# Information Game With Asymmetric Information

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Incomplete information games are games in which at least one of the players is not aware of the possible payoffs and strategies for all other players or at least one other player. Incomplete information can have different scenario. In the case when the attacker has superior information and exploits defender. A mathematical model of such security scenario used to formulate a strategic game with asymmetric information in [ jon]. Incomplete and Perfect Information. In this type of games the players have little information about their opponents’ payoff functions but they know the actions of all other players that were in the past. An example for those games is the Intrusion detection game, which is a 2-player zero-sum stochastic (Markov)…show more content…
Basic signaling game Patcha et. al [] presents the intrusion detection system as a basic signaling game . The defender has incomplete information because he doesn’t know what type is his opponent, which can be an attacker or a regular node. The authors define Θ as a set with elements θ and this sets represents the type of the attacker. Player 1 for example know his type and his action is α11 where α_1^1∈A^1 where A^1 is the action set for Player 1. Analogically let us assume that Player 2 will chose α_1^2∈A^2 and that he will have some prior beliefs about the type of Player 1. In other words the receiver will belief that the probability of the sender is a specific type is p(θ), where θ∈Θ. The return of player n will be similar as before, however know we will also need to consider the type of the player as a part of the reword function: B^n (s)=〖[B^n (s,a^1,a^2,θ)]〗_(α^1∈A^1,α^2∈A^2,θ∈Θ,), n=1,2 A Player 1 will have the following strategy: w^1 (s|θ) over actions α1 , conditional on the type of opponent is playing the game. Analogically for Player 2 the strategy will be represented by the following distribution function w^2 (s|a^1 ) over actions a^2 conditional on a^1. The payoff of θ with strategy w^1 (s|θ), assuming that Player 2 has played w^2 (s|a^1 ) is the following: 〖[B^1 (s,a^1,a^2,θ)]〗_(α^1∈A^1,α^2∈A^2,θ∈Θ,)=∑_(a^1)▒∑_(α^2)▒〖w^1 (s,a^1 |θ) w^2 (s,a^2 |a^1 ) 〗 B^1 (s,a^1,a^2,θ) If Player 1 plays strategy w^1 (s|θ) then Player