An arbitrator has determined that big tobacco companies have seen their market share hurt by the 1998 health-care settlement with the states, a decision that could allow the cigarette makers to lower the payments required by the accord. The Brattle Group, a consulting firm the industry and the states agreed to have hear the case, affirmed a preliminary decision earlier this month that the settlement's restrictions on advertising had limited tobacco companies' market share. Companies like Altria ( MO), Reynolds American ( RAI) and Loews ( LTR), the owner of Lorillard, could in turn decide to withhold more than $1 billion of a scheduled $6.5 billion payment that's due next month. However, in order to reduce the payment, the companies involved in the settlement have to prove that states haven't enforced a requirement that smaller tobacco firms outside the pact set aside funds in a separate account for future use. Shares of Altria, the parent company of Philip Morris, rose 31 cents to $72.36. Reynolds American gained $1.70, or 1.6%, to $108.28, and Loews was adding 65 cents to $101.33.