Consider a game $G=($:$N,(S_i{)}_{\{iinN\}},(u_i{)}_{\{iinN\}}$:$)$ where $S_i$ is finite for all iinN. Stppose the players are pessimistic and the utility of player i for a mixed strategy profile $$ is defined as follows:

hat$(u{)}_i()=$min$\{u_i(s)|sinSupp()\}$

where $|>0$ for all $\{$:iinN$\}.$ Either prove or disprove the following: The game G has a mixed strategy NE when players are pessimistic.