|
Equilibrium Selection
Equilibrium selection is a concept from game theory which seeks to address reasons for players of a game to select a certain equilibrium over another. The concept is especially relevant in evolutionary game theory, where the different methods of equilibrium selection respond to different ideas of what equilibria will be stable and persistent for one player to play even in the face of deviations (and mutations) of the other players. This is important because there are various equilibrium concepts, and for many particular concepts, such as the Nash equilibrium, many games have multiple equilibria. Equilibrium Selection with Repeated Games A stage game is an n-player game where players choose from a finite set of actions, and there is a payoff profile for their choices. A repeated game is playing a number of repetitions of a stage game in discrete periods of time (Watson, 2013). A player's reputation affects the actions and behavior of the other players. In other words, how a p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Game Theory
Game theory is the study of mathematical models of strategic interactions. It has applications in many fields of social science, and is used extensively in economics, logic, systems science and computer science. Initially, game theory addressed two-person zero-sum games, in which a participant's gains or losses are exactly balanced by the losses and gains of the other participant. In the 1950s, it was extended to the study of non zero-sum games, and was eventually applied to a wide range of Human behavior, behavioral relations. It is now an umbrella term for the science of rational Decision-making, decision making in humans, animals, and computers. Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum games and its proof by John von Neumann. Von Neumann's original proof used the Brouwer fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathematical economics. His paper was f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Evolutionary Game Theory
Evolutionary game theory (EGT) is the application of game theory to evolving populations in biology. It defines a framework of contests, strategies, and analytics into which Darwinism, Darwinian competition can be modelled. It originated in 1973 with John Maynard Smith and George R. Price's formalisation of contests, analysed as strategies, and the mathematical criteria that can be used to predict the results of competing strategies. Evolutionary game theory differs from classical game theory in focusing more on the dynamics of strategy change. This is influenced by the frequency of the competing strategies in the population. Evolutionary game theory has helped to explain the basis of altruism (biology), altruistic behaviours in Darwinian evolution. It has in turn become of interest to economists, sociologists, anthropologists, and philosophers. History Classical game theory Classical non-cooperative game theory was conceived by John von Neumann to determine optimal strategies i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equilibrium Concept
In game theory, a solution concept is a formal rule for predicting how a game will be played. These predictions are called "solutions", and describe which strategies will be adopted by players and, therefore, the result of the game. The most commonly used solution concepts are equilibrium concepts, most famously Nash equilibrium. Many solution concepts, for many games, will result in more than one solution. This puts any one of the solutions in doubt, so a game theorist may apply a refinement to narrow down the solutions. Each successive solution concept presented in the following improves on its predecessor by eliminating implausible equilibria in richer games. Formal definition Let \Gamma be the class of all games and, for each game G \in \Gamma, let S_G be the set of strategy profiles of G. A ''solution concept'' is an element of the direct product \Pi_2^; ''i.e''., a function F: \Gamma \rightarrow \bigcup\nolimits_ 2^ such that F(G) \subseteq S_G for all G \in \Gamma. Rati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nash Equilibrium
In game theory, the Nash equilibrium is the most commonly used solution concept for non-cooperative games. A Nash equilibrium is a situation where no player could gain by changing their own strategy (holding all other players' strategies fixed). The idea of Nash equilibrium dates back to the time of Cournot, who in 1838 applied it to his model of competition in an oligopoly. If each player has chosen a strategy an action plan based on what has happened so far in the game and no one can increase one's own expected payoff by changing one's strategy while the other players keep theirs unchanged, then the current set of strategy choices constitutes a Nash equilibrium. If two players Alice and Bob choose strategies A and B, (A, B) is a Nash equilibrium if Alice has no other strategy available that does better than A at maximizing her payoff in response to Bob choosing B, and Bob has no other strategy available that does better than B at maximizing his payoff in response to Alice c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
N-player Game
In game theory, an ''n''-player game is a game which is well defined for any number of players. This is usually used in contrast to standard 2-player games that are only specified for two players. In defining ''n''-player games, game theorists usually provide a definition that allow for any (finite) number of players. The limiting case of n \to \infty is the subject of mean field game theory. Changing games from 2-player games to ''n''-player games entails some concerns. For instance, the Prisoner's dilemma is a 2-player game. One might define an ''n''-player Prisoner's Dilemma where a single defection results everyone else getting the sucker's payoff. Alternatively, it might take certain amount of defection before the cooperators receive the sucker's payoff. (One example of an ''n''-player Prisoner's Dilemma is the Diner's dilemma.) Analysis ''n''-player games can not be solved using minimax Minimax (sometimes Minmax, MM or saddle point) is a decision rule used in artificia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Repeated Game
