Collusion with capacity constraints under a sales maximization rationing rule

Takaomi Notsu ()
Additional contact information
Takaomi Notsu: Kyoto University

International Journal of Game Theory, 2023, vol. 52, issue 2, No 7, 485-516

Abstract: Abstract In the repeated Bertrand duopoly with capacity constraints, we introduce a sales maximization rationing rule, instead of a standard rationing rule, Efficient rule (E rule). Under our new rule, when the demand of a firm with a lower price exceeds its capacity, the consumers who are willing to buy at that price are rationed to that firm according to their unwillingness to buy. We find that the maximum one-shot total payoff under our rule is not less than that under E rule at any capacities; it is achieved by an asymmetric price pair rather than a symmetric monopoly price pair and it is strictly greater than that under E rule unless each firm’s capacity is too large. Under the one-shot total payoff maximization, total surplus under our rule is also equal to or greater than that under E rule at any capacities. Hence, our rule is also appealing to the social planner, and it is implementable due to information technology which collects information about the consumers’ willingness to pay. In the repeated game, patient firms can achieve the total payoff maximization by an equilibrium under our rule. Moreover, a range of discount factors within which the total payoff maximization can be sustained under our rule is wider than that under E rule at some capacities.

Keywords: Repeated Bertrand oligopoly; Capacity constraints; Collusion; Sales maximization rule; Simple alternating path (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s00182-022-00827-y Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jogath:v:52:y:2023:i:2:d:10.1007_s00182-022-00827-y

Ordering information: This journal article can be ordered from
http://www.springer. ... eory/journal/182/PS2

DOI: 10.1007/s00182-022-00827-y

Access Statistics for this article

International Journal of Game Theory is currently edited by Shmuel Zamir, Vijay Krishna and Bernhard von Stengel

More articles in International Journal of Game Theory from Springer, Game Theory Society
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().