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Setting Incentives for Managers: Incentive Compatibility, Similarity Rule, and Goal Congruence

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Game Theory in Management Accounting

Part of the book series: Contributions to Management Science ((MANAGEMENT SC.))

Abstract

The terms ‘incentives’ and ‘incentive compatibility’ are widely used in economics. Incentives are an important object in managerial accounting. Nevertheless—or just because?—there is a notable ambiguity in their exact meaning, especially of ‘incentive compatibility’. Likewise, in many cases it is not clear whether ‘setting the right incentives’ means ‘ensuring incentive compatibility’ or something else. This chapter depicts some important relationships between different definitions in differing economic models dealing with incentives, starting with the game theoretic definitions of incentive compatibility.

The original version of this chapter was revised. An erratum to the chapter can be found at https://doi.org/10.1007/978-3-319-61603-2_20.

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Notes

  1. 1.

    The use of this term goes back to Stephen Ross, cf. Ross (1973, 1974).

  2. 2.

    There are many facts confirming this statement. Both fields deal with the actions of so-called agents, for instance, and the revelation principle of mechanism theory (cf. Sect. 2.1) is an important element of budgeting mechanisms in management accounting (cf. Sect. 2.2).

  3. 3.

    www.britannica.com/topic/incentive-compatibility [16.02.2017].

  4. 4.

    For an earlier discussion with a narrower scope, cf. Trost (1999) .

  5. 5.

    Note that at present it is left open whether there is a stochastic influence on the outcome or not.

  6. 6.

    A weaker condition is that the transfer function t be feasible, i.e. all of these sums are less than or equal to zero. In this case there could be a surplus which would be wasted from the participants’ point of view.

  7. 7.

    In terms of game theory, this is the case of no side-payments.

  8. 8.

    The proof is based on the even more famous impossibility theorem of Arrow (1950).

  9. 9.

    Cf., for instance, d’Aspremont and Gérard-Varet (1979a, p. 31). It has to be assumed that the plausibility condition is satisfied, i.e. the space of potential messages M is equal to the space Θ i of types for every player i ∈ N. In our above description we have presumed this implicitly.

  10. 10.

    Maybe she may gain some additional but in any case incomplete information. For the sake of simplicity we will omit this aspect and restrict the information to one’s own type.

  11. 11.

    With respect to an allocation mechanism (cf. the next section) Groves and Ledyard (1987, p. 58) state: ‘There is wide acceptance of the presumption that if there exist dominant strategies, then agents will adopt them […] No sophisticated prediction of others’ behaviour is necessary.’

  12. 12.

    For an overview of allocation mechanisms with special attention to Groves mechanisms, cf. Green and Laffont (1979). Together with the Vickrey auction and the Clarke mechanism , the class of mechanisms which induce truth-telling is called the class of Vickrey-Clarke-Groves (VCG) mechanisms; cf. Vickrey (1961) and Clarke (1971).

  13. 13.

    For an overview of capital budgeting under asymmetric information, cf. Gordon et al. (2006).

  14. 14.

    ϑ(⋅ ), the type of agent i, is here the production function of her division. It plays the role of the utility function v(⋅ ) in the foregoing section.

  15. 15.

    Profit sharing becomes even more problematic if effort and effort aversion of the agents are taken into account and the free rider problem arises. This aspect is an essential element of principal agent theory; cf. the next section.

  16. 16.

    Rees (1985a, p. 5) uses this to distinguish principal agent theory from ‘the literature on incentive compatibility’.

  17. 17.

    In their overview of the agency literature dealing with capital budgeting, Gordon et al. (2006) discuss the multi-agent case as well as the case of one agent, which latter has been, presumably because of its lesser mathematical complexity, much more exhaustively analysed.

  18. 18.

    For an early but thorough overview see Rees (1985a,b). For seminal papers on agency theory, cf., for example, Jensen and Meckling (1976), Harris and Raviv (1979), Holmström (1979), Grossman and Hart (1983). Gordon et al. (2006, p. 153) stress that Jensen and Meckling (1976), Harris and Raviv (1979), Holmström (1979) and Baiman (1982) ‘have had a major impact in promoting the use of agency theory to examine managerial accounting issues.’

  19. 19.

    For existence, uniqueness, and manageability, suitable specifications of the model are necessary.

  20. 20.

    As Ross remarks, the ‘constants a and b can be chosen to satisfy outside constraints’. Cf. Ross (1974, p. 220). This could be, for example, a participation constraint.

  21. 21.

    At least the HARA class contains such important categories of utility functions as the exponential, the logarithmic, and the linear utility functions.

  22. 22.

    For example: The expected utility of the agent should be a positive monotone transformation of the expected gross return before (!) the agents’ remuneration; cf., for example, Laux (2006a, p. 376).

  23. 23.

    Because of the different language, we have cited only two of these books, cf. Laux (2006a,b).

  24. 24.

    The fundamental papers are Itami (1975) and Reichelstein (1997).

  25. 25.

    As stated by Laux (2006b, p. 324).

  26. 26.

    \(\mathbb{R}^{n}\) may contain one or more solutions or may be empty.

  27. 27.

    This corresponds with the balancedness of mechanisms in the noncooperative case.

  28. 28.

    Karagök (2006, p. 9) shows an analogous usage of the German language term ‘Anreizkompatibilität’ in the definition of the core.

  29. 29.

    In fact it could be discussed whether this is still a cooperative game. In our opinion, we have here a hybrid of cooperative and noncooperative modelling.

  30. 30.

    Cf. Forges et al. (2002, p. 9) for the Hurwicz-like setting and Forges et al. (2002, p. 22) for Bayesian incentive compatibility.

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Authors and Affiliations

  1. TU Ilmenau, Group for Finance Research, Helmholtzplatz 3, D-98693, Ilmenau, Germany

    Ralf Trost & Sebastian Heim

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Correspondence to Ralf Trost .

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  1. Institute of Economics, Brandenburg University of Technology, Cottbus, Germany

    David Mueller

  2. Faculty of Economic Sciences and Media, Ilmenau University of Technology, Ilmenau, Germany

    Ralf Trost

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Trost, R., Heim, S. (2018). Setting Incentives for Managers: Incentive Compatibility, Similarity Rule, and Goal Congruence. In: Mueller, D., Trost, R. (eds) Game Theory in Management Accounting. Contributions to Management Science. Springer, Cham. https://doi.org/10.1007/978-3-319-61603-2_1

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