In game theory, a repeated game (or iterated 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 their current action on the future actions of other players; this impact is sometimes called their reputation. Single stage game or single shot game are names for non-repeated games. Example 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 , 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, either can steal all of their competitors' customers, nearly doub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Focal Point (game Theory)
In game theory, a focal point (or Schelling point) is a solution that people tend to choose by default in the absence of communication in order to avoid Coordination game#Experimental results, coordination failure. The concept was introduced by the American economist Thomas Schelling in his book ''The Strategy of Conflict'' (1960). Schelling states that "[p]eople ''can'' often concert their intentions or expectations with others if each knows that the other is trying to do the same" in a cooperative situation (p. 57), so their action would converge on a focal point which has some kind of prominence compared with the environment. However, the conspicuousness of the focal point depends on time, place and people themselves. It may not be a definite solution. Existence The existence of the focal point is first demonstrated by Schelling with a series of questions. Here is one example: to determine the time and place to meet a stranger in New York City, but without being able to communi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetric 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. If one can change the identities of the players without changing the payoff to the strategies, then a game is symmetric. Symmetry can come in different varieties. Ordinally symmetric games are games that are symmetric with respect to the ordinal structure of the payoffs. A game is quantitatively symmetric if and only if it is symmetric with respect to the exact payoffs. A partnership game is a symmetric game where both players receive identical payoffs for any strategy set. That is, the payoff for playing strategy ''a'' against strategy ''b'' receives the same payoff as playing strategy ''b'' against strategy ''a''. Symmetry in 2x2 games Only 12 out of the 144 ordinally distinct 2x2 games are symmetric. However, many of the commonly studied 2x2 games are at least ordinally symmetric. The standard represe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hanabi (card Game)
''Hanabi'' (from Japanese 花火, fireworks) is a cooperative card game created by French game designer Antoine Bauza and published in 2010. Players are aware of other players' cards but not their own, and attempt to play a series of cards in a specific order to set off a simulated fireworks show. The types of information that players may give to each other is limited, as is the total amount of information that can be given during the game. In 2013, ''Hanabi'' won the Spiel des Jahres, an industry award for best board game of the year. Gameplay The ''Hanabi'' deck contains cards in five suits (white, yellow, green, blue, and red): three 1s, two each of 2s, 3s, and 4s, and one 5. The game begins with 8 available information tokens and 3 fuse tokens. To start the game, players are dealt a hand containing five cards (four for 4 or 5 players). As in blind man's bluff, players can see each other's cards but they cannot see their own. Play proceeds around the table; each turn, a pla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Risk Dominance
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. A Nash equilibrium is considered payoff dominant if it is Pareto superior to all other Nash equilibria in the game. When faced with a choice among equilibria, all players would agree on the payoff dominant equilibrium since it offers to each player at least as much payoff as the other Nash equilibria. Conversely, a Nash equilibrium is considered risk dominant if it has the largest basin of attraction (i.e. is less risky). This implies that the more uncertainty players have about the actions of the other player(s), the more likely they will choose the strategy corresponding to it. The payoff matrix in Figure 1 provides a simple two-player, two-strategy example of a game with two pure Nash equilibria. The strategy pair (Hunt, Hunt) is payoff dominant since payoffs are higher for both players compared to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pareto Efficiency
In welfare economics, a Pareto improvement formalizes the idea of an outcome being "better in every possible way". A change is called a Pareto improvement if it leaves at least one person in society better off without leaving anyone else worse off than they were before. A situation is called Pareto efficient or Pareto optimal if all possible Pareto improvements have already been made; in other words, there are no longer any ways left to make one person better off without making some other person worse-off. In social choice theory, the same concept is sometimes called the unanimity principle, which says that if ''everyone'' in a society (strict inequality, non-strictly) prefers A to B, society as a whole also non-strictly prefers A to B. The Pareto frontier, Pareto front consists of all Pareto-efficient situations. In addition to the context of efficiency in ''allocation'', the concept of Pareto efficiency also arises in the context of productive efficiency, ''efficiency in prod ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equilibrium Refinement
In game theory, a solution concept is a formal rule for predicting how a game will be played. These predictions are called "solutions", and describe which strategies will be adopted by players and, therefore, the result of the game. The most commonly used solution concepts are Economic equilibrium, equilibrium concepts, most famously Nash equilibrium. Many solution concepts, for many games, will result in more than one solution. This puts any one of the solutions in doubt, so a game theorist may apply a refinement to narrow down the solutions. Each successive solution concept presented in the following improves on its predecessor by eliminating implausible equilibria in richer games. Formal definition Let \Gamma be the class of all games and, for each game G \in \Gamma, let S_G be the set of strategy profiles of G. A ''solution concept'' is an element of the direct product \Pi_2^; ''i.e''., a function F: \Gamma \rightarrow \bigcup\nolimits_ 2^ such that F(G) \subseteq S_G for al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
