AN n-PERSON RUBINSTEIN BARGAINING GAME

2009 ◽  
Vol 11 (01) ◽  
pp. 111-115 ◽  
Author(s):  
PÄR TORSTENSSON
Keyword(s):  
Subgame Perfect Equilibrium ◽  
Bargaining Game ◽  
Discount Factor ◽  
Bargaining Model ◽  
Perfect Equilibrium ◽  
Large Discount ◽  
Alternating Offers ◽  
Rule Out

When Herrero (1985) extends Rubinstein's (1982) alternating-offers bargaining model to the case of three or more players any agreement can be supported as a subgame perfect equilibrium (SPE) outcome, given a sufficiently large discount factor. We show that this is not the case when players demand shares for themselves instead of proposing agreements to each other. Although it is possible to rule out agreements, the majority remains to be SPE outcomes.

scholarly journals Subgame Perfect Equilibrium in the Rubinstein Bargaining Game with Loss Aversion

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-23 ◽  
Author(s):  
Zhongwei Feng ◽  
Chunqiao Tan
Keyword(s):  
Loss Aversion ◽  
Reference Point ◽  
Bargaining Power ◽  
Subgame Perfect Equilibrium ◽  
Reference Points ◽  
Bargaining Game ◽  
The Other ◽  
Nash Bargaining ◽  
Perfect Equilibrium ◽  
High Share

Rubinstein bargaining game is extended to incorporate loss aversion, where the initial reference points are not zero. Under the assumption that the highest rejected proposal of the opponent last periods is regarded as the associated reference point, we investigate the effect of loss aversion and initial reference points on subgame perfect equilibrium. Firstly, a subgame perfect equilibrium is constructed. And its uniqueness is shown. Furthermore, we analyze this equilibrium with respect to initial reference points, loss aversion coefficients, and discount factor. It is shown that one benefits from his opponent’s loss aversion coefficient and his own initial reference point and is hurt by loss aversion coefficient of himself and the opponent’s initial reference point. Moreover, it is found that, for a player who has a higher level of loss aversion than the other, although this player has a higher initial reference point than the opponent, this player can(not) obtain a high share of the pie if the level of loss aversion of this player is sufficiently low (high). Finally, a relation with asymmetric Nash bargaining is established, where player’s bargaining power is negatively related to his own loss aversion and the initial reference point of the other and positively related to loss aversion of the opponent and his own initial reference point.

BARGAINING MODEL WITH SEQUENCES OF DISCOUNT RATES AND BARGAINING COSTS

2004 ◽  
Vol 06 (02) ◽  
pp. 265-280 ◽  
Author(s):  
AGNIESZKA RUSINOWSKA
Keyword(s):  
Discount Rate ◽  
Necessary Conditions ◽  
Subgame Perfect Equilibrium ◽  
Bargaining Model ◽  
Perfect Equilibrium ◽  
Discount Rates ◽  
Sufficient And Necessary Conditions ◽  
Subgame Perfect Equilibria ◽  
Perfect Equilibria

The paper is a kind of generalization of Rubinstein bargaining model. Rubinstein assumed that preferences of the players were constant in time, and he analyzed models in which preferences of each player were defined either by constant discount rate or by constant bargaining cost. In this paper, a bargaining model is presented, in which preferences of each player are expressed simultaneously by sequence of discount rates and sequence of bargaining costs varying in time. The results presented in the paper concern subgame perfect equilibria. There is a theorem concerning sufficient and necessary conditions for the existence of subgame perfect equilibrium of the game. Moreover, some theorems presenting forms of subgame perfect equilibria for various cases of the model analyzed have been proved here. A possibility of delay in reaching an agreement is also considered in the paper. If we analyze a class of strategies, that depend on the former history, a delay can appear for some models. The adequate examples are presented. In the paper, some applications of the bargaining model are also described.

BOUNDED RATIONALITY AND ALTERNATING-OFFER BARGAINING

1999 ◽  
Vol 01 (03n04) ◽  
pp. 241-250
Author(s):  
ANA MAULEON ◽  
VINCENT J. VANNETELBOSCH
Keyword(s):  
Bounded Rationality ◽  
Common Knowledge ◽  
Subgame Perfect Equilibrium ◽  
Bargaining Game ◽  
Time Preferences ◽  
Perfect Equilibrium ◽  
Discount Factors ◽  
Common Knowledge Of Rationality

One form of bounded rationality is a breakdown in the commonality of the knowledge that the players are rational. In Rubinstein's two-person alternating-offer bargaining game, assuming time preferences with constant discount factors, common knowledge of rationality is necessary for an agreement on a subgame perfect equilibrium (SPE) partition to be reached (if ever). In this note, assuming time preferences with constant costs of delay, we show that common knowledge of rationality is not necessary to reach always an agreement on a SPE partition. This result is robust to a generalisation, time preferences with constant discount factors and costs of delay, if the players are sufficiently patient.

