Partition Function Form Games

Kóczy, László Á.; Koczy,

doi:10.1007/978-3-319-69841-0

Cited by 30 publications

(9 citation statements)

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“…The cases can be very complicated in general, since the total number of distinct coalitions that the external retailers can form is exponential in the total number of players. Therefore, the cooperative games with externalities studied in the literature always have pre‐specified rules or behavioral assumptions for the retailers in the market (see, e.g., Bloch and van den Nouweland 2014, Kóczy 2018, Yang et al. 2019).…”

Section: Assortment Cooperation Gamementioning

confidence: 99%

Competitive and Cooperative Assortment Games under Markov Chain Choice Model

Nip

Wang

2022

Production and Operations Management

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I n this work, we study the assortment planning games in which multiple retailers interact in the market. Each retailer owns some of the products and their goal is to select a subset of products, that is, an assortment to offer to the customers so as to maximize their expected revenue. The purchase behavior of the customer is assumed to follow the Markov chain choice model. We consider two types of assortment games under the Markov chain choice model-a competitive game and a cooperative game. In the assortment competition game, we show that there always exists a pure-strategy Nash equilibrium and such equilibrium can be found in polynomial time. We also identify an easy-to-check condition for the uniqueness of the Nash equilibrium. Then we analyze the equilibrium outcome of this competition game, and compare the outcome with that in a monopolistic setting and a central planner setting. We show that under the assortment competition game, each retailer will offer a broader assortment in the equilibrium, which could include products that are not profitable in the monopolistic or the central planner setting, and it will eventually lead to a decrease in revenue for each player. Furthermore, we show that the price-of-anarchy and the price-of-stability of the game can be arbitrarily large. Motivated by these results, we further consider the assortment cooperation game under the Markov chain choice model, in which retailers are allowed to form coalitions. We consider two settings of cooperative games distinguished by the way we assume other players' behaviors outside a coalition. Interestingly, we find that when the players are assumed to be intrinsically competitive (meaning that players outside a coalition are assumed to be a collection of competing players), then there is incentive for all the players to form a grand coalition and there exists an allocation of the total revenue that makes the coalition stable (exists a core to the game). However, when the players are assumed to be intrinsically collaborative (meaning that players outside a coalition are assumed to form another coalition), then a stable coalition may not exist.

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Section: Assortment Cooperation Gamementioning

confidence: 99%

Competitive and Cooperative Assortment Games under Markov Chain Choice Model

Nip

Wang

2022

Production and Operations Management

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“… Partition function games (PFGs): This class of games evaluates side-effects of cooperation designated by the black solid line (Kóczy, 2018). The value of each coalition depends on the characteristics of the members and the way that other agents are partitioned to cooperate.…”

Section: (I)mentioning

confidence: 99%

Overlapping coalition formation in game theory: A state-of-the-art review

Mahdiraji

Razghandi

Hatami-Marbini

2021

Expert Systems with Applications

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“…The second strand of related literature deals with general partition function form games as initiated by the seminal works of Thrall (1962) and Thrall and Lucas (1963), and recently surveyed by Koczy (2018). Besides the investigation of general properties of such games (e.g., Lucas and Marcelli 1978;Maskin 2003;Hafalir 2007), there are two main issues of simultaneous interest in the corresponding works: which coalitions will form (cf.…”

Section: Related Literaturementioning

confidence: 99%

Winning coalitions in plurality voting democracies

2020

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We consider plurality voting games being simple games in partition function form such that in every partition there is at least one winning coalition. Such a game is said to be weighted if it is possible to assign weights to the players in such a way that a winning coalition in a partition is always one for which the sum of the weights of its members is maximal over all coalitions in the partition. A plurality game is called decisive if in every partition there is exactly one winning coalition. We show that in general, plurality games need not be weighted, even not when they are decisive. After that, we prove that (i) decisive plurality games with at most four players, (ii) majority games with an arbitrary number of players, and (iii) decisive plurality games that exhibit some kind of symmetry, are weighted. Complete characterizations of the winning coalitions in the corresponding partitions are provided as well.

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Partition Function Form Games

Cited by 30 publications

References 0 publications

Competitive and Cooperative Assortment Games under Markov Chain Choice Model

Competitive and Cooperative Assortment Games under Markov Chain Choice Model

Overlapping coalition formation in game theory: A state-of-the-art review

Winning coalitions in plurality voting democracies

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