Nash Bargaining

10 Key excerpts on "Nash Bargaining"

• 

  eBook - ePub

  The Persuasive Negotiator

  Tools and Techniques for Effective Negotiating

  • Florence Kennedy Rolland(Author)
  • 2020(Publication Date)
  • Routledge

    (Publisher)

  What is true for you must be true for the other negotiator, so it is fair to conclude that you both negotiate because you both expect to gain something over what you have before your bargain. Briefly put, the Nash Bargaining problem is not about how you arrive at a solution – it is solely about the content of the solution. This leaves the problem of how to arrive at a solution unaddressed and, therefore, unsolved by Nash. For those not exposed to economic theory, Nash’s assumptions seem naïve compared with the circumstances commonly found in real-world bargaining processes. Nash, for instance, assumes: • highly rational bargainers who can accurately compare each other’s desires for various things; • bargainers who have equal ‘bargaining skills’; • bargainers who have full knowledge of the tastes and preferences of the other; and • bargainers who desire to maximise their gains in bargaining. His model of bargaining uses numerical utility theory, which is an economist’s way of ‘measuring’ the satisfaction, however defined, that an individual receives from possessing this or that set of goods. Nash, fortunately, provided an arithmetical example to demonstrate his solution. He refers to Bill and Jack, though they are not brothers, nor do they have a convenient adjudicator (their elder sister, Louise). That was my device to introduce you to the Nash solution. Before trading, Bill and Jack enjoy various numerical utilities from their possessions (see Table 8.2). It is the differences in their priorities or valuations that enable Bill and Jack to solve their exchange problem. Because each of them wants something from the other, they can find mutually acceptable terms for the trade

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Game Theory

  • Michael Maschler, Eilon Solan, Shmuel Zamir(Authors)
  • 2013(Publication Date)
  • Cambridge University Press

    (Publisher)

  15 Bargaining games Chapter summary In this chapter we present bargaining games, which model situations in which two or more players bargain toward an agreed-upon outcome. The set of all possible outcomes is called the feasible set and each outcome can be attained only by the unanimous agreement of all players. Different players typically prefer different outcomes, which explains the bargaining aspect of the model. A default outcome, called the disagreement point, is realized if the players fail to reach an agreement. A solution concept for bargaining games is a function that assigns to every bargaining game an outcome that can be looked at as the outcome that would be recommended to the players by an arbitrator or a judge. We list several desirable properties that a solution concept for two-player bargaining games could satisfy and provide the unique solution concept that satisfies all these properties, namely, the Nash solution for bargaining games. Variants of the Nash solution, like the Kalai–Smorodinsky solution, are obtained by imposing a different set of properties that a solution concept should satisfy. Finally, the model and some of the results are extended to bargaining games with more than two players. It is frequently the case that two (or more) parties conduct negotiations over an issue, with the payoff to each party dependent on the outcome of the negotiation process. Examples include negotiations between employers and employees on working conditions, nations negotiating trade treaties, and company executives negotiating corporate mergers and acquisitions. In each of these cases, there is a range of outcomes available, if only the parties can come to an agreement and cooperate. Sometimes negotiations do not lead to an agreement. Employees can leave their place of work, countries can impose high tariffs, hurting mutual trade, and negotiations on mergers and acquisitions can fail, with no acquisition taking place.

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Game Theory

  • Michael Maschler, Eilon Solan, Shmuel Zamir(Authors)
  • 2020(Publication Date)
  • Cambridge University Press

    (Publisher)

  16 Bargaining games Chapter summary In this chapter we present bargaining games, which model situations in which two or more players bargain toward an agreed-upon outcome. The set of all possible outcomes is called the feasible set and each outcome can be attained only by the unanimous agreement of all players. Different players typically prefer different outcomes, which explains the bargaining aspect of the model. A default outcome, called the disagreement point, is realized if the players fail to reach an agreement. A solution concept for bargaining games is a function that assigns to every bargaining game an outcome that can be looked at as the outcome that would be recommended to the players by an arbitrator or a judge. We list several desirable properties that a solution concept for two-player bargaining games could satisfy and provide the unique solution concept that satisfies all these properties, namely, the Nash solution for bargaining games. Variants of the Nash solution, like the Kalai–Smorodinsky solution, are obtained by imposing a different set of properties that a solution concept should satisfy. Finally, the model and some of the results are extended to bargaining games with more than two players. It is frequently the case that two (or more) parties conduct negotiations over an issue, with the payoff to each party dependent on the outcome of the negotiation process. Examples include negotiations between employers and employees on working conditions, nations negotiating trade treaties, and company executives negotiating corporate mergers and acquisitions. In each of these cases, there is a range of outcomes available, if only the parties can come to an agreement and cooperate. Sometimes negotiations do not lead to an agreement. Employees can leave their place of work, countries can impose high tariffs, hurting mutual trade, and negotiations on mergers and acquisitions can fail, with no acquisition taking place.

