Enabling information sharing within organizations

Abstract

Organizations which have invested heavily in Enterprise Resource Planning (ERP) systems, intranets and Enterprise Information Portals (EIP) with standardized workflows, data definitions and a common data repository, have provided the technlogical capability to their workgroups to share information at the enterprise level. However, the responsibility of populating the repository with relevant and high quality data required for customized data analyses is spread across workgroups associated with specific business processes. In an information interdependent setting, factors such as short-term organizational focus and the lack of uniformity in information management skills across workgroups can act as impediments to information sharing. Using an analytical model of information exchange between two workgroups, we study the impact of measures (e.g., creating a perception of continuity and persistence in interactions, benefit sharing, etc.) on the performance of the workgroups and the organization. The model considers a setting we describe as information complementarity, where the payoff to a workgroup depends not only on the quality of its own information, but also on that of the information provided by other workgroups. We show how a long-term vision combined with homogeneity in information management capabilities across workgroups can lead to organizationally desirable levels of information exchange, and how benefit sharing can either help or hurt individual and organizational information exchange outcomes under different circumstances. Our analysis highlights the need for appropriate organizational enablers to realize the benefits of enterprise systems and related applications.

Appendix

1.1 Mathematical formulations

1.1.1 Derivation of Nash equilibria

The first-order conditions for the Nash equilibria are $A_{1}\alpha_{1}k_{1}^{\alpha_{1}-1}k_{2}^{\beta_{1}} = 2c_{1}k_{1}$ and $A_{2}\alpha_{2}k_{2}^{\alpha_{2}-1}k_{1}^{\beta_{2}} = 2c_{2}k_{2}$. Solving the above equations, we obtain the Nash equilibria:

$$ (k_{1}^{N}, k_{2}^{N}) = ([\gamma_{1}\gamma_{2}^{\delta_{1}}]^{1/(1- \delta_{1}\delta_{2})}, [\gamma_{2}\gamma_{1}^{\delta_{2}}]^{1/(1-\delta_{1}\delta_{2})})\hbox{ or }(0,0), $$

where $\gamma_{1} = [A_{1}\alpha_{1}/2c_{1}]^{1/(2-\alpha_{1})}$, $\gamma_{2} = [A_{2}\alpha_{2}/2c_{2}]^{1/(2-\alpha_{2})}$, δ₁ =  β₁/(2−α₁) and δ₂ =  β₂/(2−α₂).

For the case of symmetric information dependency, the two payoff functions are Π₁ =  Ak ^α₁ k ^β₂ − ck ²₁ and $\Pi_{2} = Ak_{2}^{\alpha}k_{1}^{\beta} -gck_{2}^{2}$, where c ₂ =  gc. The Nash equilibria for this case are: k ^N₁ =  [Aα/2c]^1/[2-α-β] g ^{−β/[(2-α)^2}− β²] and k ^N₂ =  [Aα/2c]^1/[2-α-β] g ^{−[2-α]/[(2-α)^2}−β²], or (0, 0).

1.1.2 Gainsharing between decision units

With symmetric benefit and cost functions, and letting B _i and C _i denote the benefit and cost respectively to workgroup i, we have: B ₁ =  Ak ^α₁ k ^β₂ , B ₂ =  Ak ^β₁ k ^α₂ , C ₁ =  ck ²₁ , and C ₂ =  ck ²₂ . Benefit sharing involves dividing the total benefit between the two workgroups, leading to a shared net benefit function given by: B =  (B ₁ +  B ₂)/2 =  1/2(Ak ^α₁ k ^β₂ ) +  1/2(Ak ^β₁ k ^α₂ )

