How should a principal reward and support agents when firm performance is characterized by success or failure?

Principal-agent models with multiple agents typically assume that the principal wishes to maximize the sum of the agents' achievements (net of the rewards paid to them). But in many settings, like R&D, all that the principal "Needs" is that at least one agent will be "successful." We identify settings where the principal actually wants agents to refrain from exerting high effort in order to save expected compensation. We show that the number of agents can decrease in the project's value for the principal. We also consider sequential efforts and investigate settings where the principal can provide support to agents

Partial pooling by independent firms with allocation according to contribution to pool

We consider two firms which pool some of their inventory. The pool is created by the firms' contributions, and a firm's entitlement for an allocation from the pool (if needed) is a function of its contribution. Transshipment from the pool is costly, but the firms can benefit from reduced risk through inventory sharing using the pool. We analyze the resulting non-cooperative game. We prove existence of a Nash equilibrium and compare it to a model with centralized control. An appropriate compensation cost for using the other firms contribution to the pool can induce the retailers to achieve centralized solutions. We also compare the optimal partial pooling strategy to the special cases of no pooling and complete pooling and discuss situations where it is likely that one of the special cases will be optimal. Numerical results confirm that in the prevalent practice of partial pooling the retailers can achieve higher expected profits than under no pooling or complete pooling and that there is a significant difference between a setting with independent players and a model of central control

Allocating Pooled Inventory According to Contributions and Entitlements

Inventory pooling, whether by centralization of stock or by mutual assistance, is known to be beneficial when demands are uncertain. But when the retailers are independent, the question is how to divide the benefits of pooling.We consider a decentralized inventory pooling scheme where retailers' entitlements to allocation in case of shortage depend on their contributions to the pool. We derive the Nash equilibrium, and specialize it to symmetric cases

On the Non-Symmetric Nash and Kalai-Smorodinsky Bargaining Solutions

Recently in some negotiation application areas the usual assumption that the negotiators are symmetric has been relaxed.  In particular, weights have been introduced to the Nash Bargaining Solution to reflect the different powers of the players. Yet operating with non-symmetric bargaining solutions and their implications is, we feel, not well understood.We analyze the properties and optimization of the non-symmetric Nash Bargaining Solution and of a non-symmetric Kalai-Smorodinsky Bargaining Solution. We provide extensive comparative statics, then comment on the  implications of the concepts in supply chain coordination contexts

Allocating Pooled Inventory According to Contributions and Entitlements

Inventory pooling, whether by centralization of stock or by mutual assistance, is known to be beneficial when demands are uncertain. But when the retailers are independent, the question is how to divide the benefits of pooling.We consider a decentralized inventory pooling scheme where retailers' entitlements to allocation in case of shortage depend on their contributions to the pool. We derive the Nash equilibrium, and specialize it to symmetric cases

Stochastic models of changes in population distribution among categories

There are very many processes in the natural and social sciences which can be represented as a set of flows of objects or people between categories of some kind. The Markov chain model has been used in the study of many of them. The basic form of the Markov chain model is, however, rarely adequate to describe social, occupational and geographical mobility processes. We shall therefore discuss a number of generalizations designed to introduce greater realism. In Chapter I we formulate and investigate a general model which results from relaxing the assumptions of sojourn-time's memorylessness and independence of origin and destination states, and of population homogeneity. The model (a mixture of semi-Markov processes) is then used in two ways. First, it provides a framework in which various special cases (which correspond to models which were used by social scientists) can be analytically compared. We pay particular attention to comparisons of rate of mobility in related versions of various models and to compatability of popular parametric forms with observed mobility patterns. Second, any result obtained for the general model can be specialized for the various cases and subcases. In Chapter II we formulate a system-model allowing interaction among individuals (components), which has been motivated by Conlisk. We define processes on this model and analyze their properties. A major effort is then devoted to establishing that when the population size becomes large, this rather complex stochastic model can be approximated by a single deterministic recursion due to Conlisk (1976). Nevertheless, we draw attention to certain aspects (particularly steady-state behavior) in which the approximation may fail. In Chapter III we address ourselves to the issue of measurement of (what we refer to as) social inheritance in intergenerational mobility processes. We distinguish between various aspects and concepts of social inheritance and outline the implications that certain "social values" may have on constructing a measure (or index). In the mathematical discussion which follows certain mechanisms for generating "families" of measures are indicated, and the properties of some particular combinations are investigated.Business, Sauder School ofGraduat