Editing Collusion (section)

== Variations ==
* <math>\frac{\pi (P_c)}{n(1-\delta)}\geq\pi(P_c)\rightarrow\frac{1}{n(1-\delta)}\geq 1 </math>
* <math>1 \geq n(1-\delta)</math>
* <math>1 \geq n-n\delta</math>
* <math>n \delta \geq n-1</math>
* <math>\delta \geq \frac{n-1}{n}</math>

Suppose this market has <math> n </math> firms. At the collusive price, the firms are symmetric, so they divide the profits equally between the whole industry, represented as <math>\frac{\pi(P_c)}{n}</math>. If and only if the profit of choosing to deviate is greater than that of sticking to collude, i.e.
* <math>\frac{\pi (P_c)}{n(1-\delta)}\geq\pi(P_c)</math> (Companies have no incentive to deviate unilaterally)
* Therefore, the cartel alliance will be stable when <math>\delta\geq \frac{n-1}{n}</math> is the case, i.e. the firm has no incentive to deviate unilaterally. So as the number of firms increases, the more difficult it is for The Cartel to maintain stability.
As the number of firms in the market increases, so does the factor of the minimum discount required for collusion to succeed.<ref>Compte et al., 2002. Olivier Compte, Frederic Jenny, Patrick Rey Capacity, constraints, mergers and collusion European Economic Review, 46 (2002), pp. 1-29</ref>

According to [[Neoclassical economics|neoclassical price-determination theory]] and [[game theory]], the independence of suppliers forces prices to their minimum, increasing [[Economic efficiency|efficiency]] and decreasing the price-determining ability of each firm.<ref name="Springer Netherlands">{{Citation|last1=Kalai|first1=Ehud|title=The Kinked Demand Curve, Facilitating Practices, and Oligopolistic Coordination|date=1994|url=https://doi.org/10.1007/978-94-011-1370-0_2|work=Imperfections and Behavior in Economic Organizations|pages=15–38|editor-last=Gilles|editor-first=Robert P.|series=Theory and Decision Library|place=Dordrecht|publisher=Springer Netherlands|language=en|doi=10.1007/978-94-011-1370-0_2|isbn=978-94-011-1370-0|access-date=2020-11-01|last2=Satterthwaite|first2=Mark A.|editor2-last=Ruys|editor2-first=Pieter H. M.|url-access=subscription}}</ref>  However if all firms collude to increase prices, loss of sales will be minimized, as consumers lack choices at lower prices and must decide between what is available. This benefits the colluding firms, as they generate more sales at the cost of [[Economic efficiency|efficiency]] to society.<ref name="stats.oecd.org"/> However, depending on the assumptions made in the theoretical model on the information available to all firms, there are some outcomes, based on Cooperative Game Theory, where collusion may have higher efficiency than if firms did not collude.<ref name=":0">{{Cite book|doi=10.1057/978-1-349-95121-5_22-1|chapter=Collusion|title=The New Palgrave Dictionary of Economics|year=1987|last1=Roberts|first1=Kevin|pages=1–5|isbn=978-1-349-95121-5}}</ref>

One variation of this traditional theory is the theory of [[kinked demand]]. Firms face a kinked demand curve if, when one firm decreases its price, other firms are expected to follow suit to maintain sales. When one firm increases its price, its rivals are unlikely to follow, as they would lose the sales gains they would otherwise receive by holding prices at the previous level.  Kinked demand potentially fosters [[supra-competitive prices]] because any one firm would receive a reduced benefit from cutting price, as opposed to the benefits accruing under neoclassical theory and certain game-theoretic models such as [[Bertrand competition]].<ref name="Springer Netherlands"/>

Collusion may also occur in auction markets, where independent firms coordinate their bids ([[bid rigging]]).<ref>{{cite journal |last1=Conley |first1=Timothy |last2=Decarolis |first2=Francesco |title=Detecting Bidders Groups in Collusive Auctions |journal=American Economic Journal: Microeconomics |date=2016 |volume=8 |issue=2|pages=1–38 |doi=10.1257/mic.20130254 }}</ref>