Organizational decision-maker bias supports merger wave formation: demonstration with logical formalization

Abstract

Imitation of firms that opt for strategic reorganizations by opting for mergers and acquisitions facilitates market wave formation. Empirical evidence on mergers and acquisitions suggests that, under uncertainty, firms regret more not following their rivals’ merger moves of yet unknown outcome than possibly failing jointly by copying them. Looking for the rationale for this bandwagon behavior, we explore the underlying decision-making framework by using formal logic and search for behavioral premises consistent with the observed outcomes. We point out three biased expectations, modeled by using a belief modal operator, that filter out relevant scenarios from the consideration set of otherwise rationally behaving decision-makers. The theorems derived from the logic model highlight the drive to imitate competitors’ merger choices for all but one of the eight possible outcomes of the decision-making framework. For the latter case, a boundary condition is given that makes imitation the predicted strategy. Our approach goes against the view that human behavior defies logic-based rendering also if such behavior can be adequately described as non-rational in an economic sense. Logic is a flexible representation tool to model even faulty behavior patterns in a transparent way; it can also help exploring the consequences of the cognitive mistakes made. Our findings suggest that threats to wealth creation may not necessarily find their origins in morally questionable organizational behavior, but rather in modalities of decision-making under uncertainty.

Appendix

1.1 Tables 4, 5 and  6.

Table 4 Premises on arithmetic operations

Table 5 Premises on research context

Table 6 Modal operator axioms applied at derivations

1.2 Proofs

We have justified the conclusions of the FOL core of the modal logic formalization with the online available Prover9 theorem prover. Getting to the ‘FOL core’ involved the following. First, we made two separate premise sets, one for beliefs and one for ‘state of affairs’ (which two sets can contradict). Second, we removed the modal operators from the formulae. Third, we derived by Prover9 and Mace4 the FOL versions of Theorems 1–3 from the premise set on beliefs, and Theorem 4 from the premise set on ‘state of affairs’. Fourth, we re-installed the modal operators to the formulae. The consecutive application of Axioms A11.1–4 (Table 6) to the re-unified premise set subsequently proves the modal logic versions of Theorems 1–3.

1.3 Ending the wave

How does the system get out the wave? Most likely: targets become too expensive as market values become exuberant due to explosive activity; and takeover premiums above market value increase along the wave (the number of remaining targets declines with increasing appetite), while real efficiency gains that could fuel ongoing merger behavior remain at bay. Managers gradually adjust their expectations accordingly, thus assigning a higher $p$ subjective probability to failure than before. In model terms, $B$ would only opt for imitation if it expects $\textit{fi}_B > \frac{rc_B }{1 - p}$ to hold. The derivation is as follows. The condition that $s_{1,6}$ (imitating) has higher expected relative payoff than $s_{4,8}$ (withholding) at merger success probability $p$ is expressed as:

$$\begin{aligned} p(rc_A - rc_B ) + (1-p)(\textit{fi}_B - \textit{fi}_A + rc_A - rc_B ) > p \cdot rc_A + (1 - p)(rc_A - \textit{fi}_A). \end{aligned}$$

This gives: $\textit{fi}_B > \frac{rc_B }{1 - p}$. For example, for $p = 2/3, 3/4$ and 4/5, satisfying this inequality and so opting for imitation requires that managers expect, respectively, three, four and five times higher fitness benefits than reorganization costs. So expecting high $1-p$ failure probability is likely to block mergers beyond a threshold. Table 7 displays the relative payoff values for the general case when both fi and rc can differ for $A$ and $B$.

Table 7 $B$’s relative payoffs in the basic scenarios when fi or rc can be different for $A$ and $B$

Evaporating first-mover advantages may also make $B$ realize that benchmarking on successful practices would not likely improve its chances. In model terms, the fitness-facilitating part of belief Assumption 2 would not hold, whilst its claim on the detrimental effect of imitating bad practice would sustain. This change would allow $B$ to perceive $s_{2}$, but not $s_{5}$, see Figure 2 in the main text. Comparing then $B$’s expected relative payoffs for the perceived $s_{1,2,6}$ (imitation) and $s_{4,8}$ (withholding), and as before keeping scenario probability $p$ the same, reveals that $B$ should believe $\textit{fi}>6rc$ to hold for choosing imitation rather than abstaining.