1.1.3 Asymmetric information and truthful reporting of information capabilities

The two workgroups do not know each other’s cost parameters, but assume a probability distribution as follows: c ₁ ∼ U(c ₁₁,c ₁₂) (assumed by workgroup 2 about workgroup 1’s cost parameter) and c ₂ ∼ U(c ₂₁,c ₂₂) (vice versa). For the uniform distribution, EC₁ =  (c ₁₁ +  c ₁₂)/2 and EC₂ =  (c ₂₁ +  c ₂₂)/2, where EC₁ and EC₂ denote the expected values of c ₁ and c ₂, respectively. Letting f(c ₁) and f(c ₂) denote the probability distribution functions of the cost parameters c ₁ and c ₂, respectively, we have (for the uniform distribution): f(c ₁) =  1/(c ₁₂ − c ₁₁) and f(c ₂) =  1/(c ₂₂ − c ₂₁). For a standardized benefit function, A =  1, and for standardized uniform distributions, we set c ₁₁ =  c ₂₁ =  0, and c ₁₂ =  c ₂₂ =  1. For analytical tractability, we consider the case of constant returns to scale.

1.2 Proofs

Proof of Proposition 1a

For unequal costs, the non-zero Nash precision levels are: k ^N₁ =  [Aα/2c]^1/[2-α-β] g ^{−β/[(2-α)^2}−β²] and k ^N₂ =  [Aα/2c]^1/[2-α-β] g ^{−[2-α]/[(2-α)^2}−β²]. The Nash net benefits are: Π ^N₁ =  A(k ^N₁ )^α(k ^N₂ )^β − c(k ^N₁ )² and Π ^N₂ =  A(k ^N₂ )^α(k ^N₁ )^β − gc(k ^N₂ )². Now we construct two levels of precision which are higher than the corresponding Nash levels, and show that both workgroups can be better off than their Nash positions. Let the two workgroups provide precision levels denoted by k ^*₁ =  pk ^N₁ and k ^*₂ =  pk ^N₂ , where p =  [(α +  β)/α]^1/(2-α-β) (which is greater than 1). The net benefits at these levels of precision are: Π ^*₁ =  A(k ^*₁ )^α(k ^*₂ )^β − c(k ^*₁ )² and Π ^*₂ =  A(k ^*₂ )^α(k ^*₁ )^β − gc(k ^*₂ )². The differences in net benefits are:

$$ \begin{array}{l} \Pi_{1}^\ast - \Pi_{1}^{N} =\\ A^{2/(2-\alpha-\beta)}c^{-(\alpha+\beta)/(2-\alpha-\beta)}g^{-2\beta/((2- \alpha)^{2}-\beta^{2})} [((\alpha+\beta)/2)^{(\alpha+\beta)/(2-\alpha-\beta)} - ((\alpha+\beta)/2)^{2/(2-\alpha-\beta)}\\ - (\alpha/2)^{(\alpha+\beta)/(2-\alpha-\beta)} + (\alpha/2)^{2/(2-\alpha- \beta)}]\\ \Pi_{2}^\ast - \Pi_{2}^{N} =\\ A^{2/(2-\alpha-\beta)}c^{-(\alpha+\beta)/(2-\alpha-\beta)} g^{(\alpha^{2}-\beta^{2}-2\alpha)/((2-\alpha)^{2}-\beta^{2})} [((\alpha+\beta)/2)^{(\alpha+\beta)/(2-\alpha-\beta)} - ((\alpha+\beta)/2)^{2/(2-\alpha-\beta)}\\ - (\alpha/2)^{(\alpha+\beta)/(2-\alpha-\beta)} + (\alpha/2)^{2/(2-\alpha- \beta)}]\\ \end{array} $$

The signs of Π ^*₁ − Π ^N₁ and Π ^*₂ − Π ^N₂ depend on the sign of the term [((α + β)/2)^{(α+β)/(2-α-β)} − ((α + β)/2)^2/(2-α-β) − (α/2)^{(α+β)/(2-α-β)} +  (α/2)^{2/(2-α- β)}] because all the other relevant terms are positive. If this term is also positive, then Π ^*₁ >  Π ^N₁ and Π ^*₂ >  Π ^N₂ . From the proof of proposition 1b below, Π ^O₁ , the net benefit to unit 1 for the organizationally optimal outcome, is greater than Π ^N₁ , for the case of equal costs. Also, Π ^O₁ − Π ^N₁ (for equal costs) = A ^2/(2-α-β) c ^{−(α+β)/(2-α-β)} [((α + β)/2)^{(α+β)/(2-α-β)} − ((α + β)/2)^2/(2-α-β) − (α/2)^{(α+β)/(2-α-β)} +  (α/2)^{2/(2-α- β)}].

