јвтор: Burkov V. N.
, Goubko M. V.
Combining Incentive Schemes with Mechanisms of Counter Planning and Plan Adjustment
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Burkov V. N., Goubko M. V. Combining Incentive Schemes with Mechanisms of Counter Planning and Plan Adjustment // Game theory and Management. Collected abstracts of papers presented on the Fifth International Conference Game theory and Management. SPb.: Graduate School of Management SPbU, 2011. P. 40-42.
Planning is an essential function of management in an organization. Plans and forecasts help organizations to meet future events and conditions. For instance, sales forecasts are used to calculate production schedules, stock reserves, and purchases. Plan failures result in substantial transaction costs due to overstocks and cash deficiency, or, in contrast, emergency work, imperfect logistics, and violation of delivery terms. The expectable medium output is often preferable to the unplanned success.
A typical planning mechanism met in business is centralized, i.e. the plan is set by a principal to her agents on the basis of historical data, current circumstances, and corporate strategy. A disadvantage of such approach is that detailed private information available to agents is missed. A counter planning mechanism where agents are asked for their plans provides an alternative.
Counter planning mechanisms for individual employees were introduced in the late 60th of the XX century in Soviet economy to motivate employeesТ Уenhanced obligationsФ. The responsibility for the plan quality in the process of counter planning is supported by a system of penalties. Now, fees for deviations from the planned consumption level are typical in wholesale energy and natural gas contracts, but are less common within organizations.
Counter planning mechanisms were first studied from the game-theoretic point of view by Burkov (1977). Linear penalties were shown to be enough to achieve any specific desired plan stringency (the probability of plan underfulfilment), which is determined by the ratio πO/(πU + πO), where πU and πO are the penalty rates for plan underfulfilment and overfulfilment respectively. Surprisingly, in the linear case the principal need not even know the probability distribution of output to implement the first best. In last decades the counter planning mechanisms were implemented in several industries and demonstrated their applicability and high effectiveness.
Unfortunately, the classic theory fails to explain the absolute values of the optimal penalty rates. In this paper we equip the model of counter planning with agentТs planning costs and efforts and immerse it into the moral hazard framework. The aim of the analysis is to develop the policy recommendations on penalty strength. The policy must be simple enough to be used in management consulting projects under time pressure and lack of statistics.
Additional information arrives in the process of plan execution by an agent. When agentТs output expectations change during the planning period the principal is interested in plan adjustment. To motivate timely re-planning requests the agent is faced with another system of re-planning penalties of smaller strength, as compared to the plan failure penalties.
Analogous to the simplest moral hazard model, no problem arises in the case of a risk neutral agent. The optimal combined mechanism replicates principalТs profits and costs to an agent, while constant payment is chosen to fulfill individual rationality. In the more realistic situation of a risk-averse agent (including the important case of guaranteed payment constraints) a number of biases arise from principalТs efforts to maximally secure an agent. We perform the detailed analysis of these biases to justify the following extensively used policy recommendations:
Х When H(z) is monotone, the incentive function is also monotone in z.
Х Any desired plan stringency can be implemented by the principal.
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