Quantal Response Equilibrium (QRE) is a concept in game theory used to model decision-making under uncertainty, particularly in situations where players may not choose their strategies purely rationally. The idea is that players will respond probabilistically to their payoffs, reflecting some level of bounded rationality or cognitive limitations. In traditional Nash Equilibrium, players choose their strategies to maximize their payoffs given the strategies of others, assuming that they make fully rational decisions.

"Co-opetition" is a business strategy concept that combines elements of cooperation and competition, and it is also the title of a book written by Adam M. Brandenburger and Barry J. Nalebuff, published in 1996. The authors introduce the idea that companies can benefit from cooperating with each other while still maintaining competitive edges. The book outlines how businesses can create value in markets by understanding and managing the interplay between cooperative and competitive strategies.

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.

An N-player game is a type of strategic game in which multiple players (N) participate, each making decisions that can affect not only their own outcomes but also the outcomes of other players. These games can involve various strategies, rules, and objectives, and they can be either cooperative or competitive in nature. Key characteristics of N-player games include: 1. **Multiple Players**: The game involves more than two players, with "N" representing the number of players involved.

Bertrand competition is a model of competition among firms that sell identical or homogeneous products. It is named after the French economist Joseph Bertrand, who introduced this concept in the 19th century. The key features of Bertrand competition include: 1. **Price Competition**: In this model, firms compete primarily by setting prices rather than quantities. Each firm assumes that its competitors' prices will remain stable while it changes its own price.

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.

A repeated game is a standard concept in game theory where a specific game (usually a stage game) is played multiple times by the same players. This can involve either a fixed number of repetitions (finite repeated game) or an indefinite number of repetitions (infinite repeated game). ### Key Characteristics of Repeated Games: 1. **Stage Game**: The repeated game is based on a single, well-defined game, often involving decisions that players must make simultaneously.

"Sir Philip Sidney game" typically refers to a classic board game, often called "Sidney's Game" or "The Game of Sidney," which is centered around the literary contributions of Sir Philip Sidney, a prominent English poet, and courtier of the Elizabethan era. However, it’s worth noting that there isn't a well-known board game that directly bears his name in contemporary contexts.

Ω-logic (Omega-logic) is a term that can refer to various concepts depending on the context, usually relating to formal systems in logic, mathematics, or computer science. However, it is not a widely recognized or standard term in mainstream logic or mathematics.

The cut rule, also known as the cut-elimination theorem, is a fundamental concept in proof theory and logic. It pertains to systems of deduction, particularly in sequent calculus and natural deduction. In formal logic, the "cut rule" allows for the introduction of intermediate statements in proofs, facilitating the derivation of conclusions from premises.

Existential generalization is a rule of inference used in formal logic and proof theory. It allows one to infer the existence of at least one instance of a particular property or relation from a specific case.

A valid argument form is a logical structure that ensures that if the premises are true, the conclusion must also be true. Here’s a list of some common valid argument forms: 1. **Modus Ponens (Affirming the Antecedent)** - Structure: - If P, then Q. - P. - Therefore, Q. - Example: If it rains, the ground is wet. It is raining. Therefore, the ground is wet.

Modus ponens is a rule of inference in propositional logic. It states that if you have a conditional statement of the form "If P, then Q" (written as \( P \rightarrow Q \)) and you also have the proposition P true, then you can conclude that Q is true. In symbolic terms, it is expressed as: 1. \( P \rightarrow Q \) (If P, then Q) 2. \( P \) (P is true) 3.

Modus tollens is a valid form of logical reasoning that can be summarized as follows: If we have two statements: 1. If \( P \) then \( Q \) (this is a conditional statement). 2. Not \( Q \) (the negation of the second part of the conditional). From these two statements, we can conclude: 3. Therefore, not \( P \) (the negation of the first part of the conditional).

Resolution is a crucial rule of inference in formal logic and propositional logic, primarily used in automated theorem proving and logic programming. It is based on the concept of combining clauses to produce new ones, ultimately leading to a proof of a given statement or demonstrating a contradiction. ### Key Concepts of Resolution: 1. **Clauses**: In propositional logic, a clause is a disjunction of literals (where a literal is an atomic proposition or its negation).

Transposition in logic refers to a specific form of argument or inference that involves the rearrangement of a conditional statement.

Rudolf Carnap (1891–1970) was a prominent philosopher and a key figure in the development of logical positivism and the philosophy of language. He was born in Germany and later became associated with the Vienna Circle, a group of philosophers and scientists who sought to combine ideas from logic and empiricism. Carnap's work focused on the clarification of language and the role of logical analysis in philosophical inquiry.

Higher-order logic (HOL) is an extension of first-order logic that allows quantification not only over individual variables (as in first-order logic) but also over predicates, functions, and sets. This increased expressive power makes higher-order logic more flexible and capable of representing more complex statements and concepts, particularly in areas like mathematics, computer science, and formal semantics.

Infinitary logic is an extension of classical logic that allows for formulas to have infinite lengths, enabling the expression of more complex properties of mathematical structures. Unlike standard first-order or second-order logics, where formulas are made up of a finite number of symbols, infinitary logic permits formulas with infinitely many variables or connectives.