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  Game Theory and Society

  • Weiying Zhang(Author)
  • 2017(Publication Date)
  • Taylor & Francis

    (Publisher)

  5Bargaining and patience

  Any transaction could be seen as a bargaining game. Reaching an agreement is the common interest of both parties; thus, it is Pareto improvement. However, different agreements mean different allocations of interest, so conflicts of interest exist.

  There are two approaches for analyzing the bargaining issue: The cooperative game approach and the non-cooperative game approach. Collective rationality is the starting point of the cooperative game approach and individual rationality is the starting point of the non-cooperative game approach.

  According to the cooperative game approach, the bargaining solution is determined by the bargaining power and bargaining strength (marginal contribution to the value creation) of parties involved. If the parties are symmetric, then the Nash Bargaining solution means they will evenly distribute the surplus value brought about by the transaction. This conclusion provides a source of fairness.

  According to the non-cooperative game approach, the bargaining equilibrium outcome is determined by the bargaining sequence (who bids first), the number of times bargaining takes place, the patience of the people involved, the cost of bargaining, etc. The more patient a person is, and the lower his cost of bargaining is, the more advantage he will have during the negotiation. If both parties are symmetric and allowed to bargain an unlimited number of times, then the perfect Nash equilibrium allocation is almost evenly split.

  In reality, negotiation often take many rounds, and an agreement might not even be reached. This is primarily because information about the value of the transaction, bargaining power, and patience is incomplete. The process of negotiation is actually a process of both parties mutually obtaining information about the other.

  People’s behavior during negotiations is restricted by social norms. These social norms include procedural norms and substantial norms. Violating these social norms will lead to a breakdown in negotiations. Experiments with “The Ultimatum Game” show that the fairness concept held by most people, and has an important impact on the outcome of negotiations. However, this does not prove that people are irrational. Misalignment between theoretical projections and reality are primarily because theorists have too little information.

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Introduction to Game Theory in Business and Economics

  • Thomas J. Webster(Author)
  • 2018(Publication Date)
  • Routledge

    (Publisher)

  In general, n individuals with equal bargaining power will each receive a one-n th share. In fact, the method of backward induction discussed in the previous chapter will lead to precisely this outcome in most negotiations. In general, there are two questions that must be answered when analyzing bargaining sce-narios. First, what are the bargaining rules? Second, what happens if the players fail to reach an agreement? In most retail establishments, for example, the seller posts a fixed asking price. The customer must decide whether to accept or reject this price. This is an example of a take-it-or-leave-it bargaining rule. In the case of collective bargaining, union representatives may propose a wage and benefit package. Management may accept the offer, reject the offer and wait for the union to modify its proposal, or reject the proposal and make a counteroffer. In some cases, the order of play is determined by custom or law. In other cases, strategic considerations may determine the sequencing of the bargaining process. In the next section, we will examine the bargaining process as a static game in which the players negotiate the distribution of a divisible object of value. In subsequent sections, we will analyze the bargaining process as a sequential move game in which the length of time it takes to reach an agreement is an important determinant in the outcome of the game. Nash Bargaining We will begin our discussion of the bargaining process by going back to something a bit more basic. In a Nash Bargaining game, the players “haggle” over the distribution of a divisible object of value, such as a cash amount. In this game, the players agree to submit their bids simultane-ously. If the sum of the players’ bids is less than the available amount, each player receives the bid amount and the game ends. If the sum of the players’ bids is greater than the amount available, the players receive nothing.

