Knowledge markets in firms: knowledge sharing with trust and signalling

Abstract

Knowledge sharing and learning are critically important to the success of knowledge management. In this research, we study the design of incentive rewards to facilitate knowledge transfer utilizing an internal knowledge market within organizations. The internal knowledge market is modelled as a marketplace where knowledge providers can send signals about their knowledge and learners may voluntarily acquire the knowledge based on the signals. Three types of knowledge recipients are differentiated with respect to their signalling threshold functions: knowledge connoisseur, knowledge public, and knowledge dilettante. In addition, a knowledge recipient may be either humble or arrogant, with different propensities for learning characterized by different learning inhibition cost functions. For different knowledge recipients, we study the knowledge providers’ best signalling strategies and the firm's optimal design of reward structures. Knowledge providers will adopt different signalling strategies if they lack the necessary trust that knowledge recipients will accurately report their learning. We analyse how the firm can offer learning rewards and employ IT support to improve the trust so as to increase knowledge transfer. This research provides valuable insights for practitioners to manage an internal knowledge market.

Appendices

Appendix A

Proof of Lemma 1: The first-order condition of worker i's surplus shows that

which indicates that the optimal signal strength s _i ^* increases in k _i but decreases in k _j because μ(k _j ) decreases in k _j and ∂² c _i /∂s _i ∂k _i <0. □

Appendix B

Proof of Lemma 2: s _i ^* has to be in the range between two signal threshold functions α(k _j ) and β(k _j ). Otherwise, worker i will take different actions for signalling s _i , either sending no signal or sending the signal at the expiring threshold function β(k _j ), that is,

If the best signal s _i ^* is so weak that it is less than the active threshold function α(k _j ), worker j will not have enough interest to learn k _i . Thus, worker i should not send any signals. If the best signal s _i ^* is so strong that is greater than the expiring threshold function β(k _j ), worker j will not learn k _j because she has obtained enough knowledge from the signal. Therefore, worker i should decrease the signal strength to β(k _j ). However, for the actual signal to stay at β(k _j ) when s _i ^*>β(k _j ), the net benefit for signalling has to be positive, which requires the sufficient condition β(k _j )⩾s̃ _i (k _i , k _j ). This condition will be satisfied if k _j ^β<k˜ _j ^β, or if the intersection A between curves s _i ^* and s̃ _i is below the curve β(k _j ), as demonstrated in Figure B1, that is, β(k̂ _j )⩾s _i ^*(k _i , k̂ _j )=s̃ _i (k _i , k̂ _j ). From Figure 2,

Figure B1

Threshold effects on worker's choice of best signal.

Therefore, if the following condition holds,

worker i will always send β(k _j ) when s _i ^*>β(k _j ).

To explore the effect of active threshold α(k _j ), we compare the threshold knowledge level k _j ^α, where s _i ^*(k _i , k _j ^α)=α(k _j ^α), with k̂ _j . Eq. (B.1) indicates that s̃ _i is always greater than α(k _j ). Therefore, k̂ _j is always less than k _j ^α, which implies that worker i will not signal even for some s _i ^* that is greater than the active threshold level α(k _j ).

In summary, if the condition in Eq. (B.2) holds, worker j will have a strategy of sending her signal s _i as summarized in Eq. (3). □

Appendix C

Proof of Proposition 1: Given the expected probability of knowledge k _j to be learned from worker i's signalling strategy (Eq. (4)), the firm maximizes its expected payoff

by choosing a best sharing reward r _s . □

Appendix D

Proof of Proposition 2: Worker i's individual-rationality constraint indicates that

for which the Envelope theorem suggests that,

which implies that the individual-rationality constraints can be reduced into

Since when worker i's knowledge k _i =0, her payoff π _i =w _i , therefore, the firm should offer the participation reward as w _i =U ₀.

Alternatively, the firm's expected profit can be rewritten as

Therefore, the firm maximizes π by choosing the optimal r _s . □

Appendix E

Design of sharing reward for arrogant recipients: five cases

Here are five possible cases for an individual provider's expected payoff.

Case I: When 0⩽k _j ^l<k _j ^βV, where k _j ^βV is the expiring threshold knowledge level determined by s _i ^V, an individual provider's expected payoff is

in which s _i ^V is the modified signal strength based on the belief q ₂ by

Case II: When k _j ^βV⩽k _j ^l<k _j ^β, an individual provider's expected payoff is

Case III: When k _j ^β⩽k _j ^l<k̂ _j ^V, as shown in Figure 9a, an individual provider's expected payoff is

where s _i ^* is still the same as that with complete trust.

Case IV: When k̂ _j ^V⩽k _j ^l<k̂ _j , an individual provider's expected payoff is

Case V: When k _j ^l⩾k̂ _j , an individual provider's expected payoff is

Since worker i's knowledge level is not observable, the firm can only maximize its expected payoff based on these five cases, that is, the firm's decision problem is now formulated as

in which k̂ _i , k̂ _i ^V, k _i ^β, k _i ^βV are worker i's threshold knowledge levels where k̂ _j (k̂ _i )=k̂ _j ^V(k̂ _i ^V)=k _j ^β(k _i ^β)=k _j ^βV(k _i ^βV)=k _j ^l=L ⁻¹(r _l ).

Appendix F

Design of sharing reward for humble recipients: five cases

Here are five possible cases for an individual provider's expected payoff.

Case I: When 0⩽k _j ^l<k _j ^βV, an individual provider's expected payoff is

Case II: When k _j ^βV⩽k _j ^l<k _j ^β, an individual provider's expected payoff is

Case III: When k _j ^β⩽k _j ^l<k̂ _j ^V, as shown in Figure 9b, an individual provider's expected payoff is

Case IV: When k _j ^V⩽k _j ^l<k̂ _j , an individual provider's expected payoff is

Case V: When k _j ^l⩾k̂ _j , an individual provider's expected payoff is