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Perfect Bayesian Equilibrium
In game theory, a Perfect Bayesian Equilibrium (PBE) is an equilibrium concept relevant for dynamic games with incomplete information (sequential Bayesian games). It is a refinement of Bayesian Nash equilibrium (BNE). A perfect Bayesian equilibrium has two components -- ''strategies'' and ''beliefs'': * The strategy of a player in given information set specifies his choice of action in that information set, which may depend on the history (on actions taken previously in the game). This is similar to a sequential game. * The belief of a player in a given information set determines what node in that information set he believes the game has reached. The belief may be a probability distribution over the nodes in the information set, and is typically a probability distribution over the possible ''types'' of the other players. Formally, a belief system is an assignment of probabilities to every node in the game such that the sum of probabilities in any information set is 1. The strate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayesian Nash Equilibrium
In game theory, a Bayesian game is a game that models the outcome of player interactions using aspects of Bayesian probability. Bayesian games are notable because they allowed, for the first time in game theory, for the specification of the solutions to games with incomplete information. Hungarian economist John C. Harsanyi introduced the concept of Bayesian games in three papers from 1967 and 1968: He was awarded the Nobel Prize for these and other contributions to game theory in 1994. Roughly speaking, Harsanyi defined Bayesian games in the following way: players are assigned by nature at the start of the game a set of characteristics. By mapping probability distributions to these characteristics and by calculating the outcome of the game using Bayesian probability, the result is a game whose solution is, for technical reasons, far easier to calculate than a similar game in a non-Bayesian context. For those technical reasons, see the Specification of games section in this article ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subgame Perfect Nash Equilibrium
In game theory, a subgame perfect equilibrium (or subgame perfect Nash equilibrium) is a refinement of a Nash equilibrium used in dynamic games. A strategy profile is a subgame perfect equilibrium if it represents a Nash equilibrium of every subgame of the original game. Informally, this means that at any point in the game, the players' behavior from that point onward should represent a Nash equilibrium of the continuation game (i.e. of the subgame), no matter what happened before. Every finite extensive game with perfect recall has a subgame perfect equilibrium. Perfect recall is a term introduced by Harold W. Kuhn in 1953 and ''"equivalent to the assertion that each player is allowed by the rules of the game to remember everything he knew at previous moves and all of his choices at those moves"''. A common method for determining subgame perfect equilibria in the case of a finite game is backward induction. Here one first considers the last actions of the game and determines w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Divine Equilibrium
The Divinity Criterion or Divine Equilibrium or Universal Divinity is a refinement of Perfect Bayesian equilibrium in a signaling game proposed by Banks and Sobel (1987). One of the most widely applied refinement is the D1-Criterion. It is a restriction of receiver's beliefs to the type of senders for whom deviating towards an off-the-equilibrium message could improve their outcome compared to the equilibrium payoff. The Intuitive and Divinity Criterion: Interpretation and Step-by-Step Examples Felix Munoz-Garcia, Ana Espinola-Arredondo, Journal of Industrial Organization Education. Volume 5, Issue 1, Pages 1–20, ISSN (Online) 1935-5041, DOI: 10.2202/1935-5041.1024, March 2011 In addition to the restriction suggested by the Intuitive Criterion, the Divinity Criterion considers only those types which are most likely to send the off-the-equilibrium message. If more than one sender could benefit from the deviation, the Intuitive Criterion assigns equal probabilities for all the send ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intuitive Criterion
The intuitive criterion is a technique for equilibrium refinement in signaling games. It aims to reduce possible outcome scenarios by restricting the possible sender types to types who could obtain higher utility levels by deviating to off-the-equilibrium messages, and to types for which the off-the-equilibrium message is not equilibrium dominated. Background A signaling game is a game in which one player ("sender") has private information regarding his type. He sends a signal ("message") to the other player ("receiver") to indicate his type. The receiver then takes an action. Both the signal and the receiver action can affect both players' utilities. A '' Perfect Bayesian equilibrium (PBE)'' in such a game consists of three elements. * A ''sender strategy'' - a function from the sender type to a signal that maximizes this type's utility given the receiver strategy. * A ''receiver belief'' - a function from the signal to a probability distribution over sender types; the belief mu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sequential Equilibrium
Sequential equilibrium is a refinement of Nash Equilibrium for extensive form games due to David M. Kreps and Robert Wilson. A sequential equilibrium specifies not only a strategy for each of the players but also a belief for each of the players. A belief gives, for each information set of the game belonging to the player, a probability distribution on the nodes in the information set. A profile of strategies and beliefs is called an assessment for the game. Informally speaking, an assessment is a perfect Bayesian equilibrium if its strategies are sensible given its beliefs and its beliefs are confirmed on the outcome path given by its strategies. The definition of sequential equilibrium further requires that there be arbitrarily small perturbations of beliefs and associated strategies with the same property. Consistent assessments The formal definition of a strategy being sensible given a belief is straightforward; the strategy should simply maximize expected payoff ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jump Bidding
