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.

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.

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 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.

Interpreting Knowledge in the Backward Induction Problem

Episteme ◽  
2011 ◽  
Vol 8 (3) ◽  
pp. 248-261 ◽  
Author(s):  
Ken Binmore
Keyword(s):  
Common Knowledge ◽  
Perfect Information ◽  
Backward Induction ◽  
Finite Games ◽  
Common Knowledge Of Rationality

AbstractRobert Aumann argues that common knowledge of rationality implies backward induction in finite games of perfect information. I have argued that it does not. A literature now exists in which various formal arguments are offered in support of both positions. This paper argues that Aumann's claim can be justified if knowledge is suitably reinterpreted.

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

Quantifying Commitment in Nash Equilibria

2019 ◽  
Vol 21 (02) ◽  
pp. 1940011
Author(s):  
Thomas A. Weber
Keyword(s):  
Nash Equilibrium ◽  
Normal Form ◽  
Nash Equilibria ◽  
Dynamic Game ◽  
Subgame Perfect Equilibrium ◽  
Canonical Extension ◽  
Perfect Equilibrium ◽  
Form Game ◽  
Normal Form Game ◽  
The Given

To quantify a player’s commitment in a given Nash equilibrium of a finite dynamic game, we map the corresponding normal-form game to a “canonical extension,” which allows each player to adjust his or her move with a certain probability. The commitment measure relates to the average overall adjustment probabilities for which the given Nash equilibrium can be implemented as a subgame-perfect equilibrium in the canonical extension.

Sign in / Sign up

Export Citation Format

Share Document