Therefore, [((α + β)/2)^{(α+β)/(2-α-β)} − ((α + β)/2)^2/(2-α-β) − (α/2)^{(α+β)/(2-α-β)} +  (α/2)^2/(2-α-β)] >  0.□

Proof of Proposition 1b

When the information costs are equal, the first order conditions for the organizational optimal are:

$$ \begin{array}{l} \partial (\Pi_{1}+\Pi_{2})/\partial k_{1} = A\alpha k_{1}^{\alpha-1}k_{2}^{\beta} + A\beta k_{1}^{\beta-1}k_{2}^{\alpha} - 2ck_{1} = 0\\ \partial (\Pi_{1}+\Pi_{2})/\partial k_{2} = A\beta k_{2}^{\beta-1}k_{2}^{\alpha} + A\alpha k_{2}^{\alpha-1}k_{1}^{\beta} - 2ck_{2} = 0\\ \end{array} $$

which result in α[(k ^β-α+2₂ − k ^β-α+2₁ )/(k ^2-α₂ k ^2-α₁ )] +  β[(k ^2+α-β₂ − k ^2+α-β₁ )/(k ^2-β₂ k ^2-β₁ )] =  0.

This implies that k ₁ =  k ₂. Thus, the organizational optimal is: k ^O₁ =  k ^O₂ =  [A(α + β)/2c]^1/(2-α-β). This is strictly higher than the corresponding Nash precision levels, k ^N₁ =  k ^N₂ =  [A(α)/2c]^1/(2-α-β) (obtained by setting g =  1 in the general formulation of the Nash equilibria). Since the organizational optimal is obtained as a unique solution different from the Nash, and since the net benefits to the two units at the organizational optimal are equal, it follows that the individual net benefits (Π ^O₁ and Π ^O₂ ) at the organizational optimal are strictly greater than the corresponding Nash net benefits (Π ^N₁ and Π ^N₂ ) for both workgroups.□

Proof of Propositions 2a and 2b

When the workgroups provide Pareto efficient levels of precision (i.e. precision levels superior to the Nash), let the payoffs to workgroups 1 and 2 be denoted by Π ^I₁ and Π ^I₂ respectively. For such an outcome, Π ^I₁ >  Π ^N₁ , and Π ^I₂ >  Π ^N₂ . A trigger strategy allows the two workgroups to achieve the Pareto efficient outcome, when there is no explicit end to the interactions. If a workgroup receives a level of information precision which is less than the individual Pareto optimal level, it switches to a ”punishing” strategy of providing only the single period Nash level of precision for all subsequent interactions. If one of the workgroups defects (from the Pareto level) in any one period, the series of payoffs will be as follows: Π ^D _i in the period of defection, followed by Π ^N _i for ever, thereafter. We note that Π ^D _i is higher than Π ^I _i , because it reflects the single-period gains from defection. We then compute a threshold discount factor, which makes a workgroup indifferent between “cooperative” behavior and defection. Summing up the payoffs over an infinite time horizon, we arrive at the following equation: Π ^I _i / (1 − d) =  Π ^D _i +  Π ^N _i d / (1 − d). If the left hand side of the equation is higher than the right, then workgroup i selects its Pareto optimal level, k ^I _i ; otherwise, it selects the single period Nash solution. The threshold discount factor (denoted by d ^*) for supporting the chosen Pareto efficient outcome is given by: d ^* ≥  (Π ^D _i − Π ^I _i ) / (Π ^D _i − Π ^N _i ). Note that the significance of the discount factor is that a payoff of Π ^I _i in period 2 is equivalent to d Π ^I _i in the period 1.□

