Game Theory: Pure Strategies

Understanding Pure Strategies

Game theory is a mathematical study that deals with strategies for dealing with competitive situations where the outcome of a participant’s choice of action depends critically on the actions of other participants.
A pure strategy provides a complete definition of how a player will play a game. It determines the move a player will make for any situation they could face.
Players have a set of possible strategies in every game. The number of pure strategies a player has is often mentioned in the form of a strategy set.
In simple terms, a player using a pure strategy always chooses the same action in a given situation.

Simultaneous games: These are games where all players make decisions without the knowledge of the other players’ decisions. A common example is Rock-Paper-Scissors.
Sequential games: In these games, players have some knowledge about the earlier actions, that is, players play in turns. Chess is a common example.

A dominant strategy is a pure strategy that gives the player a bigger payoff than any other strategies they could use, regardless of what the other players do.
A Nash equilibrium is a set of strategies, one for each player, such that no player has incentive to unilaterally change her action. In simpler words, when every player has chosen a strategy and no player can benefit by changing strategies while the other players keep theirs unchanged, then the current set of strategy choices and their corresponding payoffs is a Nash equilibrium.
The best response is the strategy (or strategies) which produces the most favourable outcome for a player, taking other players’ strategies as given.

The payoff matrix is a tool used in game theory to analyse strategic interactions.
It outlines the possible outcomes of a strategic interaction, and the consequences (rewards or payoffs) that each player receives depending on the strategies they each choose.
Each cell in the matrix defines the payoffs each player gets in terms of the strategies chosen by all the participating players.

Games using pure strategies often model real-life scenarios like politics, economics, biology, computer science, philosophy, etc.
For example, bidding in auctions can be modelled as a pure strategy game where each bidder decides how much they are willing to pay for the auctioned item before bidding starts.