Cooperative games

Cooperative games are a category of games in game theory where players can benefit from forming coalitions and collaborating with one another to achieve better outcomes than they could independently. In these games, the players can negotiate and make binding agreements to coordinate their strategies and share the payoffs that result from their cooperation. Key features of cooperative games include: 1. **Coalitions**: Players can form groups (coalitions) and work together.

The "airport problem" generally refers to a variety of optimization problems related to the operation and management of airports, particularly those involving scheduling, capacity management, and resource allocation. Depending on the context, it can involve several specific issues: 1. **Flight Scheduling**: Determining optimal schedules for arrivals and departures to minimize delays while maximizing the utilization of runways, gates, and other resources.

A cooperative board game is a type of board game in which players work together towards a common goal rather than competing against each other. In these games, players often take on specific roles or characters, each with unique abilities, and they must collaborate to overcome challenges presented by the game itself, such as completing objectives, defeating adversaries, or solving puzzles.

In game theory, the "core" is a concept that refers to a specific solution concept associated with cooperative games. A cooperative game is one in which players can form binding agreements and coalitions to improve their outcomes. The core is a set of achievable allocations of resources or payoffs to players that cannot be improved upon by any coalition of players.

Entitlement in the context of fair division refers to the concept of determining each participant's fair share or rightful claim to a resource or asset that is to be divided among multiple parties. The goal is to ensure that each party receives their fair portion based on predefined criteria, principles, or contributions.

Facility location in the context of cooperative game theory refers to a problem where a set of players (which could represent companies, individuals, or organizations) aim to choose locations for facilities (such as warehouses, stores, or service centers) to optimize certain objectives like minimizing costs, maximizing service quality, or balancing resources. In a cooperative game setting, players can form coalitions to collectively make decisions that benefit all members involved.

In game theory, imputation refers to a method of distributing the total payoff of a cooperative game among the players in a way that ensures certain fairness and stability conditions are met. Specifically, an imputation is a vector of payoffs assigned to each player that satisfies the following criteria: 1. **Efficiency**: The total payoff distributed to the players should equal the total worth of the coalition, meaning no value is lost in the distribution.

"Irrigation" is a type of puzzle or simulation game that typically involves managing water resources to effectively irrigate crops and maximize agricultural output. The primary goal is usually to create a network of irrigation channels that deliver water to fields while overcoming various challenges such as terrain obstacles, limited resources, and time constraints. In these games, players often have to strategically plan and construct irrigation systems, considering factors like water flow, planting schedules, and crop types.

"Lemnis Gate" is a turn-based strategy game that combines elements of first-person shooting and tactical gameplay. Developed by Ratloop Games Canada and published by Frontier Foundry, it was released in September 2021. The game is set within a time-bending arena where players control a team of characters, each with unique abilities. The gameplay consists of alternating turns, with players strategically placing their actions within a time loop that lasts 25 seconds.

A linear production game is a specific type of cooperative game that is used in the field of game theory and economics to model situations in which multiple players (agents, firms, or producers) work together to produce a common output or to achieve collective goals. The production process is characterized as linear in terms of resource inputs and outputs. ### Key Features of Linear Production Games: 1. **Linear Structure**: - The production function, which describes how inputs translate into outputs, is linear.

Mage Knight is a strategy board game designed by Vlaada Chvátil, first published in 2011. The game combines elements of adventure, role-playing, and deck-building, set in a fantasy world. Players take on the roles of powerful Mage Knights who explore a modular board, fight monsters, conquer cities, and achieve various objectives. In Mage Knight, players use a combination of action cards to move, attack, and perform various actions throughout the game.

Marvel Champions: The Card Game is a cooperative living card game designed by Fantasy Flight Games, set in the Marvel Universe. Released in 2019, the game allows players to take on the roles of iconic Marvel heroes such as Spider-Man, Iron Man, Captain Marvel, and others to battle against famous villains like Thanos, Ultron, and Green Goblin.

In cooperative game theory, the nucleolus is a solution concept that aims to find a fair distribution of resources among players in a cooperative game. Specifically, it provides a way to allocate a total payoff to players such that the allocation minimizes the maximum dissatisfaction (or excess) of coalitions of players. ### Key Concepts: 1. **Cooperative Game**: In a cooperative game, players can form coalitions and make binding agreements to distribute payoffs among themselves.

The Rendezvous problem is a classic problem in the fields of computer science, robotics, and distributed systems. The core concept involves coordinating a group of agents (or entities) to meet at a common location or time despite having limited communication capabilities or knowledge about each other's initial positions.

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.

"The Smurfs: Mission Vileaf" is a video game based on the popular Smurfs franchise, developed by OSome Studio and published by Microids. Released in November 2021, the game combines elements of platforming and action-adventure gameplay, allowing players to take on the roles of various Smurf characters, including Papa Smurf, Smurfette, and others.