  In a two-person Rock-Paper-Scissors (RPS) game, if we set a loss worth
nothing and a tie worth 1, and the payoff of winning (the incentive a) as a
variable, this game is called as generalized RPS game. The generalized RPS game
is a representative mathematical model to illustrate the game dynamics,
appearing widely in textbook. However, how actual motions in these games depend
on the incentive has never been reported quantitatively. Using the data from 7
games with different incentives, including 84 groups of 6 subjects playing the
game in 300-round, with random-pair tournaments and local information recorded,
we find that, both on social and individual level, the actual motions are
changing continuously with the incentive. More expressively, some
representative findings are, (1) in social collective strategy transit views,
the forward transition vector field is more and more centripetal as the
stability of the system increasing; (2) In the individual behavior of strategy
transit view, there exists a phase transformation as the stability of the
systems increasing, and the phase transformation point being near the standard
RPS; (3) Conditional response behaviors are structurally changing accompanied
by the controlled incentive. As a whole, the best response behavior increases
and the win-stay lose-shift (WSLS) behavior declines with the incentive.
Further, the outcome of win, tie, and lose influence the best response behavior
and WSLS behavior. Both as the best response behavior, the win-stay behavior
declines with the incentive while the lose-left-shift behavior increase with
the incentive. And both as the WSLS behavior, the lose-left-shift behavior
increase with the incentive, but the lose-right-shift behaviors declines with
the incentive. We hope to learn which one in tens of learning models can
interpret the empirical observation above.
