BACKGROUND To address the impact that out-of-pocket prices may have on medication use, it is vital to understand how the demand for medications may be affected when patients are faced with changes in the price to acquire treatment and how price responsiveness differs across medication classes.  OBJECTIVE To examine the impact of cost-sharing changes on the demand for 8 classes of prescription...

Economic guidance can be of substantial value to policymakers in principle. However, guidance delivered in the form of complex formulae and detailed mathematical characterizations of optimal policies may not be fully appreciated or warmly embraced. Consequently, insights like those of William Rogerson (2003) are particularly important. Rogerson demonstrates in a plausible setting that a pair of...

We study the cost sharing problem for cooperative games in situations where the cost function C is not available via oracle queries, but must instead be learned from samples drawn from a distribution, represented as tuples (S,C(S)), for different subsets S of players. We formalize this approach, which we call STATISTICAL COST SHARING, and consider the computation of the core and the Shapley val...

The problem of sharing the cost of a common infrastructure among a set of strategic and cooperating players has been the subject of intensive research in recent years. However, most of these studies consider cooperative cost sharing games in an offline setting, i.e., the mechanism knows all players and their respective input data in advance. In this paper, we consider cooperative cost sharing g...

A new concept of consistency for cost sharing solutions is discussed, analyzed, and related to the homonymous property within the rationing context. The class of additive and consistent mechanisms is isomorphic to the class of consistent and monotonic rationing methods. Consequently average and serial cost sharing are consistent, whereas Shapley-Shubik is not. Average cost sharing is the only s...

We describe the construction and analysis of asymmetric Cost Sharing mechanisms, in which a variety of axioms are applied to subsets of the agents/goods. We show that the analysis can be quite subtle as apparently similar axiomatizations lead to significantly different results; in particular, combinations of symmetric mechanisms can be extremely asymmetric and biased. In addition, we characteri...

Cost sharing contracts is one of the most common to coordinate green supply chains. In this paper, we examine whether it can chains in set up overconfidence. We assume that manufacturer overconfident and retailer rational. The overestimates consumers’ sensitivity product greenness accurately estimates uncertainty demand. rational cooperate through cost contracts. Then, construct a game theoreti...