We use the term shared good to denote a situation in which a good simultaneously provides heterogeneous benefits to members of a group. The ensuing decision problem for the group is to choose the character of the shared good (its quality and/or quantity) and how its costs will be shared. When the shared good quantity or quality is a variable, the voluntary contribution mechanism (VCM) -- both theoretically and in practice -- does not provide a Pareto optimal solution. The bid decay observed in VCM experiments -- interpreted as free-riding behavior -- is a well-known phenomenon. Chan et al. showed that this effect can be ameliorated through communication. Something else besides free-riding may be going on when there is heterogeneity in benefits and incomplete information. One possible explanation for the observed bid decay is that subjects reduce their bids when they cannot find a way to a solution. Although VCM bidding is repeated in experiments, these repetitions do not constitute an algorithmic search process. We develop an iterative bidding process that can lead to a Pareto optimal solution for a variable good. The process is similar to the VCM in that players use a payoff matrix to make bids. There is a mapping from bid combinations into feasible levels of the shared good. Since the sum of bids may be greater than the cost for the MFL, the method uses cost shares to cover costs exactly for the maximal feasible level (MFL) of the shared good . Our cost sharing rule is to take cost shares to be proportional to bids. The underlying algorithm provides suggestions for bidding and indicates the direction (increase or decrease) for the optimum relative to the current MFL. Cost share and shared good suggestions are based on an additional bid message: the marginal willingness to pay to increase the good level from the current MFL. Similar to the MDP process, which also uses bids, the suggested level is an increase if marginal bids exceed the marginal cost of an increase, and a decrease for the opposite condition. Because of its voluntary nature, there is welfare improvement when the level increases. The process continues until a stationary point is found. If players use the suggested cost shares for their bids, and marginal bids are truthful, the method leads to a ratio equilibrium, which is a type of cost share equilibrium proposed by Mas-Colell and Silvestre. The advantage of the cost share equilibrium is that it is automatically optimal. Preliminary experimental results based on this algorithm are very promising: bid decay is not observed in plays of the experimental game. The game uses a group of three players who must reach an agreement about the level of a shared good; the players are heterogeneous in endowments and rewards for levels of the good. The game also includes voting rules. Bid proposals are made until the group votes to stop the proposal process. At the end of the proposal process, the group votes among all generated proposals to choose the shared good level and cost distribution. It has been suggested by Walker et al. that voting can be a deterrent to free-riding.

Co-authors Richard Kiser and Steve Rassenti