For previous experimental proof-of-concept studies on the effect of common joint ventures on price competition in a pipeline network (vsmith1994) which showed that using a computer assisted network auction, cotenancy increased efficiency and reduced pipeline monopoly concerns.
Some theoretical papers on cost sharing that consider the general problem of the commons and evaluate the trade-offs between strategyproofness, efficiency and fairness. ms1999 look at the case of constant returns technology. freidman02; moulinShenker1992 look at the case of a negative production externalities. ss1999; zhou1991 look at the provision of a public good. hm1994; debR99; so2001; wo1999 look at excludable public goods.
To date there are six experimental studies of cost sharing mechanisms. chen03 studies the serial and average cost pricing mechanisms under complete information as well as limited information when there are two types of agents (two subjects are grouped per session). She found that the performance of the two mechanisms are statistically indistinguishable under complete information. Under limited information, however, the serial mechanism performs robustly better than the average cost pricing mechanism in terms of frequency of equilibrium play and system efficiency. She studies the serial and the average cost sharing rules under complete and limited information. She found that the two mechanisms are statistically indistinguishable under complete information. However, under limited information the serial rule performs better than the average cost pricing rule in terms both of equilibrium play and system efficiency. Her testing of the serial cost sharing rule involves only two subjects at the time, and it is framed as a learning process. The testing of the rule when more than two subjects are involved raises challenging experimental design questions.
chenK03 study the learning dynamics in these cost sharing games and other games under limited information. chen03; chenK03 investigate serial cost sharing and average cost pricing in complete information private good environments, and in environments with very limited information where subjects observe their own action and payoff, but not the game form or the other subjects’ choices or payoffs. They focus on the learning dynamics under these mechanisms.
rrd2002 investigate the performance of the serial mechanism with each human subject against three computerized players, where each human player knows his own cost share and payoff structure but has no information about the opponents’ payoff structures. Their information condition is between the complete information and limited information setting chen03. While in Chen’s experiment, the subjects maintain their preference parameter throughout the entire experiment. rrd2002 experiment, the subjects’ preference parameters change in each period. This implies that in each period the allocation mechanism must converge to a different Nash equilibrium allocation. They implement the serial mechanism both as a sequential game and as a simultaneous normal form game. They found that the serial mechanism leads to almost efficient allocations, and even though easier to understand and implement, the simultaneous move treatment does not lead to a better overall performance. chen03 uses a payoff table to explain both mechanisms, which is feasible for the serial mechanism with only two types of players. When the number of types increase, the serial mechanism becomes more challenging to implement in the laboratory, because the dimension of payoff tables increases with each additional type. With more than two types one needs to find alternative ways to implement the mechanism. rrd2002 has four different types, but only one of them is a human player, thus the strategic interaction between different types are simplified. Each of the two studies highlights different aspects of the cost sharing mechanisms. rrd2002 use \(U^i = \alpha _i q_i - x_i\) where \(\alpha _i\) is the marginal willingness to pay for the shared good; \(q_i\) is the chosen quantity; and \(x_i\) is the cost share. The cost function \(C(q) = 1/2 q^2\); where \(q = \sum _i q_i\), the total quantity requested. Two sets of \(\alpha \), \(\alpha _i \in [0,70]\) and \(\alpha _i \in [32,100]\). The choice of \(q_i > 0\).
All three of the above experimental studies of SCS examine serial cost sharing only for private good environments. gp2003 report experiments for the provision of excludable threshold public goods and compare the serial cost sharing mechanism with voluntary cost sharing with proportional rebates and with no rebates. They found that voluntary cost sharing with rebates outperforms serial on welfare grounds, which in turn outperforms voluntary cost sharing with no rebates. One possible reason for the difference between gp2003’s results and the two previous studies might be that gp2003 use an excludable threshold public goods, while chen03; rrd2002 use multiple levels of private goods. gp2003 compares the serial rule with voluntary cost sharing mechanisms with proportionate rebate and with no rebates. They consider the case of an excludable binary public good, while the other studies allow for multiple levels of provision of a private good.
arws2001 report an experimental study of a large-scale queueing game with the FIFO queue discipline (i.e., average cost sharing mechanism). Their results show strong support for mixed strategy equilibrium play on the aggregate level but not on the individual level.
chenR03 is an extension of chen03; rrd2002. They design an experiment to evaluate the serial and the average cost pricing mechanism in a baseline complete information environment, and a more challenging environment with limited information. In their environment, there are twelve players of four different types. The four players are rotated over the twelve subjects and each session/period contains three groups of four. Thus, the environment is more complex than the two earlier studies. The goal of chenR03 was to assess the performance of the two mechanisms in different settings, to study how human subjects learn in these different settings, and whether and how the learning dynamics leads to convergence to stage game Nash equilibrium. chenR03 compares the two rules with twelve players of four different types under various information settings. The objective is to assess the performance of the two mechanisms and to study how human subjects learn and converge to the Nash equilibrium outcome under different settings.
We know of only two applied (non-experimental) studies of cost sharing mechanisms; ferejohnFN1979; ferejohnFNP1982 for a specific application to the sharing of programming costs across network affiliates and ak; ka for an application to irrigation.