REFINEMENTS OF NASH EQUILIBRIA IN VIEW OF JEALOUS OR FRIENDLY BEHAVIOR OF PLAYERS

2002 ◽  
Vol 04 (03) ◽  
pp. 281-299 ◽  
Author(s):  
AGNIESZKA RUSINOWSKA
Keyword(s):  
Nash Equilibria ◽  
Subgame Perfect Equilibrium ◽  
Perfect Equilibrium ◽  
Infinitely Divisible ◽  
Common Assumption ◽  
Bargaining Models ◽  
The Common ◽  
Simultaneous Moves ◽  
The One ◽  
Alternating Offers

In this paper, several bargaining models, differing in some assumptions from each other, are analyzed. We consider a discrete case and a continuous case. In the former model, players bargain over a division of n objects. In the latter, parties divide one unit of infinitely divisible good. We start with an analysis of the one-round model, and then we consider a model in which players can continue to bargain. For each model, simultaneous moves as well as alternating offers of players are considered. The assumption that each player receives no more than his/her opponent proposes giving to him/her is the common assumption for all cases analyzed. Moreover, we adopt some assumptions concerning players' attitudes towards their opponents' payments, assuming that players can be either jealous or friendly. In view of the jealousy or friendliness of players, Nash equilibrium and subgame perfect equilibrium are described.

scholarly journals On gamesmen and fair men: explaining fairness in non-cooperative bargaining games

2018 ◽  
Vol 5 (2) ◽  
pp. 171709 ◽  
Author(s):  
Ramzi Suleiman
Keyword(s):  
Ultimatum Game ◽  
Golden Ratio ◽  
Subgame Perfect Equilibrium ◽  
Backward Induction ◽  
Perfect Equilibrium ◽  
Bargaining Games ◽  
Discount Factors ◽  
Proposed Model ◽  
Resource Dilemma ◽  
Alternating Offers

Experiments on bargaining games have repeatedly shown that subjects fail to use backward induction, and that they only rarely make demands in accordance with the subgame perfect equilibrium. In a recent paper, we proposed an alternative model, termed ‘economic harmony’ in which we modified the individual's utility by defining it as a function of the ratio between the actual and aspired pay-offs. We also abandoned the notion of equilibrium, in favour of a new notion of ‘harmony’, defined as the intersection of strategies, at which all players are equally satisfied. We showed that the proposed model yields excellent predictions of offers in the ultimatum game, and requests in the sequential common pool resource dilemma game. Strikingly, the predicted demand in the ultimatum game is equal to the famous Golden Ratio (approx. 0.62 of the entire pie). The same prediction was recently derived independently by Schuster (Schuster 2017. Sci. Rep. 7 , 5642). In this paper, we extend the solution to bargaining games with alternating offers. We show that the derived solution predicts the opening demands reported in several experiments, on games with equal and unequal discount factors and game horizons. Our solution also predicts several unexplained findings, including the puzzling ‘disadvantageous counter-offers’, and the insensitivity of opening demands to variations in the players' discount factors, and game horizon. Strikingly, we find that the predicted opening demand in the alternating offers game is also equal to the Golden Ratio.

Collective Risk and Distributional Equity in Climate Change Bargaining

2021 ◽  
pp. 002200272110273
Author(s):  
Aseem Mahajan ◽  
Reuben Kline ◽  
Dustin Tingley
Keyword(s):  
Climate Change ◽  
Characteristic Feature ◽  
Economic Loss ◽  
Bargaining Model ◽  
Intergovernmental Panel ◽  
Climate Negotiations ◽  
Collective Risk ◽  
International Climate ◽  
Alternating Offers ◽  
International Climate Negotiations

International climate negotiations occur against the backdrop of increasing collective risk: the likelihood of catastrophic economic loss due to climate change will continue to increase unless and until global mitigation efforts are sufficient to prevent it. We introduce a novel alternating-offers bargaining model that incorporates this characteristic feature of climate change. We test the model using an incentivized experiment. We manipulate two important distributional equity principles: capacity to pay for mitigation of climate change and vulnerability to its potentially catastrophic effects. Our results show that less vulnerable parties do not exploit the greater vulnerability of their bargaining partners. They are, rather, more generous. Conversely, parties with greater capacity are less generous in their offers. Both collective risk itself and its importance in light of the recent Intergovernmental Panel on Climate Change report make it all the more urgent to better understand this crucial strategic feature of climate change bargaining.

Step-by-Step: The Subgame-Perfect Equilibrium

2020 ◽  
pp. 125-140
Author(s):  
Manfred J. Holler ◽  
Barbara Klose-Ullmann
Keyword(s):  
Subgame Perfect Equilibrium ◽  
Perfect Equilibrium

UNIQUENESS IN RANDOM-PROPOSER MULTILATERAL BARGAINING

2009 ◽  
Vol 11 (04) ◽  
pp. 407-417 ◽  
Author(s):  
HUIBIN YAN
Keyword(s):  
Subgame Perfect Equilibrium ◽  
Characteristic Functions ◽  
Bargaining Model ◽  
Equilibrium Outcome ◽  
Multilateral Bargaining ◽  
Legislative Bargaining ◽  
Uniqueness Results ◽  
Subgame Perfect Equilibria ◽  
Perfect Equilibria ◽  
Special Case

Solution uniqueness is an important property for a bargaining model. Rubinstein's (1982) seminal 2-person alternating-offer bargaining game has a unique Subgame Perfect Equilibrium outcome. Is it possible to obtain uniqueness results in the much enlarged setting of multilateral bargaining with a characteristic function? This paper investigates a random-proposer model first studied in Okada (1993) in which each period players have equal probabilities of being selected to make a proposal and bargaining ends after one coalition forms. Focusing on transferable utility environments and Stationary Subgame Perfect Equilibria (SSPE), we find ex ante SSPE payoff uniqueness for symmetric and convex characteristic functions, considerably expanding the conditions under which this model is known to exhibit SSPE payoff uniqueness. Our model includes as a special case a variant of the legislative bargaining model in Baron and Ferejohn (1989), and our results imply (unrestricted) SSPE payoff uniqueness in this case.

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