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.

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.

scholarly journals Symmetric Subgame-Perfect Equilibria in Resource Allocation

2014 ◽  
Vol 49 ◽  
pp. 323-361 ◽  
Author(s):  
L. Cigler ◽  
B. Faltings
Keyword(s):  
Resource Allocation ◽  
Subgame Perfect Equilibrium ◽  
Efficient Allocation ◽  
Perfect Equilibrium ◽  
Use Of Resources ◽  
Strategy Profile ◽  
Global Coordination ◽  
Resource Allocation Games ◽  
Subgame Perfect Equilibria ◽  
Perfect Equilibria

We analyze symmetric protocols to rationally coordinate on an asymmetric, efficient allocation in an infinitely repeated N-agent, C-resource allocation problems, where the resources are all homogeneous. Bhaskar proposed one way to achieve this in 2-agent, 1-resource games: Agents start by symmetrically randomizing their actions, and as soon as they each choose different actions, they start to follow a potentially asymmetric "convention" that prescribes their actions from then on. We extend the concept of convention to the general case of infinitely repeated resource allocation games with N agents and C resources. We show that for any convention, there exists a symmetric subgame-perfect equilibrium which implements it. We present two conventions: bourgeois, where agents stick to the first allocation; and market, where agents pay for the use of resources, and observe a global coordination signal which allows them to alternate between different allocations. We define price of anonymity of a convention as a ratio between the maximum social payoff of any (asymmetric) strategy profile and the expected social payoff of the subgame-perfect equilibrium which implements the convention. We show that while the price of anonymity of the bourgeois convention is infinite, the market convention decreases this price by reducing the conflict between the agents.

scholarly journals Voting behavior under outside pressure: promoting true majorities with sequential voting?

2021 ◽  
Author(s):  
Friedel Bolle ◽  
Philipp E. Otto
Keyword(s):  
Voting Behavior ◽  
Subgame Perfect Equilibrium ◽  
Complete Information ◽  
Emotional Reactions ◽  
Equilibrium Strategy ◽  
Perfect Equilibrium ◽  
Roll Call ◽  
Sequential Voting ◽  
Subgame Perfect Equilibria ◽  
Perfect Equilibria

AbstractWhen including outside pressure on voters as individual costs, sequential voting (as in roll call votes) is theoretically preferable to simultaneous voting (as in recorded ballots). Under complete information, sequential voting has a unique subgame perfect equilibrium with a simple equilibrium strategy guaranteeing true majority results. Simultaneous voting suffers from a plethora of equilibria, often contradicting true majorities. Experimental results, however, show severe deviations from the equilibrium strategy in sequential voting with not significantly more true majority results than in simultaneous voting. Social considerations under sequential voting—based on emotional reactions toward the behaviors of the previous players—seem to distort subgame perfect equilibria.

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 games with almost perfect information: Dispensing with public randomization

2021 ◽  
Vol 16 (4) ◽  
pp. 1221-1248
Author(s):  
Paulo Barelli ◽  
John Duggan
Keyword(s):  
Dynamic Games ◽  
Subgame Perfect Equilibrium ◽  
Perfect Information ◽  
State Transitions ◽  
Original Game ◽  
Equilibrium Existence ◽  
Weakly Continuous ◽  
Continuous State ◽  
Subgame Perfect Equilibria ◽  
Perfect Equilibria

Harris, Reny, and Robson (1995) added a public randomization device to dynamic games with almost perfect information to ensure existence of subgame perfect equilibria (SPE). We show that when Nature's moves are atomless in the original game, public randomization does not enlarge the set of SPE payoffs: any SPE obtained using public randomization can be “decorrelated” to produce a payoff‐equivalent SPE of the original game. As a corollary, we provide an alternative route to a result of He and Sun (2020) on existence of SPE without public randomization, which in turn yields equilibrium existence for stochastic games with weakly continuous state transitions.

scholarly journals The Inefficiency of Nash and Subgame Perfect Equilibria for Network Routing

2019 ◽  
Vol 44 (4) ◽  
pp. 1286-1303 ◽  
Author(s):  
José Correa ◽  
Jasper de Jong ◽  
Bart de Keijzer ◽  
Marc Uetz
Keyword(s):  
Price Of Anarchy ◽  
Subgame Perfect Equilibrium ◽  
Network Routing ◽  
Congestion Games ◽  
Cost Functions ◽  
Worst Case ◽  
Subgame Perfection ◽  
Subgame Perfect Equilibria ◽  
Routing Games ◽  
Perfect Equilibria

This paper provides new bounds on the quality of equilibria in finite congestion games with affine cost functions, specifically for atomic network routing games. It is well known that the price of anarchy equals exactly 5/2 in general. For symmetric network routing games, it is at most (5n − 2)/(2n + 1), where n is the number of players. This paper answers to two open questions for congestion games. First, we show that the price of anarchy bound (5n − 2)/(2n + 1) is tight for symmetric network routing games, thereby answering a decade-old open question. Second, we ask whether sequential play and subgame perfection allows to evade worst-case Nash equilibria, and thereby reduces the price of anarchy. This is motivated by positive results for congestion games with a small number of players, as well as recent results for other resource allocation problems. Our main result is the perhaps surprising proof that subgame perfect equilibria of sequential symmetric network routing games with linear cost functions can have an unbounded price of anarchy. We complete the picture by analyzing the case with two players: we show that the sequential price of anarchy equals 7/5 and that computing the outcome of a subgame perfect equilibrium is NP-hard.

scholarly journals Oscillation of Second-Order Differential Equations with Multiple and Mixed Delays under a Canonical Operator

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1323
Author(s):  
Shyam Sundar Santra ◽  
Rami Ahmad El-Nabulsi ◽  
Khaled Mohamed Khedher
Keyword(s):  
Differential Equations ◽  
Necessary Conditions ◽  
Second Order ◽  
Multiple Delays ◽  
Mixed Delays ◽  
Neutral Differential Equations ◽  
Canonical Operator ◽  
Second Order Differential Equations ◽  
The Future ◽  
Sufficient And Necessary Conditions

In this work, we obtained new sufficient and necessary conditions for the oscillation of second-order differential equations with mixed and multiple delays under a canonical operator. Our methods could be applicable to find the sufficient and necessary conditions for any neutral differential equations. Furthermore, we proved the validity of the obtained results via particular examples. At the end of the paper, we provide the future scope of this study.

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