scholarly journals ALLOCATION RULES WITH OUTSIDE OPTION IN COOPERATION GAMES WITH TIME‐INCONSISTENCY

2010 ◽  
Vol 11 (1) ◽  
pp. 56-96 ◽  
Author(s):  
Harald D. Stein
Keyword(s):  
Game Theory ◽  
Bounded Rationality ◽  
Time Inconsistency ◽  
Allocation Rule ◽  
Network Games ◽  
Myerson Value ◽  
Allocation Rules ◽  
Outside Option ◽  
Coalition Structures ◽  
Dynamic Setting

In game theory agents have the possibility to make binding agreements. The agents are assumed to determine their strategies based on intended but bounded rationality. The field of strategic games provides the possibility to an agent to understand the optimality of his behaviour. In coalition and network games stability, Pareto‐efficiency and fairness of agreements is investigated. The paper shows the relationship between the different fields of game theory in the case of 3 agents. On that basis it shows the ubiquity of time‐inconsistency in dynamic setting due to bounded rationality, deception and environment changes. The paper explains why allocation rules like the Shapley‐based Aumann‐Drèze‐value and the Myerson‐value for coalition structures must be modified in dynamic setting in order to consider the influence of excluded agents, the outside option. An accordingly modified allocation rule is introduced and investigated. It is shown that the “Aumann‐Drèze‐value” and the “Myerson‐value for coalition structures” remains relevant for the case that the switching of the partner is connected with high costs. It is shown through the example of enterprise cooperation in supply chains that low partner switching costs require the introduced allocation rule that considers the outside option. Santrauka Žaidimu teorijoje agentai turi galimybe sudaryti isipareigojančius susitarimus. Agentai, kaip yra mano‐ma, numato savo strategijas riboto racionalumo salygomis. Strateginiu žaidimu sritis sudaro galimybe agentui suvokti optimalios elgsenos krypti. Straipsnyje tyrinejamas ryšys tarp skirtingu žaidimu teo‐rijos sričiu tuo atveju, kai susitarimuose dalyvauja trys agentai. Atskleidžiamas neišvengiamas agentu elgsenos nesuderinamumas del riboto racionalumo, apgavysčiu bei aplinkos pokyčiu. Straipsnyje aiš‐kinama, kad žaidimu teorijos numatomos agentu susitarimu taisykles turetu būti modifikuotos siekiant ivertinti papildomu susitarimu alternatyvu galimybe.

scholarly journals ALLOCATION RULES WITH OUTSIDE OPTION IN COOPERATION GAMES WITH TIME‐INCONSISTENCY

2010 ◽  
Vol 11 (1) ◽  
pp. 56-96
Author(s):  
Harald D. Stein
Keyword(s):  
Game Theory ◽  
Bounded Rationality ◽  
Time Inconsistency ◽  
Allocation Rule ◽  
Network Games ◽  
Myerson Value ◽  
Allocation Rules ◽  
Outside Option ◽  
Coalition Structures ◽  
Dynamic Setting

In game theory agents have the possibility to make binding agreements. The agents are assumed to determine their strategies based on intended but bounded rationality. The field of strategic games provides the possibility to an agent to understand the optimality of his behaviour. In coalition and network games stability, Pareto‐efficiency and fairness of agreements is investigated. The paper shows the relationship between the different fields of game theory in the case of 3 agents. On that basis it shows the ubiquity of time‐inconsistency in dynamic setting due to bounded rationality, deception and environment changes. The paper explains why allocation rules like the Shapley‐based Aumann‐Drèze‐value and the Myerson‐value for coalition structures must be modified in dynamic setting in order to consider the influence of excluded agents, the outside option. An accordingly modified allocation rule is introduced and investigated. It is shown that the “Aumann‐Drèze‐value” and the “Myerson‐value for coalition structures” remains relevant for the case that the switching of the partner is connected with high costs. It is shown through the example of enterprise cooperation in supply chains that low partner switching costs require the introduced allocation rule that considers the outside option. Santrauka Žaidimu teorijoje agentai turi galimybe sudaryti isipareigojančius susitarimus. Agentai, kaip yra mano‐ma, numato savo strategijas riboto racionalumo salygomis. Strateginiu žaidimu sritis sudaro galimybe agentui suvokti optimalios elgsenos krypti. Straipsnyje tyrinejamas ryšys tarp skirtingu žaidimu teo‐rijos sričiu tuo atveju, kai susitarimuose dalyvauja trys agentai. Atskleidžiamas neišvengiamas agentu elgsenos nesuderinamumas del riboto racionalumo, apgavysčiu bei aplinkos pokyčiu. Straipsnyje aiš‐kinama, kad žaidimu teorijos numatomos agentu susitarimu taisykles turetu būti modifikuotos siekiant ivertinti papildomu susitarimu alternatyvu galimybe.

scholarly journals Axiomatic Results for Weighted Allocation Rules under Multiattribute Situations

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 617
Author(s):  
Yu-Hsien Liao
Keyword(s):  
Bargaining Power ◽  
The Other ◽  
Target Type ◽  
Allocation Rule ◽  
Interactive Environments ◽  
Allocation Rules ◽  
Other Hand

In many interactive environments, operators may have to deal with different work objectives at the same time. In a realistic context, such as differences in the target type to be addressed, or changes in the behavior of other operators, operators may therefore have to cope with by adopting different work levels (strategies) at any given time. On the other hand, the importance or influence brought by operators may vary depending on many subjective and objective factors, such as the size of the constituency represented by a congressman, and the bargaining power of a business personnel which may vary. Therefore, it is reasonable that weights are apportioned to operators and arbitrary usability should be distributed according to these weights under various working levels and multiattribute situations. In pre-existing results for allocation rules, weights might be always apportioned to the “operators” or the “levels” to modify the differences among the operators or its working levels respectively. By applying weights to the operators and its working levels (strategies) simultaneously, we adopt the maximal marginal variations among working level (strategy) vectors to propose an allocation rule under multiattribute situations. Furthermore, we introduce some axiomatic outcomes to display the rationality for this weighted allocation rule. By replacing weights to be maximal marginal variations, a generalized index is also introduced.

