In game theory, grim trigger (also called the grim strategy or just grim) is a trigger strategy for a repeated game, such as an iterated prisoner's dilemma. Initially, a player using grim trigger will cooperate, but as soon as the opponent defects (thus satisfying the trigger condition), the player using grim trigger will defect for the remainder of the iterated game. 'Since a single defect by the opponent triggers defection forever, grim trigger is the most strictly unforgiving of strategies in an iterated game'.
In iterated prisoner's dilemma strategy competitions, grim trigger performs poorly even without noise, and adding signal errors makes it even worse. Its ability to threaten permanent defection gives it a theoretically effective way to sustain trust, but because of its unforgiving nature and the inability to communicate this threat in advance, it performs poorly.[1]
In Robert Axelrod's book The Evolution of Cooperation, grim trigger is called "Friedman", for a 1971 paper by
James Friedman which uses the concept.[2]
References
[1] Axelrod, Robert (2000). "On Six Advances in Cooperation Theory" (http://www.fordschool.umich.edu/research/papers/PDFfiles/ 00-003.pdf). . Retrieved 2007-11-02. (page 13)
[2] Friedman, James W. (1971). "A Non-cooperative Equilibrium for Supergames". Review of Economic Studies 38 (1): 1–12. doi:10.2307/2296617.
Collusion
Competition law Basic concepts
• History of competition law
• Monopoly • Coercive monopoly • Natural monopoly • Barriers to entry • Herfindahl–Hirschman Index • Market concentration • Market power • SSNIP test • Relevant market • Merger control Anti-competitive practices • Monopolization • Collusion • Formation of cartels • Price fixing • Bid rigging
• Product bundling and tying
• Refusal to deal • Group boycott • Essential facilities • Exclusive dealing • Dividing territories • Conscious parallelism • Predatory pricing
• Misuse of patents and copyrights
Enforcement authorities and organizations
• International Competition Network
• List of competition regulators
Collusion is an agreement between two or more persons, sometimes illegal and therefore secretive, to limit open
competition by deceiving, misleading, or defrauding others of their legal rights, or to obtain an objective forbidden by law typically by defrauding or gaining an unfair advantage. It is an agreement among firms to divide the market, set prices, or limit production.[1] It can involve "wage fixing, kickbacks, or misrepresenting the independence of the relationship between the colluding parties".[2] In legal terms, all acts affected by collusion are considered void.[3]
Collusion 84
Definition
In the study of economics and market competition, collusion takes place within an industry when rival companies cooperate for their mutual benefit. Collusion most often takes place within the market structure of oligopoly, where the decision of a few firms to collude can significantly impact the market as a whole. Cartels are a special case of explicit collusion. Collusion which is not overt, on the other hand, is known as tacit collusion.
Variations
According to neoclassical price-determination theory and game theory, the independence of suppliers forces prices to their minimum, increasing efficiency and decreasing the price determining ability of each individual firm. However, if firms collude to increase prices, loss of sales is minimized, as consumers lack alternative choices at lower prices. This benefits the colluding firms at the cost of efficiency to society.
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 will follow suit in order to maintain sales, and when one firm increases its price, its rivals are unlikely to follow, as they would lose the sales' gains that they would otherwise get 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.
Indicators
Practices that suggest collusion include: • Uniform prices
• A penalty for price discounts • Advance notice of price changes • Information exchange
Examples
Collusion is largely illegal in the United States, Canada and most of the EU due to competition/antitrust law, but implicit collusion in the form of price leadership and tacit understandings still takes place. Several examples of collusion in the United States include:
• Market division and price-fixing among manufacturers of heavy electrical equipment in the 1960s, including General Electric.[4]
• An attempt by Major League Baseball owners to restrict players' salaries in the mid-1980s.
• The sharing of potential contract terms by NBA free agents in an effort to help a targeted franchise circumvent the salary cap
• Price fixing within food manufacturers providing cafeteria food to schools and the military in 1993.
• Market division and output determination of livestock feed additive, called lysine, by companies in the US, Japan and South Korea in 1996, Archer Daniels Midland being the most notable of these.[5]
• Chip dumping in poker or any other high stake card game. There are many ways that implicit collusion tends to develop:
• The practice of stock analyst conference calls and meetings of industry participants almost necessarily results in tremendous amounts of strategic and price transparency. This allows each firm to see how and why every other firm is pricing their products.