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Contributions to the Theory of Games, Volume IV

  • Albert William Tucker, Robert Duncan Luce, Albert William Tucker, Robert Duncan Luce, Albert Tucker, Robert Luce(Authors)
  • 2016(Publication Date)
  • Princeton University Press

    (Publisher)

  The bargaining model of this paper Is essentially a generalization of Nash's theory of two-person bargaining, for the n-person case. A determinate solution for the n-person game, restricted to the Q case of transferable utility, has already been suggested by Dr. Shapley. However, his solution Is meant to define the value to each player of the prospect of having to play a given game, while our solution is meant to define the actual payoffs that the players of the game, If they act in accordance with certain rationality postulates, tend to agree upon in bargaining. Moreover, as Shapley1s theory depends on the use of the von Neumann-Morgenstern characteristic function of the game, it involves the rather unsatisfactory assumption that in the event of a conflict between two player coalitions each side would use a maximin strategy against the other side, i.e., would act on the expectation that the other side would always try to Inflict the highest possible damage on them - irrespective of the costs of this policy to themselves. This interpretation of rational behaviour in conflict situations is quite natural in the case of constant-sum games, where one side's loss is necessarily the other side's gain. But In the case of non-constant-sum games it is more natural to assume that in a conflict each side would avoid, and would also expect the other side to avoid, strategies disproportionately expensive in relation to the damage caused to the other side. Furthermore, Shapley uses a bargaining model (though this model does not play an essential role in his theory) which is based on the assumption that any player joining a coalition is able to obtain the whole increment in the value (joint profit) of this coalition that results from his joining, whereas most of us would rather predict some sort of profit-sharing agreement in this situation between the new member of the coalition and the old ones.

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Game Theory

  An Introduction

  • E. N. Barron(Author)
  • 2024(Publication Date)
  • Wiley

    (Publisher)

  367 7 Bargaining A good rule to remember for life is that when it comes to plastic surgery and sushi, never be attracted by a bargain. – Graham Norton While money doesn’t buy love, it puts you in a great bargaining position. – Christopher Marlowe Man is an animal that makes bargains: no other animal does this–no dog exchanges bones with another. –Adam Smith Bargaining is the third stage of the grief process. –David Levithan 7.1 Introduction Bargaining theory is a branch of game theory that studies how two or more parties can reach an agreement on how to divide a limited resource. The theory assumes that the parties are rational and self-interested and that they want to maximize their own gain from the bargaining process. There are many different bargaining models, but they all share some common features. First, each party has a threat point, which is the outcome they would receive if the bargaining process failed and they had to go their separate ways. Second, each party has a reserve value, which is the minimum outcome they are willing to accept in order to reach an agreement. The bargaining process begins with each party making an offer. The parties then continue to make offers and counteroffers until they reach an agreement or one of the parties decides to walk away. The outcome of the bargaining process will depend on the parties’ threat points, reserve values, and the bargaining skills of the negotiators. Bargaining theory has been used to study a wide range of phenomena, including wage negotia- tions, labor disputes, and international relations. The theory can be used to predict the outcome of bargaining processes and to develop strategies for negotiators. Game Theory: An Introduction, Third Edition. E. N. Barron. © 2024 John Wiley & Sons, Inc. Published 2024 by John Wiley & Sons, Inc.

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Advances in Game Theory

  • Melvin Dresher, Lloyd S. Shapley, Albert William Tucker, Melvin Dresher, Lloyd S. Shapley, Albert William Tucker, Melvin Dresher, Lloyd Shapley, Albert Tucker(Authors)
  • 2016(Publication Date)
  • Princeton University Press

    (Publisher)

