In the beginning of the mahjong anime/manga Akagi, thetitular character has just come in from what is called a game ofchicken, which is described as follows:

Two cars head for a cliff at full speed. It's a game of recklessdisregard for life where the person who first brakes loses.

No conditions for ties were given in the anime, but I willassume that:

Driving over the cliff is the least preferable outcomeregardless of what happens to the other person

Losing is preferable to driving over the cliff

Being in a tie is preferred over losing, and winning is the mostpreferred outcome

I believe that the games aren't equivalent:

Unlike the description of the game of chicken given onWikipedia, there is a weakly dominant strategy in the game inAkagi (i.e. braking at the edge of the cliff). But I'm notsure if the existence of weakly dominant strategies are preservedunder isomorphisms of games.

The Akagi version of chicken has a pure Nashequilibrium where both players take the same action (and bothobtain an outcome that isn't their most preferred outcome). Thisoutcome (in terms of preference rankings) doesn't exist in thestandard formulation of the game of chicken. However, thinkingabout it, it might be better to view the Akagi case assomething continuous that might then permit mixed strategies (withregards to when the player chooses to brake).

Is my reasoning here correct, or is there a better way to viewthis?

I should add that in the Akagi version, the choice iswhen to brake, which lies on a continuum in some intervalof R. (I'm not entirely sure how to formulate this mathematically,since we also need to allow for the possibility that the playerdrives off the cliff, but this is beside the point.) However, aspreviously stated, braking right at the edge should be weaklydominant, at least from an intuitive perspective.

Conversely, in the standard version, there is a binary choice("swerve" or "straight") at a single point in time. Unless it'spossible to rule out all but a few cases in the Akagiversion, it would seem that the games can't possibly be equivalent,since we can't "reduce" the Akagi case to the normal gameof chicken. (There should be no isomorphism between them if thecardinalities of the set of choices are different.) But that'sexactly the thing that I'm not completely sure about.

Moreover, I'm not sure if I'm analysing the equilibria of theAkagi case properly, particularly since it strikes me as ascenario where mixing might do better (but I'm not familiar withmixed strategies in continuous cases, and I'm too busy at themoment to test somewhat "simpler" cases).