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Cost Share Adjustment Processes for Cooperative Group Decisions About Shared Goods: A Design Approach

Group Decision and Negotiation volume 23, pages 1085–1126 (2014)Cite this article

Abstract

For group decision about shared goods, the nature of the shared good and how its cost is to be shared among group members must be determined. Complexity arises from heterogeneity in preferences and endowments and nonlinear cost. To facilitate group decision, this paper proposes special type of group decision support system, a cost share adjustment process (CSAP), in which cost shares are adjusted iteratively via algorithmic rules until unanimity is reached, ideally producing a socially optimal, cost feasible, and fair outcome. In contrast to public good literature, our designs apply for situations of nonlinear cost, with economies of scale and fixed costs. In response to impossibility theorems, a design approach is developed: design elements for CSAPs include message space, cost allocation and adjustment rules, controllers, and incentive rules, with many possibilities for specifying a process. Simulation and economic experiment are employed to compare alternative designs, in particular highlighting the incentive effects of message space. As simulation and experiment both indicate, complicated cost allocation rules for incentive purposes may impede locating group agreement. Instead, economic experiments show that unanimity Approval Voting can mitigate the effects of strategic behavior.

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Notes

  1. See Arrow and Hurwicz (1960) and Hurwicz (1971) for an economic resource allocation application. See Wong (1973) for an application of economic planning.

  2. Atkins (1974) used a mathematical programming framework for management control of budgets, investment, joint costs, etc. Cohen (1980, 1986) applied the iterative solution method to control in an organization, focusing on incentive problems of messaging.

  3. See Laub and Bailey (1978) for a two level hierarchical structure with coordinated communication for a general control problem.

  4. Chanron and Lewis (2005) study convergence in decentralized design for complex engineering systems.

  5. For tatonnement, no transactions are carried out until equilibrium is reached (Takayama 1985, p. 341).

  6. Tulkens (1978) differentiated between planning and voluntary exchange institutions: voluntary exchange is associated with market institutions and private consumption, while planning requires cooperation of citizens in an economy, with the planner acting in the best interests of the citizens. Here, both aspects apply: shared good decisions are voluntary but are made in a planning context.

  7. Similarly, Algorithmic Mechanism Design (Nisan and Ronen 2001) in computer science literature combines ideas from economics and game theory with solution algorithms for online auction design.

  8. The efficacy of computer-mediated communication (CMC) for group decision is supported by Li (2007) who compared CMC to face-to-face communication (FTF) for a group decision making process. Similar to other studies, she found that CMC groups (with 4 or 5 members) took a longer time than FTF to complete decision tasks. FTF did not have better group outcomes than CMC for the assigned tasks, because “social talk” had a negative impact on group effectiveness.

  9. Convergence and stability criteria were formulated for dynamic adjustment processes by Jordan (1987, 1995) and Mas-Colell (1986). Desirable properties are that: (i) for any initial state, the corresponding path should converge to some solution of the stationary equation system (system stability); (ii) given an equilibrium outcome, if the initial state is perturbed from the equilibrium, the process should converge to a point in the neighborhood of the equilibrium (local stability) (Mas-Colell et al. 1995; pp. 621–622).

  10. Jordan (1987, 1995) introduced controllers in the specification of adjustment processes.

  11. An algorithmic adjustment process can be viewed as a differential game between participants and the coordinator, each controlling a subset of system variables. Arrow and Hurwicz (1977) proposed formulating resource allocation as a differential game.

  12. Second order conditions are used to ensure existence of an optimum. In general there may be multiple equilibria with any pricing instrument.

  13. For the Bid/Quantity Process described below, group members also propose marginal bids which are used to determine personalized prices. A Provision Point test determines the aggregate \(\bar{Q}\) together with quantity proposals.

  14. See Chen (2008) for a review of experimental research on incentive mechanisms.

  15. Roberts (1974) pointed out that to correct for income effects, incremental taxes must be subtracted from income at each step as the bidding process proceeds.

  16. Utility improvement occurs when QS increases: \(\text{ u }^\mathrm{i}(\text{ M }_\mathrm{i}-\text{ ST }_\mathrm{i},\text{ QS })\ge \text{ u }(\text{ M }_\mathrm{i}-(\text{ T }_\mathrm{i}+\text{ b }_\mathrm{i}),\text{ QS })= \text{ u }^\mathrm{i}(\text{ M }_\mathrm{i}-\text{ T }_\mathrm{i},\text{ QF })\ge \text{ u }^\mathrm{i}(\text{ M }_\mathrm{i}-\text{ B }_\mathrm{i},\text{ QF })\).

  17. Chen and Plott (1996) used \(\upgamma =1\) and 100, suggesting that a higher parameter leads to faster convergence.

  18. The number of trials for comparison was limited for budgetary reasons but are comparable to past experiment research.

  19. Although trials for each institution were a small number, the total number of games was similar to Smith’s (1979) study.

  20. For 153 total games with “quantity only” messaging and 39 games with bid messaging of some form, the average disagreement rate over all bidding games was 20.38 %, and the average disagreement rate over all QP games was 13.6 %. The std.dev. for the disagreement rate over combined experiments is .00695, so the t-statistic is 0.0678/0.00695 \(=\) 9.75.

  21. The subsidy situation could be addressed by changing the starting point of the QP process, eg. instead of starting with equal shares letting initial shares depend on endowments. But this would require the use of private information about group members’ endowments.

