A bilevel game model for ascertaining competitive target prices for a buyer in negotiation with multiple suppliers

In this paper, a decision-support is developed for a strategic problem of identifying target prices for the single buyer to negotiate with multiple suppliers to achieve common goal of maintaining sustained business environment. For this purpose, oligopolistic-competitive equilibrium prices of suppliers are suggested to be considered as target prices. The problem of identifying these prices is modeled as a multi-leader-single-follower bilevel programming problem involving linear constraints and bilinear objective functions. Herein, the multiple suppliers are considered leaders competing in a Nash game to maximize individual profits, and the buyer is a follower responding with demand-order allocations to minimize the total procurement-cost. Profit of each supplier is formulated on assessing respective operational cost to fulfill demand-orders by integrating aggregate-production-distribution-planning mechanism into the problem. A genetic-algorithm-based technique is designed in general for solving large-scale instances of the variant of bilevel programming problems with multiple leaders and single follower, and the same is applied to solve the modeled problem. The developed decision support is appropriately demonstrated on the data of a leading FMCG manufacturing firm, which manufactures goods through multiple sourcing.

Parallel Lotteries: Insights from Alaskan Hunting Permit Allocation

We analyze the parallel lottery that is used to allocate hunting permits in the state of Alaska. Each participant is given tickets to distribute among lotteries for different types of items. Participants who win multiple items receive their favorite, and new winners are drawn from the lotteries with unclaimed items. When supply is scarce, equilibrium outcomes of parallel lotteries approximate a competitive equilibrium from equal incomes (CEEI), which is Pareto efficient. When supply is moderate, parallel lotteries exhibit two sources of inefficiency. First, some agents may benefit from trading probability shares. Second, outcomes may be “wasteful”: agents may receive nothing even if acceptable items remain unallocated. We bound both sources of inefficiency and show that each is eliminated by giving applicants a suitable number of tickets k: trades are never beneficial when k = 1, and waste is eliminated as [Formula: see text]. In addition, we show that the wastefulness of the k-ticket parallel lottery has some benefits: agents with strong preferences may prefer parallel lottery outcomes to those of any nonwasteful envy-free mechanism. These agents prefer small values of k, while agents with weak preferences prefer large values of k. Together, these results suggest that the k-ticket parallel lottery performs well under most circumstances and may be suitable for other settings where items are rationed. This paper was accepted by Gabriel Weintraub, revenue management and market analytics.

Dynamic Risked Equilibrium

We study a competitive partial equilibrium in markets where risk-averse agents solve multistage stochastic optimization problems formulated in scenario trees. The agents trade a commodity that is produced from an uncertain supply of resources. Both resources and the commodity can be stored for later consumption. Several examples of a multistage risked equilibrium are outlined, including aspects of battery and hydroelectric storage in electricity markets, distributed ownership of competing technologies relying on shared resources, and aspects of water control and pricing. The agents are assumed to have nested coherent risk measures based on one-step risk measures with polyhedral risk sets that have a nonempty intersection over agents. Agents can trade risk in a complete market of Arrow-Debreu securities. In this setting, we define a risk-trading competitive market equilibrium and establish two welfare theorems. Competitive equilibrium will yield a social optimum (with a suitably defined social risk measure) when agents have strictly monotone one-step risk measures. Conversely, a social optimum with an appropriately chosen risk measure will yield a risk-trading competitive market equilibrium when all agents have strictly monotone risk measures. The paper also demonstrates versions of these theorems when risk measures are not strictly monotone.

Short Communication: Optimally Solving the Unit-Demand Envy-Free Pricing Problem with Metric Substitutability in Cubic Time

In general, the unit-demand envy-free pricing problem has proven to be APX-hard, but some special cases can be optimally solved in polynomial time. When substitution costs that form a metric space are included, the problem can be solved in O(n4) time, and when the number of consumers is equal to the number of items—all with a single copy so that each consumer buys an item—a O(n3) time method is presented to solve it. This work shows that the first case has similarities with the second, and, by exploiting the structural properties of the costs set, it presents a O(n2) time algorithm for solving it when a competitive equilibrium is considered or a O(n3) time algorithm for more general scenarios. The methods are based on a dynamic programming strategy, which simplifies the calculations of the shortest paths in a network; this simplification is usually adopted in the second case. The theoretical results obtained provide efficiency in the search for optimal solutions to specific revenue management problems.

