Dissertations / Theses on the topic 'Sharing rule'

In noncooperative cost sharing games, individually strategic agents choose resources based on how the welfare (cost or revenue) generated at each resource (which depends on the set of agents that choose the resource) is distributed. The focus is on finding distribution rules that lead to stable allocations, which is formalized by the concept of Nash equilibrium, e.g., Shapley value (budget-balanced) and marginal contribution (not budget-balanced) rules.

Recent work that seeks to characterize the space of all such rules shows that the only budget-balanced distribution rules that guarantee equilibrium existence in all welfare sharing games are generalized weighted Shapley values (GWSVs), by exhibiting a specific 'worst-case' welfare function which requires that GWSV rules be used. Our work provides an exact characterization of the space of distribution rules (not necessarily budget-balanced) for any specific local welfare functions remains, for a general class of scalable and separable games with well-known applications, e.g., facility location, routing, network formation, and coverage games.

We show that all games conditioned on any fixed local welfare functions possess an equilibrium if and only if the distribution rules are equivalent to GWSV rules on some 'ground' welfare functions. Therefore, it is neither the existence of some worst-case welfare function, nor the restriction of budget-balance, which limits the design to GWSVs. Also, in order to guarantee equilibrium existence, it is necessary to work within the class of potential games, since GWSVs result in (weighted) potential games.

We also provide an alternative characterization—all games conditioned on any fixed local welfare functions possess an equilibrium if and only if the distribution rules are equivalent to generalized weighted marginal contribution (GWMC) rules on some 'ground' welfare functions. This result is due to a deeper fundamental connection between Shapley values and marginal contributions that our proofs expose—they are equivalent given a transformation connecting their ground welfare functions. (This connection leads to novel closed-form expressions for the GWSV potential function.) Since GWMCs are more tractable than GWSVs, a designer can tradeoff budget-balance with computational tractability in deciding which rule to implement.

碩士
國立臺北大學
財政學系
106
This paper is based on the two-dimension rent-seeking model of Faria et al. (2014). When the local government wants to provides public goods or public construction. The local government will seek some subsidy which comes from the central government. In order to gain more subsidy. It will input two-dimension effort. The first dimension effort is for expend total subsidy. The second dimension effort is to gain more subsidy. In this paper, the sharing rule of subsidy is based on two ratios. First is population ratio. Second is the effort which inputs to gain more subsidy. We focus our discussion on the effects of changing in sharing rule of subsidy on two-dimension rent-seeking activity. According to the economic intuition. There is more ratio of sharing rule is based on population ratio will reduce the rent-seeking level. However, different from the economic intuition. We found that social rent-seeking outlays may increase rather than decrease when sharing rule is more based on population ratio.

Fair division is the problem of dividing one or several goods among a set of agents in a way that satisfies a suitable fairness criterion. Traditionally studied in economics, philosophy, and political science, fair division has drawn a lot of attention from the multiagent systems community, since this field is strongly concerned about how a surplus (or a cost) should be divided among a group of agents. Arguably, the Shapley value is the single most important contribution to the problem of fair division. It assigns to each agent a share of the resource equal to the expected marginal contribution of that agent. Thus, it is implicitly assumed that individual marginal contributions can be objectively computed. In this thesis, we propose a game-theoretic model for sharing a joint reward when the quality of individual contributions is subjective. In detail, we consider scenarios where a group has been formed and has accomplished a task for which it is granted a reward, which must be shared among the group members. After observing the contribution of the peers in accomplishing the task, each agent is asked to provide evaluations for the others. Mainly to facilitate the sharing process, agents can also be requested to provide predictions about how their peers are evaluated. These subjective opinions are elicited and aggregated by a central, trusted entity, called the mechanism, which is also responsible for sharing the reward based exclusively on the received opinions. Besides the formal game-theoretic model for sharing rewards based on subjective opinions, we propose three different mechanisms in this thesis. Our first mechanism, the peer-evaluation mechanism, divides the reward proportionally to the evaluations received by the agents. We show that this mechanism is fair, budget-balanced, individually rational, and strategy-proof, but that it can be collusion-prone. Our second mechanism, the peer-prediction mechanism, shares the reward by considering two aspects: the evaluations received by the agents and their truth-telling scores. To compute these scores, this mechanism uses a strictly proper scoring rule. Under the assumption that agents are Bayesian decision-makers, we show that this mechanism is weakly budget-balanced, individually rational, and incentive-compatible. Further, we present approaches that guarantee the mechanism to be collusion-resistant and fair. Our last mechanism, the BTS mechanism, is the only one to elicit both evaluations and predictions from the agents. It considers the evaluations received by the agents and their truth-telling scores when sharing the reward. For computing the scores, it uses the Bayesian truth serum method, a powerful scoring method based on the surprisingly common criterion. Under the assumptions that agents are Bayesian decision-makers, and that the population of agents is sufficiently large so that a single evaluation cannot significantly affect the empirical distribution of evaluations, we show that this mechanism is incentive-compatible, budget-balanced, individually rational, and fair.

