How to utilize game theory with computer Security

Game theory is a blooming field that already served lot for economics, financial world and law. Now we can use game theory in computer security as well. How to use game theory for computer security? This is introduction on how we can use game theory on computer security and more things will be posted in the future.

Game theory models the interaction(s) of decision makers who have to choose actions that might be conflicting but not necessarily.

In a game there are typically two or more decision makers called Players. Players represent the basic entities of a game. A player can represent a person, a machine or group of persons. When players are inside the game they perform Actions that form their Action sets. Plan of actions within the game that a player can take is called Strategy. When all players play their strategies, it leads to an outcome, which is the vector of the actions taken by the players in that game play. An outcome gives a payoff (i.e. positive or negative reward) to each player. Being rational, each player is trying to choose the strategy that maximizes the received payoff. The payoff of a given player is derived from the preference that the player has of some outcome compared to others. A player’s preference, in the Von Neumann-Morgenstern sense, is given by a utility function that assigns to each outcome a real number. The more the player prefers an outcome, the higher the assigned number is.

Description of a Game,

·       Players (P₁, . . . , P_N ): finite number (N ≥ 2) of decision makers.

·       Action sets (A₁, . . . , A_N ): player Pi has a nonempty set Ai of actions.

·       Payoff functions u_i : (A₁,...,A_N) → R, i = 1,...,N: materialize each player’s preference, take a possible action profile and assign to it a real number.

If the action sets A_i  are finite for all players i= 1,……….,N, then the game is finite. The game is said to be zero-sum if the payoff functions are such that,

                        U­­­­­₁ + U₂ + …….. + U_N = 0.

In a game, players can gain or loss. If we add all gains together and subtract all losses then, if the sum is equal to zero we call it as a zero-sum game. It is a constant-sum game if the sum is equal to a fixed constant. If the sum can take arbitrary values, the game is variable-sum.