  THE n-PERSON BARGAINING GAME* Koichi Miyasawa § 1. INTRODUCTION When we consider a bargaining situation among persons, many compli-cated factors will be found which affect the final outcome to each participant of that bargaining. Even in the case of bargaining between two players, many theories have been proposed [1, 6, 7, 8] which have given rise to much controversy [2, 9]. In this paper we should like to generalize the idea of the Nash solution for a two-person bargaining game to the n-person case. Along this line of generalization, Harsanyi [3] has developed an interesting theory. We received recently his revised paper [4] on this problem, in which he replies to criticisms raised by Isbell [5]. The purpose of this paper is to develop a more generalized approach to the structure of the n-person bargaining game. § 2. SUMMARY In our n-person bargaining model, we take into consideration the preliminary meetings among the members of each subset — that is, of each coalition S — of the all-player set N, as well as the plenary meeting among all the players. Even though the final payoff to each player may be determined at the plenary meeting, we shall assume that the final payoff u^ S is constructed by adding up incremental payoffs which could be attributed to the effect of player i advancing from one coalition to a larger one. On the basis of this final payoff structure, we define the equilibrium strategy _ I wish to express my gratitude to Professor Oskar Morgenstem for giving me the opportunity to study at the Econometric Research Program of which he is the director and for his valuable advice and suggestions. I am greatly indebted to Dr. Robert J. Aumann for many valuable comments. 547 set as the one which satisfies an internal balance condition among the incremental payoffs (Definition 1). We take into consideration explicitly the dependence of the outcome space which a coalition S could attain on the strategy chosen by the complementary coalition S = N — S.

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Theories of Justice

  A Treatise on Social Justice, Vol. 1

  • Brian Barry(Author)
  • 2023(Publication Date)
  • University of California Press

    (Publisher)

  The Nash solution and the competing utility-based solutions we shall go on to discuss are anything but obvious to most people. Perhaps we might sum up the first point, then, by saying that the Nash solution could function as a prominent solution only for a pair of mathemati- cians. The second objection is that the problem of dividing the $100 is, after all, not a pure coordination game. (A pure coordination game is one in which the payoffs depend purely on the players' ability to reach an agreement, not on the form the agreement takes. The usual example is of two people who want to meet in some public place such as a store or an airport: it doesn't matter to either where they go so long as they both go to the same place.) It is true that a bargaining situation has something in common with a coordination game, namely, that there is a great premium on reaching agreement. Within limits, one might say, it is more important that an agreement be reached than that it be reached at one point as against another. But the limit of the truth of that is imposed precisely by the fact of a bargaining situation's not being a coordination game, so that it does make a difference at what point the agreement comes. Thus, we could imagine R saying that, much as he admires the esthetics of a fifty-fifty split, he is inclined to think that P will eventually come to see the practical attractions of a split that gives him only $30. With this, we get back to the real strength of the Nash solution: that it is not simply a unique point recommended by mathematical esthetics, but does have some real claim to capture our intuitive sense of what makes for a strong or a weak bargaining position. It may appear that what I said a little while ago knocked the bottom out of this asser- tion; but this would, I believe, be a misconception.

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Equity

  In Theory and Practice

  • H. Peyton Young, Hobart Peyton Young(Authors)
  • 2020(Publication Date)
  • Princeton University Press

    (Publisher)

  A second way that the bargainers can solve the coordination problem is to look for a payoff distribution that everyone agrees to be fair. In other words, 3 In the next chapter we shall analyze this game in greater detail. FAIR BARGAINS 119 (.62,.62) = (.67,.58) 0 1 1's utility Fig. 15. The bargaining set for two creditors dividing $90,000. they look for a solution that can be justified on objective grounds. One form of justification is to reason deductively from general equity principles, as in the derivation of formulas for allocating representation (chapter 3) and common costs (chapter 5). Another is to cite prominent authorities, like the rules of Aristotle and Maimonides for dividing contested property (chapter 4). A third approach is to appeal to precedent—to what is usual, customary, and expected in distributive problems of this sort (taxation has something of this flavor). All three of these approaches serve a similar purpose: they narrow the set of plausible outcomes, which helps to coordinate the parties' expectations about what the others are likely to accept. They also shift the discourse from making claims and demands to offering justifications and reasons, which is usually more constructive and more likely to convince others. 4. Classical Bargaining Solutions: Nash and Kalai-Smorodinsky Let us now consider what equity principles might be deployed to justify a particular solution. In previous chapters these principles were expressed in terms of the physical amounts that the claimants receive in relation to their claims. Bargaining theory takes a different approach by defining equity in terms of the claimants' utility payoffs. In other words, the discussion is grounded in the levels of welfare that the parties can attain, not on the amounts that they actually receive. This means that equity is evaluated solely in terms of the bargaining set. Let's see whether an equitable solution suggests itself by looking at the bargaining set in a particular case.

  Sign up to read

  Learn more about book