Who's Afraid of Strategic Behavior? Mechanisms for Group Purchasing

We study mechanisms to manage group purchasing among a set of buyers of a given product with a concave purchase cost function. The buyers are cost‐sensitive and willing to buy a range of product quantities at different prices. We investigate two types of mechanisms that can be used by a group purchasing organization (GPO): (a) ordering mechanisms where the buyers, without divulging private information, choose their order quantities and pay for them according to a given cost‐sharing rule or a fixed price; and (b) bidding mechanisms where the buyers announce their valuations for different quantities and the GPO determines their purchase quantities and cost‐shares according to pre‐announced schemes. Under the choice of appropriate cost‐sharing rules, we introduce a sequential joint ordering mechanism and a family of ordering strategies under which some buyers’ strategic deviations never worsen other buyers. We propose a class of bidding mechanisms with some desirable properties and show that a Nash equilibrium bid schedule always exists wherein all buyers’ profits are at least as high as those under truthful bidding. In our proposed mechanisms, some buyers’ strategic deviation from truthful bidding can only make the others better off. Thus, buyers need not worry about strategic behavior of their counterparts. We compare the performances of the system under different mechanisms and show the superiority of our proposed bidding mechanism. We show that the profits generated by our proposed bidding mechanisms under the proportional cost‐sharing rule are never dominated by the maximum profits of the first‐best fixed price

Strong Players and Stable Coalition Structures in PMAS Profit Game

In a non-negative profit game that possesses a Population Monotonic Allocation Scheme (PMAS), being a member of a larger coalition implies that your profit cannot decrease. In this paper, we refer to such games as PMAS profit games. As population monotonicity is a nice and desirable property that encourages formation of larger coalitions and implies stability of the grand coalition, we explore if this special feature of PMAS games can help in identifying additional stable coalition structures under different stability concepts in cooperative games—namely, core partitions, the von Neumann–Morgenstern (vNM) stable set, the largest consistent set, and the equilibrium process of coalition formation (EPCF)—and in developing relationships between coalition structures that are stable under these different stability concepts. We first define two special classes of players for PMAS profit games—extreme and strong players—and use them to develop an algorithm for construction of stable (core) partitions. We also use extreme players to identify absorbing states for equilibrium processes of coalition formation with high level of farsightedness. We then explore the impact of population monotonicity on the relationship between stable coalition structures under abovementioned stability concepts. While we are able to obtain some results related to stability of the grand coalition and to establish relationships between stable coalition structures under different stability notions that are consistent with the existing body of knowledge, population monotonicity in general does not add enough for strengthening of the existing results. However, we are able to show a couple of more general result that hold for arbitrary cooperative TU profit games. That is, we show that the members of vNM farsighted stable sets are core partitions, and that core partitions are members of a vNM stable sets. Moreover, we show that the members of vNM farsighted stable sets are EPCF-stable partitions

Strong Players and Stable Coalition Structures in PMAS Profit Game

In a non-negative profit game that possesses a Population Monotonic Allocation Scheme (PMAS), being a member of a larger coalition implies that your profit cannot decrease. In this paper, we refer to such games as PMAS profit games. As population monotonicity is a nice and desirable property that encourages formation of larger coalitions and implies stability of the grand coalition, we explore if this special feature of PMAS games can help in identifying additional stable coalition structures under different stability concepts in cooperative games—namely, core partitions, the von Neumann–Morgenstern (vNM) stable set, the largest consistent set, and the equilibrium process of coalition formation (EPCF)—and in developing relationships between coalition structures that are stable under these different stability concepts. We first define two special classes of players for PMAS profit games—extreme and strong players—and use them to develop an algorithm for construction of stable (core) partitions. We also use extreme players to identify absorbing states for equilibrium processes of coalition formation with high level of farsightedness. We then explore the impact of population monotonicity on the relationship between stable coalition structures under abovementioned stability concepts. While we are able to obtain some results related to stability of the grand coalition and to establish relationships between stable coalition structures under different stability notions that are consistent with the existing body of knowledge, population monotonicity in general does not add enough for strengthening of the existing results. However, we are able to show a couple of more general result that hold for arbitrary cooperative TU profit games. That is, we show that the members of vNM farsighted stable sets are core partitions, and that core partitions are members of a vNM stable sets. Moreover, we show that the members of vNM farsighted stable sets are EPCF-stable partitions