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Author information

Authors and Affiliations

  1. Department of Agricultural Economics, Purdue University, West Lafayette, IN, USA

    Edna Tusak Loehman

  2. Economic Science Laboratory, University of Arizona, Tucson, AZ, USA

    Richard Kiser

  3. Economic Science Institute, Chapman University, San Diego, CA, USA

    Stephen J. Rassenti

Authors
  1. Edna Tusak Loehman
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  2. Richard Kiser
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  3. Stephen J. Rassenti
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Corresponding author

Correspondence to Edna Tusak Loehman.

Additional information

This work was supported by NSF grant 9320937-SBR and NSF grant 9617788-SBR. Experiments were carried out at the Economic Science Laboratory, University of Arizona in 1996, 1997, 1998, 2000. Thanks to Eythan Weg, Lafayette, Indiana, for many useful discussions and encouragement along the way. Thanks also to the reviewers and editor for helpful comments.

Appendix: Rule Descriptions

Appendix: Rule Descriptions

In the instructions for each institution, each was described in terms of its general properties (computational details were a “black box.”). For share-taking processes, the initial cost allocation schedule had equal shares. After each subject makes quantity and/or bid proposals, a new cost allocation schedule is displayed on the next round, with corresponding net payoffs.

Share-taking processes with price adjustment had a similar information format: cost allocation, benefit, and net reward schedules were presented for a schedule of ten quantity levels. After seeing the information screen, each subject responded with a message about the desired shared good quantity. Summaries of proposals and resulting shares of cost for all group members by round were available as public information on history and voting screens. Instructions for the Proposal Phase were as follows, by process:

Quantity Process. “The computer will determine the group plan based on the average of members’ quantity proposals. Overall, a larger quantity means that both benefits and cost shares will increase for all group members.

Cost shares are equal in the first round. Your cost share for subsequent rounds will be calculated by the computer based on your quantity proposals relative to others’ proposals. If your quantity proposal is greater than the average proposal, your cost share will increase on the next round. Conversely, your cost share will decrease if your proposal is less than the average.”

Bid/Quantity Process. “The computer will determine the group plan based on the average of members’ quantity proposals. Overall, a larger quantity means that both benefits and cost shares will increase for all group members.

Each round, the group plan begins at the average of group members’ quantity proposals minus one. Given the newly calculated group plan, you will be asked to bid to increase the group plan to the next higher level. To make the increase to the next higher level, the total of bids must be enough to cover the extra cost for that plan. Cost shares are equal on the first round. Your cost share for subsequent rounds will be calculated by the computer based on your bids relative to others’ bids. If your bid is greater than the average, your cost share will increase on the next round. Conversely, your cost share will decrease on the next round if your bid is less than the average.”

Smith-like Process. “The computer will determine the group plan based on the average of members’ quantity proposals. Overall, a larger quantity means that both benefits and cost shares will increase for all group members.

Given the newly calculated group plan, you will be asked to propose your bid to increase the group plan to the next higher level. To make the increase, the total of bids proposed by the group must be enough to cover the increased cost for that plan.

Cost shares are equal in the first round. Your cost share for subsequent rounds will be calculated by the computer. If your bid is greater than the average bid, your cost share will increase. Conversely, if your bid is less than the average, your cost share will decrease. You can also receive a bonus—a reduced cost share—if your quantity proposal is greater than the average quantity proposal. Conversely, a quantity proposal less than the average can mean a penalty in terms of increasing your share.”

Optimal Bidding Process. Although the overall form of this game followed the proposal and approval phase format, the information format is different from the other cost share adjustment processes. A matrix displays the quantities that different levels of contributions could “buy”, in terms of the individual’s own bid and the sum of others’ bids. As for VCM, another matrix shows corresponding net rewards by own bid and sum of others’ bids.

The rules of the process were described as follows. “Each round you will:

  1. (1)

    Make a Bid, to determine a feasible commodity plan and cost shares. The sum of your bid and others’ bids will result in a Feasible Group Plan. The computer will determine this plan from the highest level that can be afforded given the total bids and the cost for each plan level. Your cost share will never be more than your bid on any round. Since the sum of bids may be greater than the required cost for the feasible plan, bids are adjusted so that excess revenue is not collected. The percent share of group cost that you will pay is the relative proportion of your bid to the sum of bids. Your net reward for each round will be based on the feasible commodity plan and your cost share.

  2. (2)

    Make an Incremental Bid, to suggest a new plan and cost share for the next round Your benefit would increase if the group plan level were to increase. Your Incremental Bid represents an extra contribution over your current cost share toward an increase in the plan level.

The Suggested Group Plan is determined by the computer in the direction of maximal group net returns.

  • If the sum of incremental bids exceeds the extra cost to increase the plan, then the Suggested Group Plan is one level higher than the current feasible plan.

  • If the sum of incremental bids is less than required, then the Suggested Group Plan is one level less than the current feasible plan.

  • If the sum of incremental bids exactly equals the extra cost, the Suggested Group plan is the same as the current feasible plan.

Your Suggested Cost Share for the next round will be in proportion to the sum of your original cost share and your incremental bid, if the plan level increases. The suggested cost shares will exactly cover the cost of the Suggested Group Plan.”

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Loehman, E.T., Kiser, R. & Rassenti, S.J. Cost Share Adjustment Processes for Cooperative Group Decisions About Shared Goods: A Design Approach. Group Decis Negot 23, 1085–1126 (2014). https://doi.org/10.1007/s10726-013-9342-x

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Keywords

  • Shared goods
  • Cost sharing
  • Cost share equilibrium
  • Public goods
  • Economic institutions
  • Experimental economics