CAPITAL ALLOCATION FOR SET-VALUED RISK MEASURES

2020 ◽  
Vol 23 (01) ◽  
pp. 2050009
Author(s):  
FRANCESCA CENTRONE ◽  
EMANUELA ROSAZZA GIANIN
Keyword(s):  
Convex Set ◽  
Risk Measures ◽  
Risk Measure ◽  
Capital Allocation ◽  
Allocation Rule ◽  
Scalar Case ◽  
Representation Theorems ◽  
Allocation Rules ◽  
The One ◽  
Definition Of

We introduce the definition of set-valued capital allocation rule, in the context of set-valued risk measures. In analogy to some well known methods for the scalar case based on the idea of marginal contribution and hence on the notion of gradient and sub-gradient of a risk measure, and under some reasonable assumptions, we define some set-valued capital allocation rules relying on the representation theorems for coherent and convex set-valued risk measures and investigate their link with the notion of sub-differential for set-valued functions. We also introduce and study the set-valued analogous of some properties of classical capital allocation rules, such as the one of no undercut. Furthermore, we compare these rules with some of those mostly used for univariate (single-valued) risk measures. Examples and comparisons with the scalar case are provided at the end.

Bi-cooperative network games: A link-based allocation rule

2018 ◽  
Vol 14 (2) ◽  
pp. 103-128 ◽  
Author(s):  
Surajit Borkotokey ◽  
Loyimee Gogoi ◽  
Diganta Mukherjee
Keyword(s):  
Allocation Rule ◽  
Cooperative Network ◽  
Network Games

scholarly journals Allocation rules for coalitional network games

2015 ◽  
Vol 78 ◽  
pp. 80-88 ◽  
Author(s):  
Jean-François Caulier ◽  
Ana Mauleon ◽  
Vincent Vannetelbosch
Keyword(s):  
Network Games ◽  
Allocation Rules

scholarly journals The Myerson value for complete coalition structures

2011 ◽  
Vol 74 (3) ◽  
pp. 427-443 ◽  
Author(s):  
Takashi Ui ◽  
Hiroyuki Kojima ◽  
Atsushi Kajii
Keyword(s):  
Myerson Value ◽  
Coalition Structures

Bounded Rationality in the Centipede Game

Episteme ◽  
2011 ◽  
Vol 8 (3) ◽  
pp. 262-280 ◽  
Author(s):  
Ashton T. Sperry-Taylor
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Bounded Rationality ◽  
Real Life ◽  
Backward Induction ◽  
Rational Behavior ◽  
Normative Analysis ◽  
Cognitive Limitations ◽  
Real People ◽  
Rational Players

AbstractNormative game theory unsatisfactorily explains rational behavior. Real people do not behave as predicted, and what is prescribed as rational behavior is normally unattainable in real-life. The problem is that current normative analysis does not account for people's cognitive limitations – their bounded rationality. However, this paper develops an account of bounded rationality that explains the rationality of more realistic behavior. I focus on the Centipede Game, in which boundedly rational players explore and test others' immediate behavior, until they can apply limited backward induction. The result is that the game has a solution in the form of a subjective Nash equilibrium, which boundedly rational players can possibly realize.

Trust strategy simulation of corporation–NPO cross alliance using evolutionary game theory

Kybernetes ◽  
2017 ◽  
Vol 46 (3) ◽  
pp. 450-465 ◽  
Author(s):  
Yidan Chen ◽  
Lanying Sun
Keyword(s):  
Game Theory ◽  
Decision Making ◽  
Nonprofit Organizations ◽  
Bounded Rationality ◽  
Evolutionary Game Theory ◽  
Evolutionary Game ◽  
Stable State ◽  
Evolutionary Strategies ◽  
Content Type ◽  
Trust Relationships

Purpose The purpose of this paper is to investigate the dynamics and evolution of trust in organizational cross alliances. Design/methodology/approach In alliances between corporations and nonprofit organizations, trust in decision-making is a dynamic process. Using the replicated dynamics model of evolutionary game theory, this paper provides a trust decision model and analyzes four scenarios under different parameters. A numerical simulation is developed to present an intuitive interpretation of the dynamic development of trust decisions and the effects of incentive and punishment mechanisms. Findings Under different parameters, bounded rationality and utilities result in different but stable evolutionary strategies; the initial probability of adopting a trust strategy leads directly to whether participants adopt the strategy when the system reaches stability after continued games; and incentive and punishment mechanisms can significantly reduce the initial probability of adopting a trust strategy where the system evolves to meet stable state needs. Practical implications The establishment of trust relationships is an important influence on the stable and coordinated development of an alliance. The proposed model can help the alliance build closer trust relationships and provide a theoretical basis for the design of the trust mechanism. Originality/value Incentive and punishment bound by some degree of trust are introduced to address the problems of trust decisions and their dynamics; the model created reflects the bounded rationality and utility of each game stage. Useful evolutionary stable strategies using different variables are proposed to address the decision-making problems of trust in cross alliances.

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