Animation and Game Design - Game Theory

Concerned with the decision-making process, where the outcome is dependent on the choices made by one or more players in a game

 

  • Game means outcome or probability

  • Games can have a negative or positive outcome

  • Responsible for game strategy

 

Zero Sum

  • A mathematical representation of a situation in which each participants gain or loss of utility is exactly balanced by the losses or gains of the utility of other participants

  • Ex: Poker, Chess, Tennis, Gambling

 

Non-zero sum

  • Situation where one's decision maker's gain (or loss) does not necessarily result in the others loss or gain

  • Ex: Candy Crush, Prisoners' Dilemma

 

Negative sum

  • Also known as Mutual Harm or Lose-Lose

  • Describes situations in which the total of gains and losses is less than zero, and the only way for one the property to  maintain the status quo is to take something from another party.

  • Ex: Chess, War Games

 

Positive sum

  • Sum of winnings and losses are greater than zero; Win-Win situation

  • Occurs when resources are somehow increased and an approach is formulated in which the desires and needs of all concerned are satisfied.

  • Ex: Any bargaining game; Any trade-related game

 

Constant sum

  • Situation or interaction in game theory where the sum of the payoffs of all players always adds up to the same to the same constant figure for any particular outcome. Thus, one player's gain must be offset by another one or more player's loss.

  • Ex: Poker, Chess

Types of Games in Game Theory

 

  • Cooperative & Non-Cooperative Games

    • Cooperative players are convinced to adopt a particular strategy through negotiations and agreements between players

    • Non-Cooperative players decide on their own strategy to maximize their profit. These provide accurate results because a very deep analysis of a problem takes place.

 

  • Normal Form & Extensive Form

    • Normal form describes a game in the form of a matrix. When the payoff and strategies of a game are represented in a tabular form. Helps in identifying the dominated strategies and Nash equilibrium. The matrix demonstrates the strategies adopted by the different players of the game and their possible outcomes

    • Extensive form describes games in the form of a decision tree. Also, they help in the representation of events that occur by chance. These games consist of a tree-like structure in which the names of players are represented on different nodes.

 

  • Simultaneous Move & Sequential Moves

    • Simultaneous - the ones in which the moves of two players is simultaneous. The two players do not have knowledge about the moves of other players.

    • Sequential - are the ones in which players are aware about the moves of players who have already adopted a strategy. The players do not have a deep knowledge about the strategies of others.

 

  • Symmetrical & Asymmetrical Games

    • Symmetry - strategies adopted by all players are the same. It can exist in short term games only because in long term games, the number of options with a player increases. Decisions made depend on strategies used and not the players.

    • Asymmeric - strategies used by players are different. The strategy that provides benefit to one player may not be the same for other players. However, decision making depends on the different types of strategies and decisions of players