Dans certaines circonstances, des actions de groupes sont plus performantes que des actions individuelles. Dans ces situations, il est préférable de former des coalitions. Ces coalitions peuvent être disjointes ou imbriquées. La littérature économique met un fort accent sur la modélisation des accords où les coalitions d’agents économiques sont des ensembles disjoints. Cependant on observe dans la vie de tous les jours que les coalitions politiques, environnementales, de libre-échange et d’assurance informelles sont la plupart du temps imbriquées. Aussi, devient-il impératif de comprendre le fonctionnement économique des coalitions imbriquées. Ma thèse développe un cadre d’analyse qui permet de comprendre la formation et la performance des coalitions même si elles sont imbriquées. Dans le premier chapitre je développe un jeu de négociation qui permet la formation de coalitions imbriquées. Je montre que ce jeu admet un équilibre et je développe un algorithme pour calculer les allocations d’équilibre pour les jeux symétriques. Je montre que toute structure de réseau peut se décomposer de manière unique en une structure de coalitions imbriquées. Sous certaines conditions, je montre que cette structure correspond à une structure d’équilibre d’un jeu sous-jacent. Dans le deuxième chapitre j’introduis une nouvelle notion de noyau dans le cas où les coalitions imbriquées sont permises. Je montre que cette notion de noyau est une généralisation naturelle de la notion de noyau de structure de coalitions. Je vais plus loin en introduisant des agents plus raffinés. J’obtiens alors le noyau de structure de coalitions imbriquées que je montre être un affinement de la première notion. Dans la suite de la thèse, j’applique les théories développées dans les deux premiers chapitres à des cas concrets. Le troisième chapitre est une application de la relation biunivoque établie dans le premier chapitre entre la formation des coalitions et la formation de réseaux. Je propose une modélisation réaliste et effective des assurances informelles. J’introduis ainsi dans la littérature économique sur les assurances informelles, quatre innovations majeures : une fusion entre l’approche par les groupes et l’approche par les réseaux sociaux, la possibilité d’avoir des organisations imbriquées d’assurance informelle, un schéma de punition endogène et enfin les externalités. Je caractérise les accords d’assurances informelles stables et j’isole les conditions qui poussent les agents à dévier. Il est admis dans la littérature que seuls les individus ayant un revenu élevé peuvent se permettre de violer les accords d’assurances informelles. Je donne ici les conditions dans lesquelles cette hypothèse tient. Cependant, je montre aussi qu’il est possible de violer cette hypothèse sous d’autres conditions réalistes. Finalement je dérive des résultats de statiques comparées sous deux normes de partage différents. Dans le quatrième et dernier chapitre, je propose un modèle d’assurance informelle où les groupes homogènes sont construits sur la base de relations de confiance préexistantes. Ces groupes sont imbriqués et représentent des ensembles de partage de risque. Cette approche est plus générale que les approches traditionnelles de groupe ou de réseau. Je caractérise les accords stables sans faire d’hypothèses sur le taux d’escompte. J’identifie les caractéristiques des réseaux stables qui correspondent aux taux d’escomptes les plus faibles. Bien que l’objectif des assurances informelles soit de lisser la consommation, je montre que des effets externes liés notamment à la valorisation des liens interpersonnels renforcent la stabilité. Je développe un algorithme à pas finis qui égalise la consommation pour tous les individus liés. Le fait que le nombre de pas soit fini (contrairement aux algorithmes à pas infinis existants) fait que mon algorithme peut inspirer de manière réaliste des politiques économiques. Enfin, je donne des résultats de statique comparée pour certaines valeurs exogènes du modèle.
When groups can perform a task more efficiently than single individuals, a desirable behavior is to form coalitions. Coalitions can be disjoint or overlapping. But, almost all the economics literature on coalition formation is mostly restricted to models where coalitions are disjoint. However, in politics, environmental issues, customs unions, informal insurance, and many other economic, social, and political interactions, we observe overlapping coalitions. How can we understand agreements involving overlapping coalitions ? How can we study their efficiency if there is no theory to model them ? My thesis solves these questions by developing a framework on coalition formation that accommodates overlapping coalitions. In the first chapter, following a non-cooperative approach, I develop a bargaining game to model the formation of overlapping coalitions. I show the existence of a subgame perfect equilibrium and I provide an algorithm that generates equilibrium outcomes for symmetric games. I establish an overlapping coalition’s representation for each network and I show that, under some conditions, they are equilibrium outcomes. The core is the most popular solution concept in cooperative game. In the second chapter, following a cooperative approach, I develop a new concept of core that accommodates overlapping coalitions, and coincides with the recursive core when coalitions do not intersect. First, I extend naively the residual game to only embody overlapping coalitions, and I obtain a range of allocations between the optimistic and the pessimistic core. Secondly, I provide a consistent notion of residual game and I show that the overlapping coalition structure core not only stands as a generalization of the coalition structure core, but also induces a refinement of the extended recursive core. As I build a theoretical framework for overlapping coalition formation, I provide applications in the remainder of the thesis. In the third chapter, I model informal insurance arrangements as a collection of overlapping trust coalitions. The model is based on empirical facts. I enrich the theoretical modeling of informal insurance arrangements by introducing four key features : the merging of the group approach and the network approach, the possibility for informal insurance organizations to overlap, the endogenous punishment scheme, and externalities. I characterize self enforcing stable informal insurance arrangements and I derive conditions under which deviation occurs. While it is always assumed in the literature that only wealthy individuals may deviate. I formally isolate conditions under which this assumption holds. Furthermore, I show that if these conditions does not hold, this assumption is violated. Finally, I provide static comparative results for consumption under two distinct sharing norms. Finally in the fourth chapter, I investigate multilateral informal insurance organizations built on networks of trust relationships. The model is based on empirical findings and nests the traditional approaches which use bilateral links or groups. I characterize self enforcing stable informal insurance organizations without imposing extreme discounting. I show that density and clustering characterize networks that match the lowest discounting for stability. While insurance is formally arranged to smooth consumption, I show that external effects such as social privileges tend to reinforce the stability of such arrangement. I use my stability results to derive comparative statics for exogenous parameters of the model. Finally, I develop a procedure in finite steps that equates consumption for all linked individuals. Contrary to the existing procedures in infinite steps, my procedure is more realistic and useful to policy makers.