Proof of Proposition 3

The effect of gainsharing on the information exchange equilibrium can be assessed by comparing the shared marginal benefit function with the individual marginal benefit function. We have ∂B ₁/∂k ₁ =  Aα k ^{α - 1}₁ k ^β₂ , and ∂B/∂k ₁ =  1/2[Aα k ^{α - 1}₁ k ^β₂ +  Aβ k ^{β - 1}₁ k ^α₂ ]. Also, the marginal cost is ∂C/∂k ₁ =  2ck ₁. When α =  β, the two marginal benefits are identical. When α >  (< ) β, the marginal shared benefit is lower (higher) than the marginal individual net benefit. Therefore, the Nash equilibrium values of k ₁ and k ₂ are lower (higher) when α >  (< ) β.□

Proof of Proposition 4

Using value functions B ₁ =  Ak ^α₁ k ^β₂ and B ₂ =  Ak ^α₂ k ^β₁ , and cost functions C ₁ =  c ₁ k ²₁ and C ₂ =  c ₂ k ²₂ , the single interaction Nash equilibrium is: $(k_{1}^{N}(ns)$, $k_{2}^{N}(ns)) = ((A\alpha/2)^{\frac{1}{2-\alpha-\beta}}(1/c_{1})^{\frac{2-\alpha} {(2-\alpha)^{2} - \beta^{2}}}(1/{\rm EC}_{2})^{\frac{\beta}{(2-\alpha)^{2} - \beta^{2}}}$, $(A\alpha/2)^{\frac{1}{2-\alpha-\beta}}(1/c_{2})^{\frac{2-\alpha} {(2-\alpha)^{2} - \beta^{2}}}(1/{\rm EC}_{1})^{\frac{\beta}{(2-\alpha)^{2} - \beta^{2}}}$) where EC₁ and EC₂ denote the expected values of c ₁ and c ₂ respectively, and ns denotes non-sharing of the cost parameter information. The net benefits from this solution are denoted by Π ^ns₁ and Π ^ns₂ :

$$ \begin{array}{l} \Pi_{1}^{\rm ns} = A (A\alpha/2)^{\frac{\alpha + \beta}{2-\alpha-\beta}} (1/c_{1})^{\frac{\alpha(2-\alpha)}{(2-\alpha)^{2} - \beta^{2}}} (1/{\rm EC}_{2})^{\frac{\alpha \beta}{(2-\alpha)^{2}-\beta^{2}}} (1/{\rm EC}_{1})^{\frac{\beta^{2}}{(2-\alpha)^{2} - \beta^{2}}} (1/c_{2})^{\frac{\beta (2-\alpha)}{(2-\alpha)^{2} - \beta^{2}}}\\ - (A\alpha/2)^{\frac{2}{2-\alpha-\beta}} (1/c_{1})^{-1+{\frac{2(2-\alpha)}{(2-\alpha)^{2} - \beta^{2}}}} (1/{\rm EC}_{2})^{\frac{2 \beta}{(2-\alpha)^{2} - \beta^{2}}}\hbox{ and}\\ \Pi_{2}^{\rm ns} = A (A\alpha/2)^{\frac{\alpha + \beta}{2-\alpha-\beta}} (1/c_{2})^{\frac{\alpha(2-\alpha)}{(2-\alpha)^{2} - \beta^{2}}} (1/{\rm EC}_{1})^{\frac{\alpha \beta}{(2-\alpha)^{2}-\beta^{2}}} (1/{\rm EC}_{2})^{\frac{\beta^{2}}{(2-\alpha)^{2} - \beta^{2}}} (1/c_{1})^{\frac{\beta (2-\alpha)}{(2-\alpha)^{2} - \beta^{2}}}\\ - (A\alpha/2)^{\frac{2}{2-\alpha-\beta}} (1/c_{2})^{-1+{\frac{2(2-\alpha)}{(2-\alpha)^{2} - \beta^{2}}}} (1/{\rm EC}_{1})^{\frac{2 \beta}{(2-\alpha)^{2} - \beta^{2}}}\\ \end{array} $$

