Population Monotonicity in Newsvendor Games

Chen, Xin; Gao, Xiangyu; Hu, Zhenyu; Wang, Qiong

doi:10.1287/mnsc.2018.3053

Cited by 9 publications

(8 citation statements)

References 39 publications

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“…In contrast to other known approaches in the literature; for example, a general theory of clubs proposed by Buchanan (1965), the duality approach has an interesting feature; that is, there always exists an optimal dual solution that defines an allocation policy in the core, which can be found in polynomial time. Motivated by the work of Chen and Zhang (2009) and Chen, Gao, Hu, and Wang (2019), Owen (1975) present a stochastic programming duality approach to the inventory centralization games and the newsvendor games, respectively. However, these articles mainly focus on demand uncertainty.…”

Section: Literature Reviewmentioning

confidence: 99%

“…We note that the newsvendor game is that players are individual newsvendors selling an identical item and facing the same per‐unit penalty cost, with the goal of attaining the minimum expected cost (Chen et al., 2019). In our study, the risk pooling game is a case of the newsvendor games, in which each farmer is a newsvendor with different cost parameters.…”

Section: Benchmark: Noncooperative Casementioning

confidence: 99%

“…We start by introducing the concept of log‐concavity; that is, a continuous random variable x is log‐concave if the logarithm of its density function

g (x)

is concave, which is given by Chen et al. (2019). In fact, log‐concave probability distributions cover various common distributions, including logistics, exponential, normal, and uniform, and have been widely applied in economics (Bagnoli & Bergstrom, 2005).…”

Section: Risk Pooling Game With a Linear Production Cost Functionmentioning

confidence: 99%

See 2 more Smart Citations

Risk pooling cooperative games in contract farming

Shi

Cao

2021

Canadian J Agri Economics

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Contract farming can be an effective measure to deal with agricultural production risks. This study provides a two‐stage stochastic programming model to analyze farmers’ cooperation in the context of contract farming under uncertainty. It provides a fair cost allocation policy for a coalition of farmers using a stochastic linear duality approach. A fair cost allocation implies that no subset of farmers has an incentive to leave the coalition. Thus, a fair allocation policy ensures the stability of a coalition. Meanwhile, the risk pooling game is shown to have population monotonicity, which means that, every time a coalition adds a new member, each farmer within the coalition will incur a smaller cost. Hence, the population monotonicity gives an incentive for coalition expansion. Our results not only provide a simple way to design fair cost allocation policies for collaboration strategies in contract farming, but also play an important role in the sustainable development of farmers’ coalitions.

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Section: Literature Reviewmentioning

confidence: 99%

Section: Benchmark: Noncooperative Casementioning

confidence: 99%

“…We start by introducing the concept of log‐concavity; that is, a continuous random variable x is log‐concave if the logarithm of its density function

g (x)

Section: Risk Pooling Game With a Linear Production Cost Functionmentioning

confidence: 99%

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Risk pooling cooperative games in contract farming

Shi

Cao

2021

Canadian J Agri Economics

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“…Owen (1975) proved that the core is nonempty for a class of linear production games using the duality theory of linear programs. The duality approach provided by Owen (1975) has been a significant tool used in analyzing cooperative games and has been applied widely in a variety of fields (Tamir, 1992; Goemans and Skutella, 2004; Chen et al, 2019). Motivated by the work of Owen (1975), Chen and Zhang (2009) took a stochastic programming duality approach to the inventory centralization games.…”

Section: Literature Reviewmentioning

confidence: 99%

Contract farming problems and games under yield uncertainty

Shi

Cao

2020

Aus J Agri & Res Econ

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This study investigates whether a group of independent agricultural producers willingly forms a coalition to jointly cope with yield uncertainty in contract farming. The agricultural producers' cooperative game problem in contract farming is formulated as a two-stage stochastic linear program. Using the strong duality theory of stochastic linear programs, we not only prove that the core of agricultural producers' cooperative game is nonempty but also provide a simple way to compute a profit allocation policy in the core. We establish the convexity of agricultural producers' cooperative game so that the game has population monotonicity, which gives agricultural producers an incentive to expand their current coalition. We then analyze the agricultural producers' cooperative game with a concave cost structure, which may exhibit economies of scale for production. Taking advantage of the proposed stochastic duality approach, the agricultural producers' cooperative game with a concave cost structure is also shown to have a nonempty core.

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“…In this section, we present an alternative description for PMAS-es in vertex cover games based on the dual linear program of the vertex cover problem, which reveals the dual-based allocation scheme nature of PMAS-es. Our description is inspired by the work of Chen et al [1].…”

Section: Dual-based Description Of Pmas-es For Vertex Cover Gamesmentioning

confidence: 99%

Population Monotonic Allocation Schemes for Vertex Cover Games

Xiao,

Fang,

2020

Preprint

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For the class of vertex cover games (introduced by Deng et al., Math. Oper. Res., 24:751-766, 1999 [2]), we investigate the population monotonic allocation schemes (introduced by Sprumont, Games Econ. Behav., 2: 378-394, 1990 [9]). We present a complete characterization for the class of vertex cover games admitting a population monotonic allocation scheme (PMAS for short), i.e., a vertex cover game has a PMAS if and only if the underlying graph is (K 3 , C 4 , P 5 )-free. Our characterization implies that the existence of a PMAS can be determined efficiently for vertex cover games. We also propose an alternative description for PMAS-es in vertex cover games based on the dual linear program of the vertex cover problem, which reveals the dualbased allocation scheme nature of PMAS-es. Moreover, we give a complete characterization for integral PMAS-es in vertex cover games via stable matchings and show that the celebrated Gale-Shapley algorithm (introduced by Gale and Shapley, Amer. Math. Monthly, 69:9-15, 1962 [4]) can be used to produce all integral PMAS-es in vertex cover games.

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Population Monotonicity in Newsvendor Games

Cited by 9 publications

References 39 publications

Risk pooling cooperative games in contract farming

Risk pooling cooperative games in contract farming

Contract farming problems and games under yield uncertainty

Population Monotonic Allocation Schemes for Vertex Cover Games

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