder behavior requires a data generation process that induces a significant number of proportionally low offers.     

On continuous-time Markov processes in bargaining

For bilateral stochastic bargaining procedures embedded in stable homogeneous continuous-time Markov processes, we show unusual limit results when time between rounds vanish. Standard convergence results require that some states are instantaneous.     

Universality of Nash components

We show that Nash equilibrium components are universal for the collection of connected polyhedral sets. More precisely for every polyhedral set we construct a so-called binary game—a game where all players have two pure strategies and a common utility function with values either zero or one—whose success set (the set of strategy profiles where the maximal payoff of one is indeed achieved) is homeomorphic to the given polyhedral set. Since compact semi-algebraic sets can be triangulated, a similar result follows for the collection of connected compact semi-algebraic sets.We discuss implications of our results for the strategic stability of success sets, and use the results to construct a Nash component with index k for any fixed integer k.     

Nash equilibrium when players account for the complexity of their forecasts

Nash equilibrium is often interpreted as a steady state in which each player holds the correct expectations about the other players' behavior and acts rationally. This paper investigates the robustness of this interpretation when there are small costs associated with complicated forecasts. The model consists of a two-person strategic game in which each player chooses a finite machine to implement a strategy in an infinitely repeated 2×2 game with discounting. I analyze the model using a solution concept called Nash Equilibrium with Stable Forecasts (ESF). My main results concern the structure of equilibrium machine pairs. They provide necessary and sufficient conditions on the form of equilibrium strategies and plays. In contrast to the “folk theorem,” these structural properties place severe restrictions on the set of equilibrium paths and payoffs. For example, only sequences of the one-shot Nash equilibrium can be generated by any ESF of the repeated game of chicken.