NEW YORK, May 20 (Reuters) - Goldman Sachs, Morgan Stanley and UBS said on Tuesday they will allow their clients to access each other's non-displayed liquidity pools, known as dark pools, in an effort to increase chances of trading orders being filled.

The agreement will allow algorithmic trading orders from each firm to tap into the additional liquidity offered by competitors' darks pools, including Goldman Sachs' SIGMA X, the largest single-broker dark pool, Morgan Stanley's MS POOL and UBS' PIN ATS.

Dark pools now account for some 10 percent of equities trading in the United States, according to New York-based consultancy TABB Group and have proliferated as investors seek to place larger orders without showing their hand to the market and risk adverse price movements.

In a statement, Morgan Stanley's managing director of electronic trading said, "These arrangements will enable us to work with trusted industry participants to deliver the same level of confidentiality our clients have come to expect from us."