Status Updates From Two-Person Game Theory (Dov...

I 2x2 games w/o sdlpt, mixed strat is unique(p1, q1). If one plays minmax, same expected payoff regardless of other plyr's move. If 2x2 has sdlpt, at leas 1 plyr has domin. strat. If neither has domin. strat, no sdlpt. Hard to extend to lgr games. (82)

Section ends with notes on mixed prudent strategies and involvement of risk to attain lgr payoffs than 0 (exp value over long-run in 2pp ZSG).

Minmax strats are certainly prudent (pure prudent=saddlepoint if coincident)

Mixed strats in 2pp ZSG will have value of game=0, EP's to plyrs will cancel exactly for right choice of p,q.

"In strat mix of game w/ saddlept, prob=1 to strat w/ saddlept and 0 to every other." (74)
There exists best strat for ea plyr in 2pp ZSG. If saddlept, at least one (if not more) best strats for ea. No sdlpt, no best pure->mix

Excellent coverage of mixed strats. beginning with game o imperfect info (variant of Castor-Pollux) with saddlept. soln (it persists-rare case...look for this first). So perfect nfo not reqd for saddlept but is sufficient.

Next step--extend minmax to games w/o saddlepts. Look for mixed strats. In ZSG quickly recognize lack of saddlept when "min entry in neither row is maximal in its column"-2 minmax not coincident