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Sequential Game
In game theory, a sequential game is defined as a game where one player selects their action before others, and subsequent players are informed of that choice before making their own decisions. This turn-based structure, governed by a time axis, distinguishes sequential games from Simultaneous game, simultaneous games, where players act without knowledge of others’ choices and outcomes are depicted in Payoff Matrix, payoff matrices (e.g., Rock paper scissors, rock-paper-scissors). Sequential games are a type of dynamic game, a broader category where decisions occur over time (e.g., Differential game, differential games), but they specifically emphasize a clear order of moves with known prior actions. Because later players know what earlier players did, the order of moves shapes strategy through information rather than timing alone. Sequential games are typically represented using Decision tree, decision trees, which map out all possible sequences of play, unlike the static matr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Backward Induction
Backward induction is the process of determining a sequence of optimal choices by reasoning from the endpoint of a problem or situation back to its beginning using individual events or actions. Backward induction involves examining the final point in a series of decisions and identifying the optimal process or action required to arrive at that point. This process continues backward until the best action for every possible point along the sequence is determined. Backward induction was first utilized in 1875 by Arthur Cayley, who discovered the method while attempting to solve the secretary problem. In dynamic programming, a method of mathematical optimization, backward induction is used for solving the Bellman equation. 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. In game theory, a variant of backward induction is used to compute subgame ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Final Position Of Lawrence-Tan 2002
Final, Finals or The Final may refer to: *Final examination or finals, a test given at the end of a course of study or training *Final (competition), the last or championship round of a sporting competition, match, game, or other contest which decides a winner for an event ** Another term for playoffs, describing a sequence of contests taking place after a regular season or round-robin tournament, culminating in a final by the first definition. Art and entertainment * ''Finals'' (comics), a four-issue comic book mini-series * ''The Finals'', a first-person shooter game Film * ''Final'' (film), a science fiction film * ''The Final'' (film), a thriller film * ''Finals'' (film), a 2019 Malayalam sports drama film Music *Final, a tone of the Gregorian mode *Final (band), an English electronic musical group *'' Final (Vol. 1)'', 2021 album by Enrique Iglesias **'' Final (Vol. 2)'', 2024 album by Enrique Iglesias * ''The Final'' (album), by Wham! *"The Final", a song by Dir en grey o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorial Game Theory
Combinatorial game theory is a branch of mathematics and theoretical computer science that typically studies sequential games with perfect information. Research in this field has primarily focused on two-player games in which a ''position'' evolves through alternating ''moves'', each governed by well-defined rules, with the aim of achieving a specific winning condition. Unlike game theory, economic game theory, combinatorial game theory generally avoids the study of games of chance or games involving imperfect information, preferring instead games in which the current state and the full set of available moves are always known to both players. However, as mathematical techniques develop, the scope of analyzable games expands, and the boundaries of the field continue to evolve. Authors typically define the term "game" at the outset of academic papers, with definitions tailored to the specific game under analysis rather than reflecting the field’s full scope. Combinatorics, Comb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sequential Auction
A sequential auction is an auction in which several items are sold, one after the other, to the same group of potential buyers. In a ''sequential first-price auction'' (SAFP), each individual item is sold using a first price auction, while in a ''sequential second-price auction'' (SASP), each individual item is sold using a second price auction. A sequential auction differs from a combinatorial auction, in which many items are auctioned simultaneously and the agents can bid on bundles of items. A sequential auction is much simpler to implement and more common in practice. However, the bidders in each auction know that there are going to be future auctions, and this may affect their strategic considerations. Here are some examples. Example 1. There are two items for sale and two potential buyers: Alice and Bob, with the following valuations: * Alice values each item as 5, and both items as 10 (i.e., her valuation is additive). * Bob values each item as 4, and both items as 4 (i.e., ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subgame Perfection
In game theory, a subgame perfect equilibrium (SPE), or subgame perfect Nash equilibrium (SPNE), is a refinement of the Nash equilibrium concept, specifically designed for dynamic games where players make sequential decisions. A strategy profile is an SPE if it represents a Nash equilibrium in every possible 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. This ensures that strategies are credible and rational throughout the entire game, eliminating non-credible threats. Every finite extensive game with complete information (all players know the complete state of the game) and perfect recall (each player remembers all their previous actions and knowledge throughout the game) has a subgame perfect equilibrium. A common method for finding SPE in finite games is backward induction, wher ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turn-based
