Question

1. What is the difference between a normal search problem and an adversarial search problem?
   
2. What does it mean when a game is called a zero-sum game? Give an example of both a zero-sum and non-zero-sum game and explain why.
   
3. Draw the entire search tree for a two player game that initially starts with a stack of seven chips. Each player takes a turn selecting a stack of chips and divides the stack into two stacks with the requirement being that the two newly created stacks must not contain the same number of chips. A player who is unable to make a move (ie. all stacks have one or two chips) loses the game.

Answer 1

Adversarial Search
Adversarial search is a search, where we examine the problem which arises when we try to plan ahead of the world and other agents are planning against us.

Zero-Sum Game

• Zero-sum games are adversarial search which involves pure competition.
• In Zero-sum game each agent's gain or loss of utility is exactly balanced by the losses or gains of utility of another agent.
• One player of the game try to maximize one single value, while other player tries to minimize it.
• Each move by one player in the game is called as ply.
• Chess and tic-tac-toe are examples of a Zero-sum game.

Non-zero sum

Non-zero sum game are those games which have various unpredictable events and has a factor of chance or luck. This factor of chance or luck is introduced by either dice or cards. These are random, and each action response is not fixed. Such games are also called as stochastic games.
Example: Backgammon, Monopoly, Poker, etc.

Normal Search Problem

Searching is a step by step procedure to solve a search-problem in a given search space.

A search problem can have three main factors:
Search Space: Search space represents a set of possible solutions, which a system may have.
Start State: It is a state from where agent begins the search.
Goal test: It is a function which observe the current state and returns whether the goal state is achieved or not.

Types of search algorithms

Based on the search problems we can classify the search algorithms into uninformed (Blind search) search and informed search (Heuristic search) algorithms.