Market equilibrium under piecewise Leontief concave utilities

For p-Leontief exchange markets with pairing economy we show that equilibria are rational and we obtain a simplex-like algorithm to compute one using the classic Lemke-Howson scheme, thereby extending the results of Ye, TCS 2007, and Codenotti, Saberi, Varadarajan and Ye, SODA 2006 for Leontief to p-Leontief utilities.