Strictly Competitive Games and Security Strategies

Strictly competitive game

• A two-player game is strictly competitive if, for any two strategy profiles $s$ and $s'$, $u_1(s) \geq u_1(s')$ if and only if $u_2(s) \leq u_2(s')$.
• $s_i$ is a security strategy for player $i$ if it solves:

• Note that a secure strategy might not be rationalizable.
• Player i's security level is the corresponding payoff.

Result

• If $s^*$ is a nash equilibrium of a strictly competitive game, then $s^*_1$ and $s^*_2$ are security strategies for player 1 and player 2.

Example

• We first find the security strategies for player 1 and player 2. For player 1, playing B would be the security strategy and for player 2, playing C or B will be the secure strategy. (Why?) Thus, the secure startegy set is, $\{(B, C), (B, B)\}$

'''mermaid graph TD; A-->B; A-->C; B-->D; C-->D; '''