the question is as follow:
suppose that two players are playing war of attrition,
that means both of them could choose either to fight or quit, if either one of them quit, the game ends, and if both of them fight, the game proceed to the next period and continue.
The reward is $10 meaning that if one of them fight and the other quit, the fighter gets the reward, and the quiter gets nothing, and if both of them quit, both of them get nothing.
The cost for them is different: player 1 has a per-period cost of $6, but player 2 has a per-period cost of 2 dollars
a) Derive a SPNE where each player uses a stationary randomizing strategy.
Firstly, i don't really know what is meant by stationary randomizing strategy, i assume that means both of them would choose to mix their strategy for every game.
Thus from my calculation, the SPNE is that player 1 would play fight and quit with probability 5/6 and 1/6 respectively and player 2 would play fight and quit with probability 5/8 and 3/8 respectively in every period.
Am i correct in doing this question?