• If the practice of the industry causes more complicated pricing, which is hard for the consumer to understand (such as risk-based pricing, hidden taxes and fees in the wireless industry, negotiable pricing), this can cause
competition based on price to be meaningless (because it would be too complicated to explain to the customer in a short advertisement). This causes industries to have essentially the same prices and compete on advertising and image, something theoretically as damaging to consumers as normal price fixing.
Barriers
There can be significant barriers to collusion. In any given industry, these may include:
• The number of firms: As the number of firms in an industry increases, it is more difficult to successfully organize, collude and communicate.
• Cost and demand differences between firms: If costs vary significantly between firms, it may be impossible to establish a price at which to fix output.
• Cheating: There is considerable incentive to cheat on collusion agreements; although lowering prices might trigger price wars, in the short term the defecting firm may gain considerably. This phenomenon is frequently referred to as "chiseling".
• Potential entry: New firms may enter the industry, establishing a new baseline price and eliminating collusion (though anti-dumping laws and tariffs can prevent foreign companies entering the market).
• Economic recession: An increase in average total cost or a decrease in revenue provides incentive to compete with rival firms in order to secure a larger market share and increased demand.
References
[1] Sullivan, arthur; Steven M. Sheffrin (2003). Economics: Principles in action (http://www.pearsonschool.com/index.
cfm?locator=PSZ3R9&PMDbSiteId=2781&PMDbSolutionId=6724&PMDbCategoryId=&PMDbProgramId=12881&level=4). Upper Saddle River, New Jersey 07458: Pearson Prentice Hall. pp. 171. ISBN 0-13-063085-3. .
[2] Collusion Law & Legal Definition (http://definitions.uslegal.com/c/collusion/)
[3] Collusion (http://encarta.msn.com/encyclopedia_761571249/Collusion.html). Archived (http://www.webcitation.org/5kwRA5eiX) 2009-10-31.
[4] Encyclopedia of white-collar & corporate crime (http://books.google.com/books?id=0f7yTNb_V3QC&pg=PA377&lpg=PA377& dq=market+division+collusion+heavy+electrical+equipment++1960). .
[5] Hunter-Gault, Charlayne (October 15, 1996). "ADM: Who's Next?". MacNeil/Lehrer Newshour (PBS). http://www.pbs.org/newshour/bb/ business/october96/adm_10-15.html.Retrieved on 2007-10-17.
• Vives, X. (1999) Oligopoly pricing, MIT Press, Cambridge MA (readable; suitable for advanced undergraduates.) • Tirole, J. (1988) The Theory of Industrial Organization, MIT Press, Cambridge MA (An organized introduction
to industrial organization)
• Tirole, J. (1986), "Hierarchies and Bureaucracies", Journal of Law Economics and Organization, vol. 2, pp. 181–214.
• Tirole, J. (1992), "Collusion and the Theory of Organizations", Advances in Economic Theory: Proceedings of the Sixth World Congress of the Econometric Society, ed by J.-J. Laffont. Cambridge: Cambridge University Press, vol.2:151-206.
Backward induction 86
Backward induction
Backward induction is the process of reasoning backwards in time, from the end of a problem or situation, to
determine a sequence of optimal actions. It proceeds by first considering the last time a decision might be made and choosing what to do in any situation at that time. Using this information, one can then determine what to do at the second-to-last time of decision. This process continues backwards until one has determined the best action for every possible situation (i.e. for every possible information set) at every point in time.
In the mathematical optimization method of dynamic programming, backward induction is one of the main methods
for solving the Bellman equation.[1][2] In game theory, backward induction is a method used to compute subgame
perfect equilibria in sequential games.[3] The only difference is that optimization involves just one decision maker, who chooses what do at each point of time, whereas game theory analyzes how the decisions of several players interact. That is, by anticipating what the last player will do in each situation, it is possible to determine what the second-to-last player will do, and so on. In the related fields of automated planning and scheduling and automated theorem proving, the method is called backward search or backward chaining. In chess it is called retrograde analysis.
Backward induction has been used to solve games as long as the field of game theory has existed. John von Neumann and Oskar Morgenstern suggested solving zero-sum, two-person games by backward induction in their
Theory of Games and Economic Behavior (1944), the book which established game theory as a field of study.[4][5]