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In economics, the Bertrand paradox–so named for its creator, Joseph Bertrand–describes a situation in which two players (frims) reaching a state of Nash equilibrium in economic competition find themselves with no profits. Face-to-face trading interactions on the New York Stock Exchange trading floor. ...
Joseph Louis François Bertrand (March 11, 1822 - April 5, 1900, born and died in Paris) was a French mathematician who worked in the fields of number theory, differential geometry, probability theory, and thermodynamics. ...
In game theory, the Nash equilibrium (named after John Forbes Nash, who proposed it) is a kind of solution concept of a game involving two or more players, where no player has anything to gain by changing only his or her own strategy unilaterally. ...
Competition is the act of striving against another force for the purpose of achieving dominance or attaining a reward or goal, or out of a biological imperative such as survival. ...
Example
Suppose two firms, A and B, sell an identical commodity, each with the same cost of production and distribution, so that customers choose the product solely on the basis of price. It follows that neither A nor B will set a higher price than the other because doing so would yield the entire market to their rival. If they set the same price, the companies will share both the market and profits. Commodity is a term with distinct meanings in both business and in Marxian political economy. ...
Wikibooks has more about this subject: Marketing Distribution is one of the four aspects of marketing. ...
On the other hand, if either firm were to lower its price, even a little, it would gain the whole market and substantially larger profits. Since both A and B know this, they will each try to undercut their competitor until the product is selling at zero economic profit. This is the pure-strategy Nash equilibrium. Recent work has shown that there may be an additional mixed-strategy Nash equilibrium with positive economic profits (see Kaplan & Wettstein, 2000, and Baye & Morgan, 1999). In game theory, the Nash equilibrium (named after John Forbes Nash, who proposed it) is a kind of solution concept of a game involving two or more players, where no player has anything to gain by changing only his or her own strategy unilaterally. ...
The Bertrand paradox rarely appears in practice because real products are almost always differentiated in some way other than price (brand name, if nothing else); firms have limitations on their capacity to manufacture and distribute; and two firms rarely have identical costs. In marketing, product differentiation is the modification of a product to make it more attractive to the target market. ...
This article is about brands in marketing. ...
Bertrand's result is paradoxical because if the number of firms goes from one to two, the price decreases from the monopoly price to the competitive price and stays at the same level as the number of firms increases further. This is not very realistic, as in reality, the price goes down as the number of firms increases. The empirical analysis shows that in the most industries with two competitors, positive profits are made. In economics, a monopoly (from the Latin word monopolium - Greek language monos, one + polein, to sell) is defined as a persistent market situation where there is only one provider of a product or service. ...
Competition is the act of striving against another force for the purpose of achieving dominance or attaining a reward or goal, or out of a biological imperative such as survival. ...
Some reasons the Bertrand paradox does not strictly apply:
- Capacity constraints–Sometimes firms have not enough capacity to satisfy all demand
- Product differentiation–If products of different firms are differentiated, then consumers may not switch completely to the product with lower price
- Dynamic competition–Repeated interaction or repeated price competition can lead to the price above MC in equilibrium.
- More money for higher price–It follows from repeated interaction: If one company sets their price slightly higher, then they will still get about the same amount of buys but more profit for each buy, so the other company will raise their price, and so on (only in repeated games, otherwise the price dynamics are in the other direction).
- Oligopoly If the two companies can agree on a price, it is in their long-term interest to keep the agreement: the revenue from cutting prices is less than twice the revenue from keeping the agreement, and lasts only until the other firm cuts its own prices.
See also Joseph Louis François Bertrand (March 11, 1822 - April 5, 1900, born and died in Paris) was a French mathematician who worked in the fields of number theory, differential geometry, probability theory, and thermodynamics. ...
Bertrand competition is a model of competition used in economics, named after Joseph Louis François Bertrand (1822-1900). ...
As a solution to the Bertrand paradox (economics) it has been suggested that each firm produces a somewhat differentiated product and consequently faces a demand curve that is downward-sloping for all price levels that the firm may charge. ...
In economics, the Edgeworth paradox describes a situation in which two players cannot reach a state of equilibrium with pure strategies, i. ...
Will the two prisoners cooperate to minimize total loss of liberty or will one of them, trusting the other to cooperate, betray him so as to go free? In game theory, the prisoners dilemma is a type of non-zero-sum game in which two players can cooperate with...
References - Baye, M.R. and J. Morgan (1997) "Necessary and sufficient conditions for existence and uniqueness of Bertrand paradox outcomes" Princeton Woodrow Wilson School, Discussion Paper in Economics, 186.
