  We consider stochastic processes where randomly chosen particles with
positive quantities x, y (> 0) interact and exchange the quantities
asymmetrically by the rule x' = c{(1-a) x + b y}, y' = d{a x + (1-b) y} (x \ge
y), where (0 \le) a, b (\le 1) and c, d (> 0) are interaction parameters.
Noninteger power-law tails in the probability distribution function of scaled
quantities are analyzed in a similar way as in inelastic Maxwell models. A
transcendental equation to determine the growth rate \gamma of the processes
and the exponent s of the tails is derived formally from moment equations in
Fourier space. In the case c=d or a+b=1 (a \neq 0, 1), the first-order moment
equation admits a closed form solution and \gamma and s are calculated
analytically from the transcendental equation. It becomes evident that at c=d,
exchange rate b of small quantities is irrelevant to power-law tails. In the
case c \neq d and a+b \neq 1, a closed form solution of the first-order moment
equation cannot be obtained because of asymmetry of interactions. However, the
moment equation for a singular term formally forms a closed solution and
possibility for the presence of power-law tails is shown. Continuity of the
exponent s with respect to parameters a, b, c, d is discussed. Then numerical
simulations are carried out and campared with the theory. Good agreement is
achieved for both \gamma and s.
