scholarly journals Allocation Rules for Games with Optimistic Aspirations

Game Theory ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Luisa Carpente ◽  
Balbina Casas-Méndez ◽  
Ignacio García-Jurado ◽  
Anne van den Nouweland
Keyword(s):  
Shapley Value ◽  
Allocation Rule ◽  
Equal Division ◽  
Allocation Rules ◽  
Null Player ◽  
Division Rule

A game with optimistic aspirations specifies two values for each coalition of players: the first value is the worth that the players in the coalition can guarantee for themselves in the event that they coordinate their actions, and the second value is the amount that the players in the coalition aspire to get under reasonable but very optimistic assumptions about the demands of the players who are not included in the coalition. In this paper, in addition to presenting this model and justifying its relevance, we introduce allocation rules and extend the properties of efficiency, additivity, symmetry, and null player property to this setting. We demonstrate that these four properties are insufficient to find a unique allocation rule and define three properties involving null players and nullifying players that allow the identification of unique allocation rules. The allocation rules we identify are the Midpoint Shapley Value and the Equal Division Rule.

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.

A Note on the Owen Value for Glove Games

2015 ◽  
Vol 17 (04) ◽  
pp. 1550014 ◽  
Author(s):  
Julia Belau
Keyword(s):  
Shapley Value ◽  
Simple Game ◽  
Computational Effort ◽  
Computationally Efficient ◽  
Owen Value ◽  
Allocation Rules ◽  
The Shapley Value ◽  
Minimal Winning Coalitions

A well-known and simple game to model markets is the glove game where worth is produced by building matching pairs. For glove games, different concepts, like the Shapley value, the component restricted Shapley value or the Owen value, yield different distributions of worth. While the Shapley value does not distinguish between productive and unproductive agents in the market and the component restricted Shapley value does not consider imbalancedness of the market, the Owen value accounts for both. As computational effort for Shapley-based allocation rules is generally high, this note provides a computationally efficient formula for the Owen value (and the component restricted Shapley value) for glove games in case of minimal winning coalitions. A comparison of the efficient formulas highlights the above-mentioned differences.

scholarly journals Redistribution of tax resources: a cooperative game theory approach

SERIEs ◽  
2021 ◽  
Author(s):  
Emilio Calvo
Keyword(s):  
Cooperative Game ◽  
Shapley Value ◽  
Financial System ◽  
Budget Allocation ◽  
Theory Approach ◽  
Moderate Degree ◽  
Allocation Rules ◽  
Economic Entity ◽  
Balanced Allocation ◽  
The Stability

AbstractWe consider the problem of how to distribute public expenditure among the different regions of an economic entity after all taxes have been collected. Typical examples are: the regions that make up a country, the states of a federal country, or the countries of a confederation of countries. We model the problem as a cooperative game in coalitional form, called the tax game. This game estimates the fiscal resources collected in each region, or coalition of regions, by differentiating between what comes from economic activity within each region and what comes from trade with the other regions. This methodology provides a measure of the disagreement within a region, or coalitions of regions, with respect to the budget received. Similarly, the stability of a budget allocation can be inferred by its situation within the core of the corresponding tax game. We consider the Spanish case as an example and show that the current regional financial system has a moderate degree of instability. We introduce two budget allocation rules, both borrowed from the cooperative games literature: the balanced allocation, which coincides with the nucleolus and with the Shapley value of the tax game, and the weighted balanced allocation, which coincides with the weighted Shapley value. We compare both budget allocation rules with the current Spanish financial system.

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 Shapley Value for Parallel Machine Sequencing Situation without Initial Order

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Shanshan Liu ◽  
Zhaohui Liu
Keyword(s):  
Polynomial Time ◽  
Shapley Value ◽  
Processing Time ◽  
Cost Allocation ◽  
Parallel Machine ◽  
Allocation Rule ◽  
The Shapley Value ◽  
Sequencing Game ◽  
Identical Machine

We consider the parallel identical machine sequencing situation without initial schedule. For the situation with identical job processing time, we design a cost allocation rule which gives the Shapley value of the related sequencing game in polynomial time. For the game with identical job weight, we also present a polynomial time procedure to compute the Shapley value.

scholarly journals Efficient Allocation of Customers to Facilities in the Multi-Objective Sustainable Location Problem

2020 ◽  
Vol 12 (18) ◽  
pp. 7634
Author(s):  
Xifeng Tang ◽  
Jiantao Wu ◽  
Rui Li
Keyword(s):  
Location Problem ◽  
Computation Time ◽  
Allocation Rule ◽  
Nsga Ii ◽  
Solution Quality ◽  
Allocation Rules ◽  
Location Allocation ◽  
Multi Objective ◽  
Sustainable Logistics ◽  
The Impact

This paper aims to evaluate the impact of customer allocation on the facility location in the multi-objective location problem for sustainable logistics. After a new practical multi-objective location model considering vehicle carbon emissions is introduced, the NSGA-II and SEAMO2 algorithms are employed to solve the model. Within the framework of each algorithm, three different allocation rules derived from the optimization of customer allocation based on distance, cost, and emissions are separately applied to perform the customer-to-facility assignment so as to evaluate their impacts. The results of extensive computational experiments show that the allocation rules have nearly no influence on the solution quality, and the allocation rule based on the distance has an absolute advantage of computation time. These findings will greatly help to simplify the location-allocation analysis in the multi-objective location problems.

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