- Baye, M.R. and J. Morgan (1999) "A folk theorem for one-shot Bertrand games," Economics Letters, 65:1, 59-65.
- Bertrand, J. (1883) "Book review of theorie mathematique de la richesse sociale and of recherches sur les principles mathematiques de la theorie des richesses", Journal de Savants 67: 499–508.
- Kaplan, T.R. and D. Wettstein (1997) "Mixed strategy equilibria with constant-returns-to-scale technology," Monaster Center Discussion Paper 97–4.
- [Kaplan, T.R. and D. Wettstein], (2000) "The Possibility of Mixed-Strategy Equilibria with Constant-Returns-to-Scale Technology under Bertrand Competition", Spanish Economic Review, 2(1):65-71.
| view | Topics in game theory | | Definitions Game theory is often described as a branch of applied mathematics and economics that studies situations where players choose different actions in an attempt to maximize their returns. ...
| Normal form game · Extensive form game · Cooperative game · Information set · Preference In game theory, normal form is a way of describing a game. ...
It has been suggested that Game tree be merged into this article or section. ...
A cooperative game is a game where groups of players (coalitions) may enforce cooperative behaviour, hence the game is a competition between coalitions of players, rather than between individual players. ...
In game theory, an information set is a set that, for a particular player, establishes all the possible moves that could have taken place in the game so far, given what that player has observed so far. ...
Preference (or taste) is a concept, used in the social sciences, particularly economics. ...
| | Equilibrium concepts Price of market balance In economics, economic equilibrium is simply a state of the world where economic forces are balanced and in the abscence of external shocks the (equilibrium) values of economic variables will not change. ...
In game theory and economic modelling, a solution concept is a process via which equilibria of a game are identified. ...
| Nash equilibrium · Subgame perfection · Bayes-Nash · Trembling hand · Proper equilibrium · Epsilon-equilibrium · Correlated equilibrium · Sequential equilibrium · Quasi-perfect equilibrium · Evolutionarily stable strategy · Risk dominance In game theory, the Nash equilibrium (named after John Forbes Nash, who proposed it) is a kind of solution concept of a game involving two or more players, where no player has anything to gain by changing only his or her own strategy unilaterally. ...
Subgame perfect equilibrium is an economics term used in game theory to describe an equilibrium such that players strategies constitute a Nash equilibrium in every subgame of the original game. ...
In game theory, a Bayesian game is one in which information about characteristics of the other players (i. ...
The trembling hand perfection is a notion that eliminates actions of players that are unsafe because they were chosen through a slip of the hand. ...
Proper equilibrium is a refinement of Nash Equilibrium due to Roger B. Myerson. ...
In game theory, an Epsilon-equilibrium is a strategy profile that approximately satisfies the condition of Nash Equilibrium. ...
In game theory, a correlated equilibrium is a solution concept that is more general than the well known Nash equilibrium. ...
Sequential equilibrium is a refinement of Nash Equilibrium for extensive form games due to David M. Kreps and Robert Wilson. ...
Quasi-perfect equilibrium is a refinement of Nash Equilibrium for extensive form games due to Eric van Damme. ...
In game theory, an evolutionarily stable strategy (or ESS; also evolutionary stable strategy) is a strategy which if adopted by a population cannot be invaded by any competing alternative strategy. ...
Risk dominance and payoff dominance are two related refinements of the Nash equilibrium (NE) solution concept in game theory, defined by John Harsanyi and Reinhard Selten. ...
| | Strategies In game theory, a players strategy, in a game or a business situation, is a complete plan of action for whatever situation might arise; this fully determines the players behaviour. ...
| Dominant strategies · Mixed strategy · Tit for tat · Grim trigger In game theory, dominance occurs when one strategy is better or worse than another regardless of the strategies of a players opponents. ...
In game theory a mixed strategy is a strategy which chooses randomly between possible moves. ...
Tit for Tat is a highly-effective strategy in game theory for the iterated prisoners dilemma. ...
Grim Trigger is a trigger strategy in game theory for a repeated game, such as an iterated prisoners dilemma. ...
| | Classes of games | Symmetric game · Perfect information · Dynamic game · Repeated game · Signaling game · Cheap talk · Zero-sum game · Mechanism design · Stochastic game In game theory, a symmetric game is a game where the payoffs for playing a particular strategy depend only on the other strategies employed, not on who is playing them. ...
Perfect information is a term used in economics and game theory to describe a state of complete knowledge about the actions of other players that is instantaneously updated as new information arises. ...
