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.

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 BACKWARD INDUCTION: MERITS AND FLAWS

2017 ◽  
Vol 50 (1) ◽  
pp. 9-24
Author(s):  
Marek M. Kamiński
Keyword(s):  
Infinite Number ◽  
Nash Equilibria ◽  
Complex Structure ◽  
Subgame Perfect Equilibrium ◽  
Perfect Information ◽  
Backward Induction ◽  
Perfect Equilibrium ◽  
Sequential Games ◽  
Theoretical Predictions

Abstract Backward induction (BI) was one of the earliest methods developed for solving finite sequential games with perfect information. It proved to be especially useful in the context of Tom Schelling’s ideas of credible versus incredible threats. BI can be also extended to solve complex games that include an infinite number of actions or an infinite number of periods. However, some more complex empirical or experimental predictions remain dramatically at odds with theoretical predictions obtained by BI. The primary example of such a troublesome game is Centipede. The problems appear in other long games with sufficiently complex structure. BI also shares the problems of subgame perfect equilibrium and fails to eliminate certain unreasonable Nash equilibria.

scholarly journals What Do Bargainers' Preferences Look Like? Experiments with a Convex Ultimatum Game

2003 ◽  
Vol 93 (3) ◽  
pp. 672-685 ◽  
Author(s):  
James Andreoni ◽  
Marco Castillo ◽  
Ragan Petrie
Keyword(s):  
Risk Aversion ◽  
Bargaining Power ◽  
Ultimatum Game ◽  
Subgame Perfect Equilibrium ◽  
The Other ◽  
Perfect Equilibrium

The ultimatum game, by its all-or-nothing nature, makes it difficult to discern what kind of preferences may be generating choices. We explore a game that convexifies the decisions, allowing us a better look at the indifference curves of bargainers while maintaining the subgame-perfect equilibrium. We conclude that bargainers' preferences are convex and regular but not always monotonic. Money-maximization is the sole concern for about half of the subjects, while the other half reveal a preference for fairness. We also found, unexpectedly, the importance of risk aversion among money-maximizing proposers, which in turn generates significant bargaining power for fair-minded responders.

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 Computing Nash Equilibria of Unbounded Games

10.29007/1wpl ◽  
2018 ◽  
Author(s):  
Martin Escardo ◽  
Paulo Oliva
Keyword(s):  
Nash Equilibria ◽  
Proof Theory ◽  
A Priori ◽  
Subgame Perfect Equilibrium ◽  
Backward Induction ◽  
Closed Formula ◽  
Perfect Equilibrium ◽  
Finite Games ◽  
Game Theoretic ◽  
Theoretic Technique

Using techniques from higher-type computability theory and proof theory we extend the well-known game-theoretic technique of backward induction to finite games of unbounded length. The main application is a closed formula for calculating strategy profiles in Nash equilibrium and subgame perfect equilibrium even in the case of games where the length of play is not a-priori fixed.

Government Positions for Sale - A Model of Grand Corruption

2012 ◽  
Vol 14 (2) ◽  
pp. 1-25 ◽  
Author(s):  
Hans J. Czap ◽  
Kanybek D. Nur-tegin
Keyword(s):  
Developing Countries ◽  
Subgame Perfect Equilibrium ◽  
Backward Induction ◽  
Perfect Equilibrium ◽  
Two Stage ◽  
Stage Game ◽  
The Given

This paper develops a model for a particular type of grand corruption often encountered in developing countries, namely, the sale of government positions by autocratic rulers. A two-stage game is considered, where the autocrat moves first to maximize his revenue from the sale of positions in the cabinet by choosing a price that must be paid by interested politicians. The latter become bureaucrats who maximize their utility from bribe revenues for the given price set by the president. Backward induction yields subgame-perfect equilibrium levels of corruption of the president and bureaucrats. A key insight from this analysis is that conventional tools of fighting corruption become ineffective when corruption at the very top is ignored. The model is distinctive in its treatment of individual moral costs of being corrupt and in its consideration of a revolutionary constraint on the autocrat's choices.

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

scholarly journals Dinamicke igre ulaska na trziste

2005 ◽  
Vol 50 (165) ◽  
pp. 121-144
Author(s):  
Bozo Stojanovic
Keyword(s):  
Nash Equilibrium ◽  
Dynamic Games ◽  
Nash Equilibria ◽  
Dynamic Game ◽  
Backward Induction ◽  
Perfect Equilibrium ◽  
Equilibrium Concept ◽  
Reasonable Solution ◽  
Multiple Nash Equilibria ◽  
Entry Games

Market processes can be analyzed by means of dynamic games. In a number of dynamic games multiple Nash equilibria appear. These equilibria often involve no credible threats the implementation of which is not in the interests of the players making them. The concept of sub game perfect equilibrium rules out these situations by stating that a reasonable solution to a game cannot involve players believing and acting upon noncredible threats or promises. A simple way of finding the sub game perfect Nash equilibrium of a dynamic game is by using the principle of backward induction. To explain how this equilibrium concept is applied, we analyze the dynamic entry games.

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