If the two workgroups truthfully report their respective cost parameters, the Nash equilibrium is:

$$ (k_{1}^{N}({\rm ts}), k_{2}^{N}({\rm ts})) = ((A\alpha/2)^{\frac{1}{2-\alpha-\beta}} (1/c_{1})^{\frac{2-\alpha}{(2-\alpha)^{2} - \beta^{2}}} (1/c_{2})^{\frac{\beta}{(2-\alpha)^{2} - \beta^{2}}}, (A\alpha/2)^{\frac{1}{2-\alpha-\beta}} (1/c_{2})^{\frac{2-\alpha}{(2-\alpha)^{2} - \beta^{2}}} (1/c_{1})^{\frac{\beta}{(2-\alpha)^{2} - \beta^{2}}}) $$

Letting ts denote truthful sharing, the net benefits resulting from this equilibrium are:

$$ \begin{array}{l} \quad\Pi_{1}^{\rm ts} = A (A\alpha/2)^{\frac{\alpha + \beta}{2-\alpha-\beta}} (1/c_{1})^{\frac{\alpha(2-\alpha)}{(2-\alpha)^{2} - \beta^{2}} + \frac{\beta^{2}}{(2-\alpha)^{2} - \beta^{2}}} (1/c_{2})^{\frac{\alpha \beta}{(2-\alpha)^{2}-\beta^{2}} + \frac{\beta (2-\alpha)}{(2-\alpha)^{2} - \beta^{2}}}\\ - (A\alpha/2)^{\frac{2}{2-\alpha-\beta}} (1/c_{1})^{-1+{\frac{2(2-\alpha)}{(2-\alpha)^{2} - \beta^{2}}}} (1/c_{2})^{\frac{2 \beta}{(2-\alpha)^{2} - \beta^{2}}},\hbox{ and}\\ \Pi_{2}^{\rm ts} = A (A\alpha/2)^{\frac{\alpha + \beta}{2-\alpha-\beta}} (1/c_{2})^{\frac{\alpha(2-\alpha)}{(2-\alpha)^{2} - \beta^{2}} + \frac{\beta^{2}}{(2-\alpha)^{2} - \beta^{2}}} (1/c_{1})^{\frac{\alpha \beta}{(2-\alpha)^{2}-\beta^{2}} + \frac{\beta (2-\alpha)}{(2-\alpha)^{2} - \beta^{2}}}\\ - (A\alpha/2)^{\frac{2}{2-\alpha-\beta}} (1/c_{2})^{-1+{\frac{2(2-\alpha)}{(2-\alpha)^{2} - \beta^{2}}}} (1/c_{1})^{\frac{2 \beta}{(2-\alpha)^{2} - \beta^{2}}}\\ \end{array} $$

The expected values of the net benefits Π ^ns₁ and Π ^ts₁ are:

$$ E(\Pi_{1}^{\rm ns}) = \int\!\!\int \Pi_{1}^{\rm ns} f(c_{1}) f(c_{2})\,dc_{1} \,dc_{2},\hbox{ and }E(\Pi_{1}^{\rm ts}) = \int\!\!\int \Pi_{1}^{\rm ts} f(c_{1}) f(c_{2})\,dc_{1} \,dc_{2}. $$

For a standardized benefit function and uniform distribution, the expected net benefits simplify to:

$$ \begin{array}{l} E(\Pi_{1}^{\rm ns}) = [(\alpha/2)^{\frac{\alpha + \beta}{2-\alpha-\beta}} (2)^{\frac{\alpha \beta}{(2-\alpha)^{2}-\beta^{2}}} (2)^{\frac{\beta^{2}}{(2-\alpha)^{2} - \beta^{2}}}] / [(1 - {\frac{\alpha(2-\alpha)}{(2-\alpha)^{2} - \beta^{2}}}) (1 - {\frac{\beta(2-\alpha)}{(2-\alpha)^{2} - \beta^{2}}})]\\ - (\alpha/2)^{\frac{2}{2-\alpha-\beta}} (2)^{\frac{2 \beta}{(2-\alpha)^{2} - \beta^{2}}} / (2-{\frac{2(2-\alpha)}{(2-\alpha)^{2} - \beta^{2}}})\\ E(\Pi_{1}^{\rm ts}) = [(\alpha/2)^{\frac{\alpha + \beta}{2-\alpha-\beta}}] / [(1 - {\frac{\alpha(2-\alpha)}{(2-\alpha)^{2} - \beta^{2}}} - {\frac{\beta^{2}}{(2-\alpha)^{2} - \beta^{2}}}) (1 - {\frac{\beta(2-\alpha)}{(2-\alpha)^{2} - \beta^{2}}} - {\frac{\alpha \beta}{(2-\alpha)^{2}-\beta^{2}}})]\\ - [(\alpha/2)^{\frac{2}{2-\alpha-\beta}}] / [(1 - {\frac{2 \beta}{(2-\alpha)^{2} - \beta^{2}}}) (2-{\frac{2(2-\alpha)}{(2-\alpha)^{2} - \beta^{2}}})]\\ \end{array} $$

As Fig. 2 indicates, E(Π ^ts₁ ) >  E(Π ^ns₁ ).□

Fig. 2

Expected net benefit difference (sharing minus non-sharing) versus α

Proof of Propositions 5a and 5b

Let c ^s₁ denote the stated cost parameter of workgroup 1 (as reported to workgroup 2). If workgroup 2 reports its true parameter, the equilibrium changes to: $(k_{1}^{N}({\rm false})$, $k_{2}^{N}({\rm false})), = ((A\alpha/2)^{\frac{1}{2-\alpha-\beta}} (1/c_{1}^{s})^{\frac{\beta^{2}}{(2-\alpha)(2-\alpha)^{2} - \beta^{2}}} (1/c_{1})^{\frac{1}{2-\alpha}} (1/c_{2})^{\frac{\beta}{(2-\alpha)^{2} - \beta^{2}}}$, $(A\alpha/2)^{\frac{1}{2-\alpha-\beta}} (1/c_{2})^{\frac{2-\alpha}{(2-\alpha)^{2} - \beta^{2}}} (1/c_{1}^{s})^{\frac{\beta}{(2-\alpha)^{2} - \beta^{2}}}$)

When c ^s₁ <  c ₁, k ^N₂ (false) >  k ^N₂ (ts) and k ^N₁ (false) >  k ^N₁ (ts), where ts refers to the case of truthful sharing above. □

1.3 Numerical examples

A	α	β	c 1	c 2
15.00	0.80	0.20	1.75	5.25

k-values		Associated payoffs
k 1	k 2	Π1	Π2	Π1 + Π2
3.66	1.67	23.48	14.67	38.15	Pareto efficient
3.64	1.67	23.53	14.63	38.16	Pareto efficient
3.62	1.67	23.58	14.60	38.18	Pareto efficient
3.66	1.65	23.37	14.73	38.10	Pareto efficient
3.66	1.63	23.26	14.80	38.06	Pareto efficient
3.66	1.61	23.14	14.85	37.99	Pareto efficient
3.81	1.74	23.45	14.64	38.09	Pareto efficient
3.52	1.60	23.45	14.64	38.09	Pareto efficient
4.10	1.87	23.15	14.45	37.60	Pareto efficient
3.22	1.47	23.15	14.45	37.60	Pareto efficient
2.93	1.34	22.54	14.08	36.62	Nash outcome

1. Observation: There can be many Pareto efficient solutions, superior to the Nash equilibrium

1.3.1 Pareto inferior organizational optimal

The following example shows a case where the organizationally desirable outcome makes one unit worse off than its Nash position.

A 1	α1	β1	c 1	A 2	α2	β2	c 2
10.00	0.30	0.70	2.00	10.00	0.70	0.30	6.00

k values		Associated payoffs
k 1	k 2	Π1	Π2	Π1 + Π2
0.69	0.61	5.35	4.09	9.44	Nash outcome
1.50	1.30	9.07	3.43	12.50	Best organizational outcome
1.30	0.90	6.67	5.19	11.86	One Pareto efficient outcome