We give a detailed characterization of optimal trades under budget constraints in a prediction market with a cost-function-based automated market maker. We study how the budget constraints of individual traders affect their ability to impact the market price. As a concrete application of our characterization, we give sufficient conditions for a property we call budget additivity: two traders wi...

We have already introduced the notions of MRT coming out of the budget constraint and MRS 1 coming from a consumer’s preferences. In our discussion of the consumer’s problem we talked about how, for example, if MRS < MRT at a point on the budget line, it means that the consumer is willing to give up good 2 for good 1 at slower rate than the market. Or put another way, the market put a lower val...

We decentralize incentive efficient allocations in large adverse selection economies by introducing a Walrasian market for mechanisms, that is, for menus of contracts. Facing a budget constraint, informed individuals choose lotteries over mechanisms, while firms supply (slots at) mechanisms at given prices. An equilibrium requires that firms cannot favorably change, or cut, prices. We show that...

In the present paper, we adopt the usual assumptions of the collective approach, i.e., individualism and efficiency, to study household labor supply. The theoretical innovation is twofold. Firstly, we incorporate in the initial setting the decision to participate to the labor market. Secondly, we abandon the assumption of linearity of the budget constraint. We show that (i) structural elements ...

We separate the “rentier” portion of the budget constraint of the representative agent from the “income-plus-distributed profits” segment. The former’s wealth consists exclusively of returns on government bonds, the latter’s wealth is wage income from working for firms plus the distributed profits of the latter. The non-neoclassical element is the non-imposition of the market-clearing assumptio...

We study the edge-connectivity survivable network design problem with an additional linear budget constraint. We give a strongly polynomial time (3, 3)-approximation algorithm for this problem, by extending a linear programming based technique of iterative rounding. Previously, a (4, 4)-approximation algorithm for this problem was known. The running time of this previous algorithm is not strong...

We extend the Bipolar Theorem of Brannath and Schachermayer (1999) to the space of nonnegative càdlàg supermartingales on a filtered probability space. We formulate the notion of fork-convexity as an analogue to convexity in this setting. As an intermediate step in the proof of our main result we establish a conditional version of the Bipolar theorem. In an application to mathematical finance w...

An automated market maker is a natural and common mechanism to subsidize information acquisition, revelation, and aggregation in a prediction market. The sought-after prediction aggregate is the equilibrium price. However, traders with budget constraints are restricted in their ability to impact the market price on their own. We give a detailed characterization of optimal trades in the presence...

Budget constraints are commonly considered in real decision frameworks; however, the literature has rarely addressed the design of contracts for supply chains with budget-constrained members and in which capital costs are considered. In this article, we study supply chain coordination of budget-constrained members when a financial market is unavailable. We propose a revenue-sharing-and-buy-back...