A Note on the Existence of the Competitive Equilibrium in Grossman and Shapiro (1984)

In their seminal paper, Grossman, G. M., and C. Shapiro. 1984. “Informative Advertising with Differentiated Products.” The Review of Economic Studies 51: 63–81 assume that it is not profitable for a firm to deviate to the supercompetitive price of Salop, S. C. 1979. “Monopolistic Competition with outside Goods.” The Bell Journal of Economics 10: 141–56. In this note, it is shown that this assumption is violated if, roughly, each firm reaches less than half of all consumers unless it is a duopoly. This implies that most of the simulations in Grossman, G. M., and C. Shapiro. 1984. “Informative Advertising with Differentiated Products.” The Review of Economic Studies 51: 63–81 are not actually equilibria. More importantly, this implies that for their equilibrium to exist nearly all consumers must receive at least one ad. For example, with just four firms in the market, at least 96% of the consumers must receive at least one ad, and this percentage increases with the number of firms in the market.

Market power and urban housing development

This paper investigates the relationship between market power and urban housing development in a two-period, partial equilibrium model of a durable rental housing market with a fixed stock of homogeneous land, a convex housing construction technology, and no externalities. We contrast the planning solution and the monopoly solution. Since we employ social surplus analysis, the competitive equilibrium coincides with the planning solution. Thus, we contrast the competitive equilibrium and the monopoly solution. On a priori grounds, one expects less housing to be produced under monopoly than under competition. The monopolist can produce less housing by constructing housing at lower density, holding land off the market, or developing his land later. We show that the monopolist: (i) will never hold land off the market for both periods, (ii) may develop either a higher or lower proportion of her land in the first period than under competition, and (iii) in both periods will construct at lower density than under competition.

On an “Important Principle” of Arrow and Debreu

In their seminal 1954 paper on the existence of competitive equilibrium, Arrow and Debreu state what they call an “important principle”, namely that it is necessary for the existence of equilibrium that every consumer has some asset or can supply some labour service which has a positive price at equilibrium. It does not seem to have been noticed that this claim is incorrect. We provide a very simple model of a private ownership economy with three goods where a competitive equilibrium exists, but consumers who have nothing to sell but their labour end up with zero wealth in equilibrium. As zero wealth must be taken to mean non-survival, and the Arrow–Debreu model is frequently interpreted as assuming that all consumers can survive without trade, we also briefly discuss the issue of non-survival in equilibrium. We finally point out that our example illustrates the possibility that technological progress may result in a situation where the value of work becomes negligible.

Can Market Participants Report Their Preferences Accurately (Enough)?

In mechanism design theory it is common to assume that agents can perfectly report their preferences, even in complex settings in which this assumption strains reality. We experimentally test whether real market participants can report their real preferences for course schedules “accurately enough” for a novel course allocation mechanism, approximate competitive equilibrium from equal incomes (A-CEEI), to realize its theoretical benefits. To use market participants’ real preferences (i.e., rather than artificial “induced preferences” as is typical in market design experiments), we develop a new experimental method. Our method, the “elicited preferences” approach, generates preference data from subjects through a series of binary choices. These binary choices reveal that subjects prefer their schedules constructed under A-CEEI to their schedules constructed under the incumbent mechanism, a bidding points auction, and that A-CEEI reduces envy, suggesting subjects are able to report their preferences accurately enough to realize the efficiency and fairness benefits of A-CEEI. However, preference-reporting mistakes do meaningfully harm mechanism performance. One identifiable pattern of mistakes was that subjects had relatively more difficulty reporting cardinal as opposed to ordinal preference information. The experiment helped to persuade the Wharton School to adopt the new mechanism and helped guide aspects of its practical implementation, especially around preference reporting. This paper was accepted by Yan Chen, decision analysis.