In auction theory, jump bidding is the practice of increasing the current price in an English auction, substantially more than the minimal allowed amount. Puzzle At first glance, jump bidding seems irrational. Apparently, in an English auction, it is a dominant strategy for each buyer whose price is above the displayed price, to always bid the minimal allowed increment (e.g. one cent) above the displayed price. By bidding higher, the bidder gives up the opportunity to win the item at a lower price. However, in practice buyers increase the displayed price much more than the minimal allowed increment. Buyers may even sometimes offer an increase on their own high bid, seemingly irrationally. Several explanations have been suggested to this behavior. Reducing bidding costs When bidding is costly, or when time is costly, jump-bidding allows the bidders to reduce their total costs and get to the outcome faster. Signaling Consider two veteran bidders, that compete with each ot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jump Bidding
In auction theory, jump bidding is the practice of increasing the current price in an English auction, substantially more than the minimal allowed amount. Puzzle At first glance, jump bidding seems irrational. Apparently, in an English auction, it is a dominant strategy for each buyer whose price is above the displayed price, to always bid the minimal allowed increment (e.g. one cent) above the displayed price. By bidding higher, the bidder gives up the opportunity to win the item at a lower price. However, in practice buyers increase the displayed price much more than the minimal allowed increment. Buyers may even sometimes offer an increase on their own high bid, seemingly irrationally. Several explanations have been suggested to this behavior. Reducing bidding costs When bidding is costly, or when time is costly, jump-bidding allows the bidders to reduce their total costs and get to the outcome faster. Signaling Consider two veteran bidders, that compete with each ot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
English Auction
An English auction is an open-outcry ascending dynamic auction. It proceeds as follows. * The auctioneer opens the auction by announcing a suggested opening bid, a starting price or reserve for the item on sale. * Then the auctioneer accepts increasingly higher bids from the floor and sometimes from other sources, for example online or telephone bids, consisting of buyers with an interest in the item. The auctioneer usually determines the minimum increment of bids, often making them larger as bidding reaches higher levels. * The highest bidder at any given moment is considered to have the standing bid, which can only be displaced by a higher bid from a competing buyer. * If no competing bidder challenges the standing bid within the time allowed by the auctioneer, the standing bid becomes the winner, and the item is sold to the highest bidder at a price equal to their bid. *If no bidder accepts the starting price, the auctioneer either begins to lower the starting price in increme ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Public Good (economics)
In economics, a public good (also referred to as a social good or collective good)Oakland, W. H. (1987). Theory of public goods. In Handbook of public economics (Vol. 2, pp. 485-535). Elsevier. is a good that is both non-excludable and non-rivalrous. For such goods, users cannot be barred from accessing or using them for failing to pay for them. Also, use by one person neither prevents access of other people nor does it reduce availability to others. Therefore, the good can be used simultaneously by more than one person. This is in contrast to a common good, such as wild fish stocks in the ocean, which is non-excludable but rivalrous to a certain degree. If too many fish were harvested, the stocks would deplete, limiting the access of fish for others. A public good must be valuable to more than one user, otherwise, the fact that it can be used simultaneously by more than one person would be economically irrelevant. Capital goods may be used to produce public goods or services th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free-rider Problem
In the social sciences, the free-rider problem is a type of market failure that occurs when those who benefit from resources, public goods (such as public roads or public library), or services of a communal nature do not pay for them or under-pay. Free riders are a problem because while not paying for the good (either directly through fees or tolls or indirectly through taxes), they may continue to access or consume it. Thus, the good may be under-produced, overused or degraded. Additionally, it has been shown that despite evidence that people tend to be cooperative by nature, the presence of free-riders cause this prosocial behaviour to deteriorate, perpetuating the free-rider problem. The free-rider problem in social science is the question of how to limit free riding and its negative effects in these situations. Such an example is the free-rider problem of when property rights are not clearly defined and imposed. The free-rider problem is common with public goods which are n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Repeated Game
In game theory, a repeated game is an extensive form game that consists of a number of repetitions of some base game (called a stage game). The stage game is usually one of the well-studied 2-person games. Repeated games capture the idea that a player will have to take into account the impact of his or her current action on the future actions of other players; this impact is sometimes called his or her reputation. ''Single stage game'' or ''single shot game'' are names for non-repeated games. For the real-life example of a repeated game, consider two gas stations that are adjacent to one another. They compete by publicly posting pricing and have the same and constant marginal cost c (the wholesale price of gasoline). Assume that when they both charge p = 10, their joint profit is maximized, resulting in a high profit for everyone. Despite the fact that this is the best outcome for them, they are motivated to deviate. By modestly lowering the price, anyone can steal all of their ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multi-stage Game
In game theory, a multi-stage game is a sequence of several simultaneous games played one after the other. This is a generalization of a repeated game In game theory, a repeated game is an extensive form game that consists of a number of repetitions of some base game (called a stage game). The stage game is usually one of the well-studied 2-person games. Repeated games capture the idea that a ...: a repeated game is a special case of a multi-stage game, in which the stage games are identical. Multi-Stage Game with Different Information Sets As an example, consider a two-stage game in which the stage game in ''Figure 1'' is played in each of two periods: The payoff to each player is the simple sum of the payoffs of both games. Players cannot observe the action of the other player within a round; however, at the beginning of Round 2, Player 2 finds out about Player 1's action in Round 1, while Player 1 does not find out about Player 2's action in Round 1. For Player 1, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