Timekeeping is relevant to many types of games, including video games, tabletop role-playing games, board games, and sports. The passage of time must be handled in a way that players find fair and easy to understand. In many games, this is done using real-time and/or turn-based timekeeping. In real-time games, time within the game passes continuously. However, in turn-based games, player turns represent a fixed duration within the game, regardless of how much time passes in the real world. Some games use combinations of real-time and turn-based timekeeping systems. Players debate the merits and flaws of these systems. There are also additional timekeeping methods, such as timelines and progress clocks. Real-time In real-time games, time progresses continuously. This may occur at the same or different rates from the passage of time in the real world. For example, in '' Terraria'', one day-night cycle of 24 hours in the game is equal to 24 minutes in the real world. In a multi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorial Game Theory
Combinatorial game theory is a branch of mathematics and theoretical computer science that typically studies sequential games with perfect information. Research in this field has primarily focused on two-player games in which a ''position'' evolves through alternating ''moves'', each governed by well-defined rules, with the aim of achieving a specific winning condition. Unlike game theory, economic game theory, combinatorial game theory generally avoids the study of games of chance or games involving imperfect information, preferring instead games in which the current state and the full set of available moves are always known to both players. However, as mathematical techniques develop, the scope of analyzable games expands, and the boundaries of the field continue to evolve. Authors typically define the term "game" at the outset of academic papers, with definitions tailored to the specific game under analysis rather than reflecting the field’s full scope. Combinatorics, Comb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Revenge
Revenge is defined as committing a harmful action against a person or group in response to a grievance, be it real or perceived. Vengeful forms of justice, such as primitive justice or retributive justice, are often differentiated from more formal and refined forms of justice such as distributive justice or restorative justice. Function in society Social psychologist Ian Mckee states that the desire for the sustenance of power motivates vengeful behavior as a means of impression management: "People who are more vengeful tend to be those who are motivated by power, by authority and by the desire for status. They don't want to lose face". Vengeful behavior has been found across a majority of human societies throughout history. Some societies encourage vengeful behavior, which is then called a feud. These societies usually regard the honor of individuals and groups as of central importance. Thus, while protecting their reputation, an avenger feels as if they restore the pre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trust (social Science)
Trust is the belief that another person will do what is expected. It brings with it a willingness for one social entity, party (the trustor) to become vulnerable to another party (the trustee), on the presumption that the trustee will act in ways that benefit the trustor. In addition, the trustor does not have control over the actions of the trustee. Scholars distinguish between generalized trust (also known as social trust), which is the extension of trust to a relatively large circle of unfamiliar others, and particularized trust, which is contingent on a specific situation or a specific relationship. As the trustor is uncertainty, uncertain about the outcome of the trustee's actions, the trustor can only develop and evaluate expectations. Such expectations are formed with a view to the motivations of the trustee, dependent on their characteristics, the situation, and their interaction. The uncertainty stems from the risk of failure or harm to the trustor if the trustee does n ... [...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] |
Determined Game
Determinacy is a subfield of game theory and set theory that examines the conditions under which one or the other player of a game has a winning strategy, and the consequences of the existence of such strategies. Alternatively and similarly, "determinacy" is the property of a game whereby such a strategy exists. Determinacy was introduced by Gale and Stewart in 1950, under the name determinateness. The games studied in set theory are usually Gale–Stewart games—two-player games of perfect information in which the players make an infinite sequence of moves and there are no draws. The field of game theory studies more general kinds of games, including games with draws such as tic-tac-toe, chess, or infinite chess, or games with imperfect information such as poker. Basic notions Games The first sort of game we shall consider is the two-player game of perfect information of length ω, in which the players play natural numbers. These games are often called Gale–Stew ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strictly Determined Game
In game theory, a strictly determined game is a two-player zero-sum game that has at least one Nash equilibrium with both players using pure strategies. The value of a strictly determined game is equal to the value of the equilibrium outcome. Most finite combinatorial games, like tic-tac-toe, chess, draughts, and go, are strictly determined games. Notes The study and classification of strictly determined games is distinct from the study of Determinacy, which is a subfield of set theory. See also * Solved game A solved game is a game whose outcome (win, lose or tie (draw), draw) can be correctly predicted from any position, assuming that both players play perfectly. This concept is usually applied to abstract strategy games, and especially to games with ... References Game theory game classes {{Mathapplied-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