Manufacturers’ competition and cooperation in sustainability: Stable recycling alliances

Rather than organizing disposal of consumer-generated waste themselves, many states and countries have passed legislation that makes producers responsible for the proper disposal (i.e., recycling) of the products that they bring to the market. We study the stability of producers’ strategies emerging under such legislation. In our paper, the producers compete with multiple differentiated products in consumer markets but may consider cooperating when recycling those products to benefit from economies of scale. Products made by different producers or sold in different markets might still be considered for joint recycling. Our main questions are when and whether firm-based recycling strategies (i.e., separately recycling products falling under same brand) or market-based recycling strategies (i.e., separately recycling products falling in the same product category) emerge as stable outcomes. To that end, we analyze a series of simple producer-market configurations. We first look at an asymmetric market model with two producers making three products in two markets, and then, we look at a symmetric market model with two producers competing with four products in two markets. Our results show that, with intense market competition and differentiated market sizes, producers may recycle their products on their own without cooperating with others. In some instances, they can add a product from their competitor to their recycling mix. Because these outcomes are never socially optimal, they may reduce social welfare and require government intervention. Otherwise, with less intense competition or more equitable market shares, all-inclusive (market-based) recycling is the most common stable outcome with high (low) scale economies, and the firms’ independent choices might lead to social optima

Green Recycling Networks

One of the biggest obstacles to recycling consumer goods is the high cost of material separation. The recovered value from recycling increases as the disassembly of the discarded product is easier. For example, recovery of high-value reusable components from a car, television set or cell phone may be too labor-intensive, making recycling companies forgo that option and simply “grind the product ” to recover less valuable raw materials such as steel, precious metals or plastic instead of more valuable components. At the same time, competitive pressures force firms to differentiate their products when competing for consumers. Such differentiation is accrued through, e.g., product design and material selection choices that are different from competitors. Product differentiation leads thus to waste streams that are more diverse in terms of aggregate material stream composition, which is much more difficult to separate and, hence, increases the recycling costs. One approach would be to recycle products at the level where they are more homogeneous, i.e., at the firm level. The second big obstacle to recycling are economies of scale. Significant set-up costs are often required to set a recycling infrastructure (e.g., to set up collection sites, to certify the processes of participating recyclers, to administer financial flows between consumers, manufacturers and recyclers, …). Therefore, when firms compete with differentiated products, the

On the core of m-attribute games

We study a special class of cooperative games with transferable utility (TU), called (Formula presented.) -attribute games. Every player in an (Formula presented.) -attribute game is endowed with a vector of (Formula presented.) attributes that can be combined in an additive fashion; that is, if players form a coalition, the attribute vector of this coalition is obtained by adding the attributes of its members. Another fundamental feature of (Formula presented.) -attribute games is that their characteristic function is defined by a continuous attribute function (Formula presented.) —the value of a coalition depends only on evaluation of (Formula presented.) on the attribute vector possessed by the coalition, and not on the identity of coalition members. This class of games encompasses many well-known examples, such as queueing games and economic lot-sizing games. We believe that by studying attribute function (Formula presented.) and its properties, instead of specific examples of games, we are able to develop a common platform for studying different situations and obtain more general results with wider applicability. In this paper, we first show the relationship between nonemptiness of the core and identification of attribute prices that can be used to calculate core allocations. We then derive necessary and sufficient conditions under which every (Formula presented.) -attribute game embedded in attribute function (Formula presented.) has a nonempty core, and a set of necessary and sufficient conditions that (Formula presented.) should satisfy for the embedded game to be convex. We also develop several sufficient conditions for nonemptiness of the core of (Formula presented.) -attribute games, which are easier to check, and show how to find a core allocation when these conditions hold. Finally, we establish natural connections between TU games and (Formula presented.) -attribute games