In game theory, a sequential game is a game where one player chooses his action before the others chooses theirs. ...
In game theory, a repeated game (or iterated game) is an extensive form game which consists in some number of repetitions of some base game (called a stage game). ...
Signaling games are dynamic games with two players, the sender (S) and the receiver (R). ...
Cheap Talk is a term used in Game Theory for pre-play communication which carries no cost. ...
Zero-sum describes a situation in which a participants gain (or loss) is exactly balanced by the losses (or gains) of the other participant(s). ...
Mechanism design is a sub-field of game theory. ...
In game theory, a stochastic game is a competitive game with probabilistic transitions played by two players. ...
| | Games Game theory studies strategic interaction between individuals in situations called games. ...
| Prisoner's dilemma · Coordination game · Chicken · Battle of the sexes · Stag hunt · Matching pennies · Ultimatum game · Minority game · Rock, Paper, Scissors · Pirate game · Dictator game · Public goods game · Nash bargaining game Will the two prisoners cooperate to minimize total loss of liberty or will one of them, trusting the other to cooperate, betray him so as to go free? In game theory, the prisoners dilemma is a type of non-zero-sum game in which two players can cooperate with...
In game theory, the Nash equilibrium (named after John Nash) is a kind of optimal strategy for games involving two or more players, whereby the players reach an outcome to mutual advantage. ...
It has been suggested that Peace war game be merged into this article or section. ...
The Battle of the Sexes is a two player game used in game theory. ...
In game theory, the Stag Hunt is a game first discussed by Jean-Jacques Rousseau. ...
Matching Pennies is the name for a simple example game used in game theory. ...
The Ultimatum game is an experimental economics game in which two parties interact anonymously and only once, so reciprocation is not an issue. ...
Minority Game is a game proposed by Yi-Cheng Zhang and Damien Challet from the University of Fribourg. ...
It has been suggested that Janken be merged into this article or section. ...
The Pirate Game is a simple mathematical game. ...
The dictator game is a very simple game in experimental economics, similar to the ultimatum game. ...
The Public goods game is a standard of experimental economics; in the basic game subjects secretly choose how many of their private tokens to put into the public pot. ...
The Nash Bargaining Game is a simple two player game used to model bargaining interactions. ...
| | Theorems | Minimax theorem · Purification theorems · Folk theorem · Revelation principle · Arrow's Theorem Minimax is a method in decision theory for minimizing the expected maximum loss. ...
In game theory, the purification theorem was contributed by Nobel laurate John Harsanyi in 1973[1]. The theorem aims to justify a puzzling aspect of mixed strategy Nash equilibria: that each player is wholly indifferent amongst each of the actions he puts non-zero weight on, yet he mixes them...
In game theory, folk theorems are a class of theorems which imply that in repeated games, any outcome is a feasible solution concept, if under that outcome the players minimax conditions are satisfied. ...
The revelation principle of economics can be stated as, To any equilibrium of a game of incomplete information, there corresponds an associated revelation mechanism that has an equilibrium where the players truthfully report their types. ...
In voting systems, Arrow’s impossibility theorem, or Arrow’s paradox demonstrates the impossibility of designing a set of rules for social decision making that would meet all of a certain set of criteria. ...
| | Related topics | Mathematics · Economics · Behavioral economics · Evolutionary game theory · Population genetics · Behavioral ecology · Adaptive dynamics · List of game theorists · Social trap · Tragedy of the commons Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ...
Face-to-face trading interactions on the New York Stock Exchange trading floor. ...
Nobel Prize in Economics winner Daniel Kahneman, was an important figure in the development of behavioral finance and economics and continues to write extensively in the field. ...
Evolutionary game theory (EGT) is the application of game theory in evolutionary biology. ...
Population genetics is the study of the distribution of and change in allele frequencies under the influence of the four evolutionary forces: natural selection, genetic drift, mutation, and migration. ...
Behavioral ecology is the study of the ecological and evolutionary basis for animal behavior, and the roles of behavior in enabling an animal to adapt to its environment (both intrinsic and extrinsic). ...
Adaptive Dynamics is a set of techniques for studying long-term phenotypical evolution developed during the 1990s. ...
This is a list of notable economists, mathematicians, political scientists, and computer scientists whose work has added substantially to the field of game theory. ...
Social trap is a term used by psychologists to describe a situation in which a group of people act to obtain short-term individual gains, which in the long run leads to a loss for the group as a whole. ...
It has been suggested that Tyranny of the Commons be merged into this article or section. ...
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