The Paris–Harrington theorem is a result in the field of mathematical logic and combinatorics, specifically in the area of set theory and the study of large cardinals. It is a form of combinatorial principle that exemplifies the limits of certain deductive systems, particularly in relation to the axioms of Peano arithmetic and other standard set theories.

Auction sniping refers to the practice of placing a winning bid on an item at the last possible moment in an online auction. This strategy aims to prevent other bidders from responding with counter-bids, increasing the chances of winning the auction at a lower price. Typically associated with platforms like eBay, sniping is often executed using automated tools or software, which can place bids just seconds or milliseconds before the auction ends.

Jump bidding is a bidding strategy commonly used in online auctions, particularly in the context of auctioning items or in real estate. It occurs when a bidder places a significantly higher bid than the current highest bid, in a way that disrupts normal bidding patterns. This strategy can serve several purposes: 1. **Psychological Impact**: By making a large bid, the jump bidder can intimidate other bidders or convey a sense of urgency, potentially discouraging them from participating further.

The Shapley value is a solution concept from cooperative game theory that provides a way to fairly distribute the total gains or payouts of a cooperative game among its players based on their individual contributions. Named after mathematician Lloyd Shapley, it takes into account the contribution of each player to the overall outcome of the coalition they form with other players.

A transposition table is a data structure used in the field of computer science, particularly in artificial intelligence and game-playing algorithms, to optimize the performance of search algorithms such as those used in chess engines, Go programs, and other combinatorial games. The main purpose of a transposition table is to store previously computed results of game positions to avoid redundant calculations and speed up the search process. ### How Transposition Tables Work 1.

Cristina Bicchieri is a notable Italian philosopher and social scientist known for her work in the fields of behavioral economics, social norms, and the philosophy of social science. She is a professor at the University of Pennsylvania and has made significant contributions to understanding how social norms influence individual behavior and decision-making. Bicchieri's research often explores the interplay between individual preferences and social expectations, and she is recognized for developing theoretical frameworks that analyze how norms can be changed and how they impact social cooperation.

Steven J. Brams is an American political scientist, game theorist, and professor known for his work in the fields of political science, game theory, and decision-making. He is particularly noted for his contributions to voting theory, fair division, and strategic behavior. Brams has developed various models and methods for analyzing and improving political processes and decision-making systems. He has published numerous papers and books on these subjects, including works on fair division, which focus on how to allocate resources fairly among individuals.

The Folk theorem is a concept in game theory that describes conditions under which cooperation can emerge as a stable strategy in repeated games. Specifically, it states that in infinitely repeated games with a finite set of players, if the game's stage payoffs are sufficiently high, then any feasible payoff that is individually rational can be sustained as a Nash equilibrium through a strategy that involves punishment for deviations from cooperation.

M equilibrium refers to a specific type of equilibrium in various contexts, but it most commonly relates to chemical equilibria or economic models. Here are two interpretations of M equilibrium: 1. **Chemical Equilibrium**: In the context of chemistry, M equilibrium could refer to a state in a chemical reaction where the concentrations of reactants and products remain constant over time. At this point, the rate of the forward reaction equals the rate of the reverse reaction.

Pooling equilibrium is a concept from game theory and economics, particularly in the context of signaling games. It occurs when different types of players (or agents) in a market send the same signal, making it impossible for observers (or other players) to differentiate between them based on that signal. In a pooling equilibrium, all players choose the same action or strategy, so their different types (e.g.

The Gift-exchange game is a concept used in economics and social science to study the dynamics of reciprocity, trust, and social norms within interactions between individuals. It is typically framed as a specific type of game in experimental economics, where participants make decisions involving gifts or resources to one another. Here’s a basic outline of how the Gift-exchange game typically works: 1. **Players**: There are generally two players involved: a "giver" and a "receiver.

The Platonia dilemma refers to a philosophical and mathematical concept related to self-reference, paradoxes, and the nature of mathematical objects. The term itself is not widely recognized or standardized in philosophical discourse, but it often points to issues raised in discussions about mathematics, particularly in relation to Platonism and formalism.

"Guess 2/3 of the average" refers to a common game or experimental economics concept known as the "2/3 of the average game." In this game, all participants are asked to independently choose a number between 0 and 100. The objective is to guess 2/3 of the average of all chosen numbers. Here's how it generally works: 1. Each participant selects a number. 2. The average of all numbers chosen is calculated.

A job scheduling game refers to a scenario in game theory where multiple players (or agents) are involved in scheduling tasks or jobs over a set of resources, often with the objective of optimizing their own performance measures, such as minimizing completion time, maximizing resource utilization, or reducing costs. In such games, players may have different objectives, constraints, and strategies. The key components typically include: 1. **Players**: Each participant has their own jobs to schedule and competing interests in optimizing their outcomes.

The Telephone Game, also known as "Chinese Whispers," is a popular children's game that illustrates how information can be distorted as it is transmitted from one person to another. In the context of game theory, it can represent the challenges of communication, information sharing, and signal distortion. ### How It Works 1. A group of participants sits in a line or circle. 2. The first player whispers a message into the ear of the second player.

Chess theoreticians are individuals who study and analyze chess strategy, tactics, openings, endgames, and overall game theory. They often focus on the theoretical aspects of chess, which involve developing and refining chess knowledge and concepts. This can include: 1. **Opening Theory**: Analyzing various opening moves and their consequences, studying established opening lines, and discovering new strategies.

A chess opening refers to the initial moves of a chess game and encompasses the strategies and theories associated with these early moves. The opening phase typically lasts until about the first 10 to 20 moves, depending on the specific game and style of play. The purpose of the opening is to achieve several key objectives: 1. **Control the Center**: Central control is crucial in chess, as it allows for greater mobility of pieces and can lead to more tactical opportunities.

In chess, a pawn structure refers to the arrangement and configuration of pawns on the board, which significantly influences the strategic aspects of a position. The pawn structure is crucial because pawns are the only pieces that cannot move backward, and their positioning can determine the strengths and weaknesses of both sides. Key aspects of pawn structure include: 1. **Pawn Chains**: A diagonal line of pawns supporting each other. They can create strong defensive formations and control key squares.

In chess, the endgame scenario often involves various pieces left on the board when most of the material has been exchanged. One specific endgame that can occur is the "queen and pawn versus queen" endgame. ### Queen and Pawn vs. Queen Endgame 1. **Material Imbalance**: This endgame consists of one player having a queen and a pawn, while the other player has just a queen.